So if I start typing random numbers, e.g. 12425653564... and just keep going until I've got a higher number than every quark or lepton or whatever in my brain, or whatever other parameter could be used to hold information, that doesn't count? I feel that I could be said to 'know' the number - I can certainly say it out loud, though it may have sufficient digits for that to take a while.
How about imaginary numbers? Or irrational ones?
I suppose I suspect that I'm not making sense exactly, but I feel like the words we're using - 'know' particularly - are causing some problems.
Kind of a bad example, since it's self-defeating. You can't type a number that your brain is theoretically incapable of encoding, the scale just doesn't work out. You'll run out of time before you run out of neurons.
I got the feeling he meant like picturing two balls (heh) in his mind.
But you can't really picture 48234618675324 discrete objects at once even if you understand the number.
Right! So we've got 'picture' and 'understand' separated out here. Why is 'know' only 'picture' and not 'understand'?
Iunno. I can imagine/know something perfectly mathematically round (not composed of those annoying atoms), I don't think my mind's eye has the resolution for it, though.
So if I start typing random numbers, e.g. 12425653564... and just keep going until I've got a higher number than every quark or lepton or whatever in my brain, or whatever other parameter could be used to hold information, that doesn't count? I feel that I could be said to 'know' the number - I can certainly say it out loud, though it may have sufficient digits for that to take a while.
How about imaginary numbers? Or irrational ones?
I suppose I suspect that I'm not making sense exactly, but I feel like the words we're using - 'know' particularly - are causing some problems.
Got to a number with more digits than leptons in your brain. Not a larger number than, so no that doesn't count. You could not store all of those digits in a computer, and it would take many times your life to type or read them, and you could not remember them all at once.
Just like you can not remember all of the digits of Pi at once, and beyond a point the numbers needed to calculate the next digit in Pi would be too large for your brain to work with even using external storage.(Pi has more digits than there is matter in the universe, to the extent that Pi has digits at all)
Re: the original question, it doesn't really matter if it's "knowable" or not, nor does the definition of "knowable" matter. If you're asking if the number has some kind of non-physical existence, the physicalist response is that your idea of the number - whether it's a very general idea, a specific grasp of the amount in question, or just a symbol for "really really really lots of things" - physically resides in your brain, by whatever means mental information is encoded in our neurology. By definition, the mind, and all of the information (however you define information) that it contains, physically exists through that same biological mechanism. Any number, or infinity, or nothing, can be said to have that manner of physical existence.
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Tiger BurningDig if you will, the pictureRegistered User, SolidSaints Tuberegular
Are we typing in binary? Because I'm pretty sure that typing in base 10 it's possible to type out a number corresponding to pretty much any collection of discrete (defined however) physical objects in the universe.
Are we typing in binary? Because I'm pretty sure that typing in base 10 it's possible to type out a number corresponding to pretty much any collection of discrete (defined however) physical objects in the universe.
Are we typing in binary? Because I'm pretty sure that typing in base 10 it's possible to type out a number corresponding to pretty much any collection of discrete (defined however) physical objects in the universe.
These are all questions that I can answer about various physical objects that I interact with on a daily basis (barring fundamental physical particles, but I'm talking about things like cars, buildings, dogs, etc).
Sort of, and sort of not. Ultimately when you refer to such objects, you are "really" still referring to a collection of neurons in your mind. Your observations and experiences with said object, which are undoubtedly not all the same as someone else's.
Woah, woah, woah. Hold the phone here. When I talk about an object in the world, I'm referring to a collection of neurons in my brain? Because that seems very mistaken. When I talk about an object in the world, I'm talking about that object. Are you trying to maintain that there isn't actually an object there for me to refer to? If not, then how do I fail to refer to it?
No, we would be thinking two different things about the number 2, not be thinking of two different number 2s.
You'd be talking about two very different things, each with many different labels, but both of which are sometimes labeled 2/two because of some loose similarities between them. It's like if I said "rock" and meant a type of music but you thought I meant a stone. We're talking about different rocks, not different things about rock.
Oh, if you want to avoid the talk of platonic universals, you are in for a world of trouble.
I welcome the trouble, because I'm pretty sure platonic universals are equivalent to religion.
Well, no one is literally a platonist these days. So it's not as though I'm accepting the baggage that goes along with some of the crazier aspects of plato's metaphysics (the realm of the forms, the rememberance theory of knowledge, etc). It would probably derail the thread too much to go into why platonic universals aren't like religion really at all. I would suggest though that you start your reading with Bertrand Russell. A man who was not a fan of religion, yet argued quite persuasively for a form of platonism.
"The only way to get rid of a temptation is to give into it." - Oscar Wilde
"We believe in the people and their 'wisdom' as if there was some special secret entrance to knowledge that barred to anyone who had ever learned anything." - Friedrich Nietzsche
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Tiger BurningDig if you will, the pictureRegistered User, SolidSaints Tuberegular
Are we typing in binary? Because I'm pretty sure that typing in base 10 it's possible to type out a number corresponding to pretty much any collection of discrete (defined however) physical objects in the universe.
Why in the world would the base matter?
Posh's point, or so I took it, is that there is an ordinary integer number greater than that corresponding to every particle in the universe, or the brain, or whatever other arbitrarily large collection of physical objects one chooses, and that this number is no more or less real, no more or less sensible or understood, than the number corresponding to the exact number of "whatever large number of things", or the number 23, for that matter.
Tiger Burning on
Ain't no particular sign I'm more compatible with
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MrMisterJesus dying on the cross in pain? Morally better than us. One has to go "all in".Registered Userregular
Re: the original question, it doesn't really matter if it's "knowable" or not, nor does the definition of "knowable" matter. If you're asking if the number has some kind of non-physical existence, the physicalist response is that your idea of the number - whether it's a very general idea, a specific grasp of the amount in question, or just a symbol for "really really really lots of things" - physically resides in your brain, by whatever means mental information is encoded in our neurology. By definition, the mind, and all of the information (however you define information) that it contains, physically exists through that same biological mechanism. Any number, or infinity, or nothing, can be said to have that manner of physical existence.
This is unsatisfying for the reason I gave earlier: one can concede that one's beliefs about numbers are physical, but maintain that numbers themselves are not. The reductive naturalist has to not only explain how our beliefs can be physical, but how all of their objects can be as well. There are, as far as I know, two main ways of doing this for mathematical statements. The first is fictionalism: fictionalists claim that mathematical statements are literally false--they quantify over abstract objects, which do not actually exist--but that they nonetheless are useful for our purposes. They then have to give some explanation of why a categorically false area of discourse has this handy property of usefulness (as well as to explain why math certainly seems true). The second is nominalism: nominalists claim that mathematical statements are not about abstract objects per se, but rather are a more complicated way of saying things about everyday spatiotemporal objects. So math consists in true statements, they're just not of the form that their surface grammar seems to indicate. The nominalist then has to explain exactly how this paraphrase from math into ordinary object language is supposed to be carried out in a way that preserves at the very least most of the interesting fragments of mathematics.
These tasks are very hard. For instance, I was recently reading a book review of a recent nominalist which pointed out that the paraphrase she gave of math into physical object language ultimately descended into statements about geometric relations between spacetime points: but it's unclear how 'nominalist' this really is when it helps itself as 'physical object language' to the mathematical characterizations of geometry between points with real-valued coordinates and etc. And I think that the common view is that Hartry Field has the most worked-out fictionalist view, but that even his account struggles to explain why math has truth-preserving features and also to explain enough of it to ground its applications in science.
Also, you don't have to go to the large end of the number line to start getting perplexities for people who think that every truth is physically encoded in some straightforward way. There are already more real numbers between 0 and 1 than particles that have ever or will ever exist. There are more tautologies than thoughts: for instance, A->A is a tautology, and if you substitute every thought ever thought, in turn, for A, you will get a list just as long. If these are physically encoded, it is not in the straightforward way of being written down, or even thought about. Not to mention the straightforward point that 2 + 2 = 4 before anyone ever lived, and it will afterward as well.
This is unsatisfying for the reason I gave earlier: one can concede that one's beliefs about numbers are physical, but maintain that numbers themselves are not.
In maintaining that numbers harbor a separate existance outside of information with physical representation you are asserting that they exist as metaphysical objects; And therefor physical closure is false.
That's not exiting physical closure by counterexample from within the physical.
Re: the original question, it doesn't really matter if it's "knowable" or not, nor does the definition of "knowable" matter. If you're asking if the number has some kind of non-physical existence, the physicalist response is that your idea of the number - whether it's a very general idea, a specific grasp of the amount in question, or just a symbol for "really really really lots of things" - physically resides in your brain, by whatever means mental information is encoded in our neurology. By definition, the mind, and all of the information (however you define information) that it contains, physically exists through that same biological mechanism. Any number, or infinity, or nothing, can be said to have that manner of physical existence.
This is unsatisfying for the reason I gave earlier: one can concede that one's beliefs about numbers are physical, but maintain that numbers themselves are not. The reductive naturalist has to not only explain how our beliefs can be physical, but how all of their objects can be as well. There are, as far as I know, two main ways of doing this for mathematical statements. The first is fictionalism: fictionalists claim that mathematical statements are literally false--they quantify over abstract objects, which do not actually exist--but that they nonetheless are useful for our purposes. They then have to give some explanation of why a categorically false area of discourse has this handy property of usefulness (as well as to explain why math certainly seems true). The second is nominalism: nominalists claim that mathematical statements are not about abstract objects per se, but rather are a more complicated way of saying things about everyday spatiotemporal objects. So math consists in true statements, they're just not of the form that their surface grammar seems to indicate. The nominalist then has to explain exactly how this paraphrase from math into ordinary object language is supposed to be carried out in a way that preserves at the very least most of the interesting fragments of mathematics.
These tasks are very hard. For instance, I was recently reading a book review of a recent nominalist which pointed out that the paraphrase she gave of math into physical object language ultimately descended into statements about geometric relations between spacetime points: but it's unclear how 'nominalist' this really is when it helps itself as 'physical object language' to the mathematical characterizations of geometry between points with real-valued coordinates and etc. And I think that the common view is that Hartry Field has the most worked-out fictionalist view, but that even his account struggles to explain why math has truth-preserving features and also to explain enough of it to ground its applications in science.
Also, you don't have to go to the large end of the number line to start getting perplexities for people who think that every truth is physically encoded in some straightforward way. There are already more real numbers between 0 and 1 than particles that have ever or will ever exist. There are more tautologies than thoughts: for instance, A->A is a tautology, and if you substitute every thought ever thought, in turn, for A, you will get a list just as long. If these are physically encoded, it is not in the straightforward way of being written down, or even thought about. Not to mention the straightforward point that 2 + 2 = 4 before anyone ever lived, and it will afterward as well.
Let me continue to assume an utterly physicalist position, with the understanding that I am not a champion of ontological minutiae: the numbers themselves, as discrete entities, don't have to exist in our brains as individual little nodes of meaning. Mathematics is a system of abstract rules, and it exists in any person's mind to whatever extent they understand that system. The number 0.2345 doesn't have to exist, itself, as a number in someone's brain - in fact, it could be argued based on cognitive observations that only a very limited array of numbers exist as fully formed, completely grasped, independent concepts of quantity in someone's mind, if they can do so at all. All that is required is the system of symbols and operations capable of generating that number. For the moment that we read and discuss a given number, or manipulate it or write it down or what have you, it likely has some kind of individual physical existence in a neurological sense, but this is likely not persistent. On the other hand, a number like pi probably has a permanent spot in many of our brains, even though we are unable to fully grasp the nature of the quantity it represents in the same sense that we fully grasp the nature of the quantity of, say, 3.
All this to say, the "object" of these thoughts is not necessarily separate from the thoughts themselves. The abstract system in question is self-contained and tautological. If you think about "2," you are not applying your thought to a non-physical, external entity; you are applying a system of abstraction that is physically extant in your brain.
Was 2+2=4 really true before anyone lived, and was "all bachelors are men but not all men are bachelors" true before our planet was more than a swirl of cosmic dust? I don't know if I would say so. Or rather, I don't know if I would say they are "true" in a way that is meaningfully related to temporal or spatial position, just as I would not necessarily say they "exist" in an abstract sense. If I create a completely meaningless but internally consistent system where hurgadurp equals flipadiggaboo, can that gibberish statement be described as "true" or "false" in a way that has any meaning outside of a description of that internal consistency? Was it true for all of time, before I even thought of it? Did it exist beforehand?
I think there are grounds for a physicalist to reject the notion that such an abstraction has some sort of timeless non-physical existence; the systems and rubrics that produce these statements and contain these logics do physically exist in our mind. Any statement of their independent truth or existence can only be made from within those systems.
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TerribleMisathrope23rd Degree IntiateAt The Right Hand Of The Seven HornsRegistered Userregular
edited June 2012
Certainly, the 2 line hypothesis supporting reductive materialism is far from convincing, considering the far more exact conjectures of Riemann and others that remain unproven. Seems like a large burden of proof has not been met and this hypothesis is likely unprovable ITFP, thanks, minimally, to highly imprecise language.
Let's just go on assuming that it is the case when we are tasked with a physics problem and continue to not care at all other times, unless your are one of those religious folk who just assume that it is false at all times, in which case - carry on, crazy diamond!
When I talk about an object in the world, I'm referring to a collection of neurons in my brain? Because that seems very mistaken. When I talk about an object in the world, I'm talking about that object. Are you trying to maintain that there isn't actually an object there for me to refer to? If not, then how do I fail to refer to it?
For our purposes, "actually" and "there" don't make a lot of sense. But yes, when you talk about an object in the world, you are specifically talking about your mental construct of that object, formed by your observations and ideas about it. Another person has different experiences with it, and thus a somewhat different mental construct, but you two are able to reach enough common ground on it to have a useful conversation.
If you did not have experiences and observations and memories in your head about the object, you would not know of any such object. Having them gives you something to talk about.
Suppose one time you saw a completely different object, but you thought it was the same object, and it did something weird. Later, when talking about the object, would you not actually be talking about a mental construct you have that mistakenly conflates two different objects? Would you not be talking about an object which also does that weird thing, even though the "actual" object does no such thing? Of course. You're always talking about your mental construct.
Well, no one is literally a platonist these days. So it's not as though I'm accepting the baggage that goes along with some of the crazier aspects of plato's metaphysics (the realm of the forms, the rememberance theory of knowledge, etc). It would probably derail the thread too much to go into why platonic universals aren't like religion really at all. I would suggest though that you start your reading with Bertrand Russell. A man who was not a fan of religion, yet argued quite persuasively for a form of platonism.
Surely you've been in enough threads with me by now that we can skip the part where you invite me to start my reading. I did AP ind. study projects in high school covering major philosophers, and I minored in philosophy at a pretty good university. I'm not saying that makes me right or anything, or even an expert, but just, you know, whatever. We don't need Russell, surely _J_ will come along soon enough to argue his own form of athiest platonism.
The first is fictionalism: fictionalists claim that mathematical statements are literally false--they quantify over abstract objects, which do not actually exist--but that they nonetheless are useful for our purposes. They then have to give some explanation of why a categorically false area of discourse has this handy property of usefulness (as well as to explain why math certainly seems true).
I believe this is on the right track, except then, as you point out, what exactly can be true? I would say that math is fiction, but not necessarily false. Link wields the Master Sword. Fiction, but not false. 2 + 2 = 4. Fiction, but not false. Quite useful, in fact, and thus quite likely to be revered as a pure form of truth. Fiction only equates to falsehood if physical/material reality equates to truth. And I'm not a fan of that latter part.
his account struggles to explain why math has truth-preserving features and also to explain enough of it to ground its applications in science.
This is a tough problem, and IMO is very similar to the qualia dilemma. But I don't think fictionalism necessarily requires that one answer why math is so useful. It only requires a good argument for why it is fiction. My personal philosophy, that I came up with years ago in a fever-induced hallucination and have struggled to fully recall and conceive ever since, is actually very similar to the nominalist explanation you gave, except that it relates to the thought process and the connections between neurons, not mathematically defined points in space. In general, that mathematics is an abstract model of one key aspect of how our brains are wired to make sense of and operate within our observations of the universe, one we can isolate and work wonders with, and then reapply to our interactions with the universe to make even better sense of observations of it. Sort of like how math and logic can be represented by simple circuitry, passing currents. In fact, that's the most fundamental mechanism we'ver ever developed for representing it.
Also, you don't have to go to the large end of the number line to start getting perplexities for people who think that every truth is physically encoded in some straightforward way. There are already more real numbers between 0 and 1 than particles that have ever or will ever exist. There are more tautologies than thoughts: for instance, A->A is a tautology, and if you substitute every thought ever thought, in turn, for A, you will get a list just as long. If these are physically encoded, it is not in the straightforward way of being written down, or even thought about. Not to mention the straightforward point that 2 + 2 = 4 before anyone ever lived, and it will afterward as well.
Srsly. I'd suggest that even for "2" to be a valid concept, you'd need to have two obects which are entirely indistinguishable from one another. Which is sort of a contradiction.
When I talk about an object in the world, I'm referring to a collection of neurons in my brain? Because that seems very mistaken. When I talk about an object in the world, I'm talking about that object. Are you trying to maintain that there isn't actually an object there for me to refer to? If not, then how do I fail to refer to it?
For our purposes, "actually" and "there" don't make a lot of sense. But yes, when you talk about an object in the world, you are specifically talking about your mental construct of that object, formed by your observations and ideas about it. Another person has different experiences with it, and thus a somewhat different mental construct, but you two are able to reach enough common ground on it to have a useful conversation.
If you did not have experiences and observations and memories in your head about the object, you would not know of any such object. Having them gives you something to talk about.
Suppose one time you saw a completely different object, but you thought it was the same object, and it did something weird. Later, when talking about the object, would you not actually be talking about a mental construct you have that mistakenly conflates two different objects? Would you not be talking about an object which also does that weird thing, even though the "actual" object does no such thing? Of course. You're always talking about your mental construct.
So when I refer to the blue ball over there, I am in fact really referring to a particular group of cells in my brain? But there is actually an object out there.
What if I point at the blue ball? And say something like "that blue ball is over there." Am I still referring to a group of cells in my brain? What am I pointing at?
Well, no one is literally a platonist these days. So it's not as though I'm accepting the baggage that goes along with some of the crazier aspects of plato's metaphysics (the realm of the forms, the rememberance theory of knowledge, etc). It would probably derail the thread too much to go into why platonic universals aren't like religion really at all. I would suggest though that you start your reading with Bertrand Russell. A man who was not a fan of religion, yet argued quite persuasively for a form of platonism.
Surely you've been in enough threads with me by now that we can skip the part where you invite me to start my reading. I did AP ind. study projects in high school covering major philosophers, and I minored in philosophy at a pretty good university. I'm not saying that makes me right or anything, or even an expert, but just, you know, whatever. We don't need Russell, surely _J_ will come along soon enough to argue his own form of athiest platonism.
I really don't want to offend J here. But I'll take Russell's position over his.
I'm glad that we can skip all reading then. What do you think is a good rejoinder to Russell's objection to Price's resemblance theory of nominalism? Do you think that there is a good way to respond to the objection that Quine's update to nominalism fails because of the empty set?
"The only way to get rid of a temptation is to give into it." - Oscar Wilde
"We believe in the people and their 'wisdom' as if there was some special secret entrance to knowledge that barred to anyone who had ever learned anything." - Friedrich Nietzsche
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MrMisterJesus dying on the cross in pain? Morally better than us. One has to go "all in".Registered Userregular
This is unsatisfying for the reason I gave earlier: one can concede that one's beliefs about numbers are physical, but maintain that numbers themselves are not.
In maintaining that numbers harbor a separate existance outside of information with physical representation you are asserting that they exist as metaphysical objects; And therefor physical closure is false.
Not so. Numbers are non-physical, but do not causally interact with anything physical. Hence, the physical is stil causally closed. If they don't causally interact with anything physical, how do we know about them? That's what I answer in the last two sections of the OP.
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MrMisterJesus dying on the cross in pain? Morally better than us. One has to go "all in".Registered Userregular
Let me continue to assume an utterly physicalist position, with the understanding that I am not a champion of ontological minutiae: the numbers themselves, as discrete entities, don't have to exist in our brains as individual little nodes of meaning. Mathematics is a system of abstract rules, and it exists in any person's mind to whatever extent they understand that system. The number 0.2345 doesn't have to exist, itself, as a number in someone's brain - in fact, it could be argued based on cognitive observations that only a very limited array of numbers exist as fully formed, completely grasped, independent concepts of quantity in someone's mind, if they can do so at all. All that is required is the system of symbols and operations capable of generating that number. For the moment that we read and discuss a given number, or manipulate it or write it down or what have you, it likely has some kind of individual physical existence in a neurological sense, but this is likely not persistent. On the other hand, a number like pi probably has a permanent spot in many of our brains, even though we are unable to fully grasp the nature of the quantity it represents in the same sense that we fully grasp the nature of the quantity of, say, 3.
All this to say, the "object" of these thoughts is not necessarily separate from the thoughts themselves. The abstract system in question is self-contained and tautological. If you think about "2," you are not applying your thought to a non-physical, external entity; you are applying a system of abstraction that is physically extant in your brain.
This is a less straightforward, and hence more plausible, way to try to reduce math to people's thoughts about it. It is not that individual token mathematical statements are physical by virtue of being physically thought (a view I think is hopeless, for the reasons above), but that all mathematical statements are physical in virtue of enough of the central elements of math as a whole being physically thought. But I still think you are underestimating the difficulties here.
To start, just consider my belief that the sun is round. This belief has a straightforward predicative form: is ascribes a property (roundness) to a thing (the sun). We can say that the belief refers to the sun, and that it is true if and only if the sun has that property, roundness. Notice that my belief that 2 is prime has the exact same surface syntax: it appears to be ascribing a property (primeness) to a thing (the number 2). If it functioned as a regular descriptive sentence, we would say that it refers to the number 2, and is true if and only if the number 2 has the property, primeness. But we can't say this, at least if we don't think that the number 2 and the property of primeness literally exist.
It's okay if two sentences with the same surface grammar nevertheless have different deep logical structures: for instance, 'nothing is bigger than itself' has the same surface grammar as 'the sun is round' and '2 is prime'--that of a predication onto 'nothing'--but that is not its deep form (if it were really predicative, nothing would have to be a thing--ew). So maybe statements about math, like that statement about nothing, only appear to have a standard descriptive form. But if we want to make this claim, then we should be able to say what the real deep logical form actually is, and whatever form we claim should be able to explain the central features of mathematics. And it's not clear anyone has managed to do this in an anti-realist way.
For instance, the straightforward reading of math makes it easy to see how mathematical statements can be true: '2 is prime' is true if 2 has the property of being prime, just like 'the sun is round' is true if the sun has the property of being round. But on your proposal, the object of a mathematical thought is the thought itself. But then it is very hard to see how they can be true. For one thing, self-referential sentences are fraught with paradox, and considered meaningless on standard solutions to the liar paradox. For another, although some beliefs might be self-fulfilling, e.g. "I have at least one belief" can make itself true by being held, it is difficult to see how mathematical beliefs have anything like that character. It also seems to imply that, by destroying or altering your brain I could destroy or alter mathematical truths--after all, by destroying or altering the objects of ordinary beliefs I can make them false. Finally, it certainly seems that when we both consider whether Goldbach's conjecture is true, we think about the same thing; but if our mathematical beliefs are actually about our own brains then we are not thinking about the same thing. We are each actually thinking about our own brain. This threatens ugly consequences: if we aren't actually thinking about the same thing, then are we even disagreeing when I say "Goldbach's conjecture is true" and you say "Goldbach's conjecture is false"? If our beliefs have different objects, which we merely use the same words to express, how can they contradict each other? After all, when I say "the bank is closed" and you say "the bank is open" we only disagree if we're talking about the same bank. So it seems we could not. But isn't that wrong--don't we actually contradict each other when we take differing stands on Goldbach's conjecture?
This particular post was addressed to you, but many of these objections would apply just as well to the anti-realist theories other posters are putting forward about math. I think it is under-appreciated how much difficulty there is in trying to actually give a precise, adequate characterization of math on non-realist grounds.
Was 2+2=4 really true before anyone lived, and was "all bachelors are men but not all men are bachelors" true before our planet was more than a swirl of cosmic dust? I don't know if I would say so. Or rather, I don't know if I would say they are "true" in a way that is meaningfully related to temporal or spatial position, just as I would not necessarily say they "exist" in an abstract sense. If I create a completely meaningless but internally consistent system where hurgadurp equals flipadiggaboo, can that gibberish statement be described as "true" or "false" in a way that has any meaning outside of a description of that internal consistency? Was it true for all of time, before I even thought of it? Did it exist beforehand?
Math would still be math even if we used silly names, and if you offer rigorous definitions of your terms then they no longer count as gibberish.
I think there are grounds for a physicalist to reject the notion that such an abstraction has some sort of timeless non-physical existence; the systems and rubrics that produce these statements and contain these logics do physically exist in our mind. Any statement of their independent truth or existence can only be made from within those systems.
A final question: if I read you correctly, you take the systems of the brain to be explanatorily prior to the truth or falsity of individual mathematical judgments (sometimes people say the same, but for systems of social enforcement: 2+2 = 4 because your teacher will slap your knuckles if you say anything else). Individual judgements are mathematically correct or incorrect insofar as they follow from the beliefs encoded in certain neural systems. But there seems to be a dilemma in regard to how we read 'follow from.' If 'follow from' is read as 'mathematically follows from by way of valid proof,' then we are presupposing a notion of mathematical correctness in our definition of mathematical correctness, and hence have actually done nothing to show how to define it away in terms of physical systems. But if we read 'follows from' as 'is a causal result of' then it is impossible for anyone to ever have a false mathematical belief (so long as it was the causal result of their relevant neural system). But surely some people do have false mathematical beliefs (that are causal results of their relevant neural system)--for some years before it was proved to generate paradox, the naive axiom of comprehension was held true. This was a mistake, but I cannot see how to say why without adverting to an abstract fact of the matter which existed before, and independently of, anyone's thought about it.
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MrMisterJesus dying on the cross in pain? Morally better than us. One has to go "all in".Registered Userregular
I'm sorry for derailing the thread, the heat was getting to me and my original skim through of the OP made it read like the positivist (or as Hayek called it constructivist) phenomenon which is the social science version of "everything is best explained by physics"
I think that you're off the mark about some things (like the relation of positivism to odious politics--the Vienna Circle philosophers were actually, by and large, radical leftists, a political orientation is find not odious at all); however, I don't think you're off the mark about the "reductive naturalists think everything is best explained by physics bit." They do, at least as I've set things up. And reductivism can be just as much an attack on the autonomy of the special sciences (like economics, biology, psychology, etc.) as it is an attack on realist theories of math, ethics, or whatnot.
Now I really want to know what MrMister wrote on economics but removed from the OP.
Ask and ye shall receive:
How could one resist the [reductivist] argument above? Here is one way: one could say that although everything is ‘realized’ in physical stuff, not everything is ‘reducible’ to physical stuff. So, for instance, the fact that I shout ‘duck’ is realized in a particular configuration of vibrations in the air, and those configurations of air are unabashedly physical. But we cannot reduce linguistics to physics, because the fact that a term means duck is not just the same thing as being that particular configuration of vibrations. After all, many different vibrations can mean duck. ‘Agacharse’ also means to duck. ‘Duck’ said underwater means duck, and so on. Because of the multiple realizability of meanings in physical matter, the meaningful generalizations of linguistics (e.g. ‘duck’ cannot grammatically combine with the suffix ‘ate’) are not going to be expressable as generalizations in physics.
For a sense of the difficulty: try asking how one would go about translating true generalizations in economics into the language of physics given that cowrie shells, dollar bills, gold coins, feathers, franc notes, and pennies can all count as ‘money;’ that factories, cows, human slaves, shovels, and tractors can all count as ‘capital,’ etc. What are the physical characterizations of 'supply' and 'demand?' If we require that our laws of science take a simple unified form, then the relation between supply and demand will be so characterizable in economic terms but not physical ones--where the best you'll get is that physical laws entail that:
and that some effect in supply is defined as {A or C or .... }
and some resultant economic effect is defined as {B or D or ...}
This prima facie looks like a worse candidate for a law than "supply bears such-and-such relation to demand." The latter seems simple and unified, rather than gerrymandered. And it seems to be a better explanation. It contains all of the relevant information and none of the irrelevant information, and it explains why and how that information relates to produce the outcomes it does. This is the classic argument for the autonomy (and non-reducibility) of the special sciences to physics.
This sort of non-reductive view faces a challenge, though. Return to the case where I say ‘duck!’ and you duck. It seems simply true to say that the vibrations in the air caused you to duck. But if the linguistic facts are not reducible to, or not identical to, those very same vibrations, how could the linguistic fact that ‘duck’ means duck also have caused you to duck? There is a threat of causal exclusion here--once we have described the micro-physical causal chain leading to your act of ducking, anything else we add over and above would seem to be extraneous. Few accept the view that every linguistic utterance involves a perfectly overlapping set of overdetermined causes (whether there are ever overdetermined causes is already controversial). The exclusion argument threatens to show that if the special sciences really are irreducible to physics, then as a consequence they must also be causally irrelevant--bad news for economics, say, which at least ostensibly is trying to describe causal interactions between market forces.
But does physics provide a physical mechanism for the effects of gravitation?
Well, physicists talk about the curvature of space-time, but then other physicists go into detail so great that I can't understand the science myself. So yes, physicists do provide a physical mechanism. Several, really.
But then, whether anyone understands gravity is separate from whether it is physical or not. 'Physical' includes fields and waves and rays and so on. Not just matter.
No need to extend as far as economics. The study of multiple atoms alone already involves substantial amounts of handwaving with regards to what exactly the constituent subatomic entities are doing; it is simply too difficult to tractably manipulate save in special cases.
But the strength of reductive science is in generality - in conservation laws and the like, where we assert very little about specific entities but make strong statements about their aggregates. There is no point in economics or any apparently irreducible science at which one overturns the Laws of Thermodynamics. And if there appears to be a conflict - if we, e.g., hypothetically try to drag Solow growth theory into geologic time scales - it seems reasonable to defer to the 'more fundamental' science.
The reductionism is not absent, but buried; the economic laws are but a map to the territory that is the intractably complicated set of physical laws, and really only the physics of fundamental forces and particles tries to say that their map is too the territory. Does any other science forward that claim, in the halls of respectable academia? Peculiarly aggressive natural philosophers of mind, perhaps?
Don't you need it to be a priori and universally - that is, for everyone - true that all individuals are weakly-reliably rational? If not, for any given individual, they have no internal way of introspecting their way to deductive reliability and your argument becomes yet another empirical one. Other people think like me, therefore...?
Yet one need only walk down to the mental health ward of your university's medicine or psychiatry faculty to discover individuals who cannot plausibly be said to have a weakly-reliably process of rationality.
There are a couple ways to go here. One is to saw--the people in the mental ward are rational, just closer to the minimal threshold than most. For instance, someone in the grips of a delusion may decide that they need their lungs taken out because the government has put spy cameras inside them; they will then go to an emergency room and demand service. Although the delusion is certainly crazy, notice that what they do in response to it is in fact instrumentally rational (to at least some degree). Emergency rooms are where you go to get emergency surgery. And this form of rationality is part of what grounds our attribution of the possession of the concept 'emergency room' to the patient, as well as our characterization of their action as intentional rather than, say a reflex spasm. Again, how exactly you count and characterize their beliefs is going to be important to the plausibility of this point.
Quite right - it certainly would feel rational (actually, the hypothesis that many insane people are actually economically rational actors with highly distorted preferences has a lot of adherents). Yet it clearly cannot, in your words, restrict you from going "too far wrong". I would regard this observation as a weakness rather than a strength of your argument, so I don't know where you are going with it.
It depends on what you mean by 'too far wrong.' I am not trying to give a theory which renders paranoid schizophrenia a priori impossible; that would be a bad plan, given that it actually exists and what actually exists cannot be a priori impossible. Instead I'm trying to give a reason to think that it is part of what it is to possess concepts, and to be a mind, that one be rational. And, on some descriptions, the paranoid schizophrenic is not a counterexample to my claim, because the paranoid schizophrenic, although they get some important things wrong, nonetheless gets a great deal of things right in the routine course of concept application.
The importance of 'rationality as a default for minds' is supposed to be providing an explanatory connection between our beliefs in, say, mathematical propositions, and the truth of those propositions. Since mathematical propositions are non-physical that explanation can't go by way of the propositions themselves, or their physical bases, causing the corresponding beliefs in us by way of perception. So instead we secure a connection by saying: our beliefs in mathematical propositions are non-accidentally true because it is in the nature of those beliefs to be rational--because if they were sufficiently irrational, they wouldn't be beliefs at all. The goal is to render non-mysterious how, in absence of any causal interchange, our beliefs about non-physical propositions could be any better than random guesses.
It's worth noting that, if this works, it gives us a lot. Realists traditionally have a problem explaining how we could know about the relevant subject matter, but are good at explaining both why we should care about it once we do and how the semantics works. Anti-realists traditionally are very good at explaining how we could know about the subject matter, but terrible at explaining why we should care about it and how the semantics works. So: if the story I've told works out, then Realism will have a good explanation on all fronts--knowledge, importance, and semantics--ergo, we'll have an available view with no glaring flaws. That doesn't come along all that often! Of course, 'it would be nice if this were true, ergo this is true' is a bad argument. But at least it explains why this is a view worth fully investigating, even if it initially seems implausible.
Don't you need it to be a priori and universally - that is, for everyone - true that all individuals are weakly-reliably rational? If not, for any given individual, they have no internal way of introspecting their way to deductive reliability and your argument becomes yet another empirical one. Other people think like me, therefore...?
Yet one need only walk down to the mental health ward of your university's medicine or psychiatry faculty to discover individuals who cannot plausibly be said to have a weakly-reliably process of rationality.
There are a couple ways to go here. One is to saw--the people in the mental ward are rational, just closer to the minimal threshold than most. For instance, someone in the grips of a delusion may decide that they need their lungs taken out because the government has put spy cameras inside them; they will then go to an emergency room and demand service. Although the delusion is certainly crazy, notice that what they do in response to it is in fact instrumentally rational (to at least some degree). Emergency rooms are where you go to get emergency surgery. And this form of rationality is part of what grounds our attribution of the possession of the concept 'emergency room' to the patient, as well as our characterization of their action as intentional rather than, say a reflex spasm. Again, how exactly you count and characterize their beliefs is going to be important to the plausibility of this point.
Quite right - it certainly would feel rational (actually, the hypothesis that many insane people are actually economically rational actors with highly distorted preferences has a lot of adherents). Yet it clearly cannot, in your words, restrict you from going "too far wrong". I would regard this observation as a weakness rather than a strength of your argument, so I don't know where you are going with it.
It depends on what you mean by 'too far wrong.' I am not trying to give a theory which renders paranoid schizophrenia a priori impossible; that would be a bad plan, given that it actually exists and what actually exists cannot be a priori impossible. Instead I'm trying to give a reason to think that it is part of what it is to possess concepts, and to be a mind, that one be rational. And, on some descriptions, the paranoid schizophrenic is not a counterexample to my claim, because the paranoid schizophrenic, although they get some important things wrong, nonetheless gets a great deal of things right in the routine course of concept application.
The importance of 'rationality as a default for minds' is supposed to be providing an explanatory connection between our beliefs in, say, mathematical propositions, and the truth of those propositions. Since mathematical propositions are non-physical that explanation can't go by way of the propositions themselves, or their physical bases, causing the corresponding beliefs in us by way of perception. So instead we secure a connection by saying: our beliefs in mathematical propositions are non-accidentally true because it is in the nature of those beliefs to be rational--because if they were sufficiently irrational, they wouldn't be beliefs at all. The goal is to render non-mysterious how, in absence of any causal interchange, our beliefs about non-physical propositions could be any better than random guesses.
It's worth noting that, if this works, it gives us a lot. Realists traditionally have a problem explaining how we could know about the relevant subject matter, but are good at explaining both why we should care about it once we do and how the semantics works. Anti-realists traditionally are very good at explaining how we could know about the subject matter, but terrible at explaining why we should care about it and how the semantics works. So: if the story I've told works out, then Realism will have a good explanation on all fronts--knowledge, importance, and semantics--ergo, we'll have an available view with no glaring flaws. That doesn't come along all that often! Of course, 'it would be nice if this were true, ergo this is true' is a bad argument. But at least it explains why this is a view worth fully investigating, even if it initially seems implausible.
Once again, I have the very rare but very Kyrie Eleison (geddit?)experience of having someone else being able to articulate the half-formed things I am failing to think.
I can't help thinking that the definition of rationality is important here. Some people seem to view it as a kind of property of the universe, others as a property of our minds. When I was young and loved Zen and The Art of Motorcycle Maintenance, I started thinking of it as an intellectual tool developed to be able to handle things we couldn't perceive - whether that is the future, metaphysics, or something far away. Research on language development has made me start to think of language as something we have an innate aptitude for. So perhaps rationality is something we have a natural aptitude for too?
When I start to think about things like this I really feel the limits of language - like I want to say maybe that rationality is the kind of thinking that humans are good at, and that there could be other forms of... useful cognition?... that other entities might be good at instead of maths. But I can't even manage to write what that might be.
Apparently my elders were wrong and I should have been taking more drugs when young, not less.
A lot of very intelligent people felt that they had derived Euclid's Fifth Postulate (the parallel line postulate - you know, Euclidean and non-Euclidean geometry and whatnot) from the other four. They turned out to be wrong.
It seems quite possible to hypothesize causal interchange. What kind of physical minds would tend to exist, in a universe with Unreasonably Effective mathematics...? Anthropic-principle style, if you will.
This is unsatisfying for the reason I gave earlier: one can concede that one's beliefs about numbers are physical, but maintain that numbers themselves are not.
In maintaining that numbers harbor a separate existance outside of information with physical representation you are asserting that they exist as metaphysical objects; And therefor physical closure is false.
Not so. Numbers are non-physical, but do not causally interact with anything physical. Hence, the physical is stil causally closed. If they don't causally interact with anything physical, how do we know about them? That's what I answer in the last two sections of the OP.
Hmmm, went back and reread it, and I still don't get it - though I obviously misread what you said about casual closure.
I just can't bring myself to buy the premise that any information can be "non-physical". Several of the examples provided - democracy, the prudency of running from bears - are really just complex sets of information regarding the physical (Running from bears for instance, is only prudent if bears pose a threat to ones survival or if ones survival is considered a priority. The former depends on physical facts and the latter is survival instinct, which is not an abstract concept, it's physical hardcoding) and refering to them as non-physical occurs only because it's complex to explain in terms of information regarding the physical.
Mathematics is less obvious because its information about how classify sets rather than classifications in their own right, but I don't think there's anything to suggest they would have a non-physical existance.
To pose an example, there is only a difference in complexity between storing and treating numbers in our minds, and them having a non-physical existance, and storing/treating any and all computer software, which would then too have a non-physical existance.
Which seems like a very weird result.
(As a sort of preemptive aside; We have to allow the definition of sets without requiring the enumeration of all elements of that set. In other words if a number can be uniquely defined in words, then the number is uniquely defined , period. The reason why is that otherwise we would lose the ability to call something an apple, because an apple is just a set of cells which is a set of molecules which is a set of atoms which is a set of... If we required the enumeration of every element within a set to define a set, rather than the "rule" by which we can identify the set, it would be impossible to call a set-of-sets an apple because I'm pretty sure none of us actually could characterize every single sub-atomic particle in an apple.
Hence, the definition of a large number - or any of the irrational or surreal numbers - must be allowed, without requiring us to wallow through all the elements of such sets. If you actually required that, you couldn't tell me what an apple was)
I just can't bring myself to buy the premise that any information can be "non-physical". Several of the examples provided - democracy, the prudency of running from bears - are really just complex sets of information regarding the physical (Running from bears for instance, is only prudent if bears pose a threat to ones survival or if ones survival is considered a priority. The former depends on physical facts and the latter is survival instinct, which is not an abstract concept, it's physical hardcoding) and refering to them as non-physical occurs only because it's complex to explain in terms of information regarding the physical.
You jumped from "physical" to "regarding the physical". The two are different concepts.
I just can't bring myself to buy the premise that any information can be "non-physical". Several of the examples provided - democracy, the prudency of running from bears - are really just complex sets of information regarding the physical (Running from bears for instance, is only prudent if bears pose a threat to ones survival or if ones survival is considered a priority. The former depends on physical facts and the latter is survival instinct, which is not an abstract concept, it's physical hardcoding) and refering to them as non-physical occurs only because it's complex to explain in terms of information regarding the physical.
You jumped from "physical" to "regarding the physical". The two are different concepts.
Walk me through it.
edit: As in, give me the criteria for what constitutes non-physical objects. Refering to information that is stored/transmitted physically and is about the operation of physical systems - however complex those systems may be - as non-physical strikes me as completely arbitrary
I must admit that I thought this thread was going to be a prime example of philosophical wankery, but I did enjoy the little discussion about the physicality of "democracy".
Let me know when your non-empirical philosophy has developed a new medical cure or a better method of construction. At that point in time I may be interested in becoming a subscriber.
So when I refer to the blue ball over there, I am in fact really referring to a particular group of cells in my brain? But there is actually an object out there.
What if I point at the blue ball? And say something like "that blue ball is over there." Am I still referring to a group of cells in my brain? What am I pointing at?
A group of brain cells is telling your arm to position in a way that your brain logically relates to another group of cells storing an observation of what another group of cells consider a blue ball. This is all kind of silly. Forget the "groups of cells," I think you're focusing on that in an attempt to avoid the more intuitive thrust of what I said. You are, of course, referring to what you think is a blue ball and where you think it is. And some of what you think about it is likely different from what others think about it. Like I said, for all we know you are also confusing it with a completely different blue sphere you saw another time. You can't possibly know if that's the case or not. It's all a matter of what you're thinking, and trying to communicate.
I really don't want to offend J here. But I'll take Russell's position over his.
I'm glad that we can skip all reading then. What do you think is a good rejoinder to Russell's objection to Price's resemblance theory of nominalism? Do you think that there is a good way to respond to the objection that Quine's update to nominalism fails because of the empty set?
Lol, maybe next we'll start responding to each other with [cite]. Instead of vague name-dropping in an attempt to out-authority me, why don't you explain LoserForHireX's stance on the matter? Russell and Price and Quine aren't here to defend themselves, and I think most people would rather read the thread and read forumer's arguments.
I just can't bring myself to buy the premise that any information can be "non-physical". Several of the examples provided - democracy, the prudency of running from bears - are really just complex sets of information regarding the physical (Running from bears for instance, is only prudent if bears pose a threat to ones survival or if ones survival is considered a priority. The former depends on physical facts and the latter is survival instinct, which is not an abstract concept, it's physical hardcoding) and refering to them as non-physical occurs only because it's complex to explain in terms of information regarding the physical.
Well, "information," by its nature, is that which informs. It is a matter of mind, and is entangled in the paradox of qualia. Other than the "cluster of brain cells" connection, information is quite separated from the physical. It is decidedly mental. Though, I don't completely disagree with your stance that information necessarily emerges from sense data.
Let me know when your non-empirical philosophy has developed a new medical cure or a better method of construction. At that point in time I may be interested in becoming a subscriber.
So when I refer to the blue ball over there, I am in fact really referring to a particular group of cells in my brain? But there is actually an object out there.
What if I point at the blue ball? And say something like "that blue ball is over there." Am I still referring to a group of cells in my brain? What am I pointing at?
A group of brain cells is telling your arm to position in a way that your brain logically relates to another group of cells storing an observation of what another group of cells consider a blue ball. This is all kind of silly. Forget the "groups of cells," I think you're focusing on that in an attempt to avoid the more intuitive thrust of what I said. You are, of course, referring to what you think is a blue ball and where you think it is. And some of what you think about it is likely different from what others think about it. Like I said, for all we know you are also confusing it with a completely different blue sphere you saw another time. You can't possibly know if that's the case or not. It's all a matter of what you're thinking, and trying to communicate.
I'm just trying to understand whether or not there are objects out there. But your position isn't terribly clear on whether there is or not. You are really trying hard to push for some sort of epistemic argument, when I'm asking a metaphysical question. What manner of objects exist? Is there a thing out there? Regardless of what it is that we can know about it, is there are a thing out there to know about? And you seem to waffle in between trying to deny that there is, and using language that indicates that you believe that there is an object there.
I'm doing all of this of course to try to tease out whether or not when I refer to "democracy" I'm referring to an object. If I am referring to an object, is it a physical object like the blue ball? How is it when it appears to share no properties in common with the blue ball (it doesn't have mass, color, shape, etc)?
I really don't want to offend J here. But I'll take Russell's position over his.
I'm glad that we can skip all reading then. What do you think is a good rejoinder to Russell's objection to Price's resemblance theory of nominalism? Do you think that there is a good way to respond to the objection that Quine's update to nominalism fails because of the empty set?
Lol, maybe next we'll start responding to each other with [cite]. Instead of vague name-dropping in an attempt to out-authority me, why don't you explain LoserForHireX's stance on the matter? Russell and Price and Quine aren't here to defend themselves, and I think most people would rather read the thread and read forumer's arguments.
I'm not trying to out authority you, Yar. Also, that's not vague name dropping. That's legitimate reference to well thought out and detailed arguments concerning the very subject that we're talking about.
As for my stance, I'm convinced by Russell's counter to Price's resemblance nominalism (that it fails to account for resemblance itself). I also think that Quine's failure concerning the empty set is pretty damning (that it creates false equivalencies for uninstantiated universals), and it extends to any nominalism that attempts to use sets (including trope theory). So there, that's my position. If you want a fuller argument I have a paper I wrote on trope theory and the empty set weakness that I'd be happy to email you.
"The only way to get rid of a temptation is to give into it." - Oscar Wilde
"We believe in the people and their 'wisdom' as if there was some special secret entrance to knowledge that barred to anyone who had ever learned anything." - Friedrich Nietzsche
I'm just trying to understand whether or not there are objects out there. But your position isn't terribly clear on whether there is or not. You are really trying hard to push for some sort of epistemic argument, when I'm asking a metaphysical question. What manner of objects exist? Is there a thing out there? Regardless of what it is that we can know about it, is there are a thing out there to know about? And you seem to waffle in between trying to deny that there is, and using language that indicates that you believe that there is an object there.
I'm doing all of this of course to try to tease out whether or not when I refer to "democracy" I'm referring to an object. If I am referring to an object, is it a physical object like the blue ball? How is it when it appears to share no properties in common with the blue ball (it doesn't have mass, color, shape, etc)?
Well it doesn't help that a blue ball doesn't have any of those properties save as a enumerated list of components (molecules, atoms, quarks). All solids have a vapor pressure (in addition to the stress and ablation of bouncing such a ball) so the mass, shape, and composition of the ball will be in flux as well. The ball will likely have dye molecules that are the major contribution to the color as apposed to the polymer substrate so the ball doesn't have just one color.
But that's kind of besides the point. I would say that neither the ball nor democracy are physical objects, but concepts/labels that are reducible to physical objects (molecules/atoms/quarks/atomic forces/etc). But for tractability we still refer to them as "objects". Ball as a collection of atoms that share some features. Democracy as a collection of atoms that exist in people's brains and our aural and written languages. Each can be considered on any level of abstraction but have levels of extraction that is practical for each. The ball, classical and statistical mechanics. Democracy, social science (and neuroscience eventually).
I'm just trying to understand whether or not there are objects out there.
Then I'd say that my answer is a weak yes, there are probably objects out there, but we can't say for sure anything about them (even that they exist for certain), because all we have are our own observations, memories, measurements, etc. For all we know, these could be mere shadows or after-effects of the "objects out there." They could be categorically but consistently inaccurate and misleading. Another way to put it is that it doesn't really matter, it's a somewhat meaningless question. If by "out there" you mean "independent of what thoughts a thinking mind might put together about them," then how could you possibly ever even conceive of such an existence? All we can ever have are the thoughts our minds construct.
I'm doing all of this of course to try to tease out whether or not when I refer to "democracy" I'm referring to an object. If I am referring to an object, is it a physical object like the blue ball? How is it when it appears to share no properties in common with the blue ball (it doesn't have mass, color, shape, etc)?
Right, back on target. As I hinted at before, you are confusing degrees of certainty for actual certainty. What if we agreed that the mass of Democracy was the sum of all the masses of all the humans who are alive and who have ever voted? Or perhaps the total mass of all property owned by a Democractic government? Would Democracy not then have mass? Of course, you could argue that such things aren't really democracy, that they are arbitrary masses that are only minimally or nominally related to decmocracy. I could also argue that your measurement of the mass of a blue ball is arbitrary, because in 1,000 years it will have a very different mass, or because you're actually also measuring the mass of all the bacteria and dust on the surface of the ball. And don't even get me started on whether or not the air inside the ball counts towards its mass or not.
The difference is that despite a lack of absolute certainty, an object like a blue ball is simple enough, objective enough, that we can pretty easily come to an agreement, even come to an internationally agreed upon standard, for how we measure its mass and we can use such measurements to communicate usefully. Democracy, on the other hand, is far more subjective, and thus while we certainly could come up with a way to measure its mass, it would be far harder or perhaps impossible to come to any standard agreement on a useful measurement of the mass of Democracy. But these are not a hard and fast distinction; they are degrees.
I say one concept is more objective than the other. Enough so that for the sake of simplicity and usefulness, we can thus say that one is an object and the other only a subject. But if we're getting hardcore about it and looking for ontological truth, the distinction eventually disappears, and they are both simply on a continuum of objectivity and subjectivity. Even the blue ball is still a somewhat different collection of thoughts in each individual person's mind, and will always have a slightly different mass each time you measure it. More importantly, even the ball is ultimately open to an infinite number of attacks as to what it "really" is or isn't, attacks that can make even its being seem subjective.
As for my stance, I'm convinced by Russell's counter to Price's resemblance nominalism (that it fails to account for resemblance itself). I also think that Quine's failure concerning the empty set is pretty damning (that it creates false equivalencies for uninstantiated universals), and it extends to any nominalism that attempts to use sets (including trope theory). So there, that's my position. If you want a fuller argument I have a paper I wrote on trope theory and the empty set weakness that I'd be happy to email you.
Sorry if I didn't make it clear, but what I'm interested in, if it's possible, is a succinct summary of your thoughts to replace phrases like "Russell's counter" and "resemblance" and "Quine's failure" and "uninstantiated universals." We can all go look these up, but who knows if we'll even read the same parts you're referring to, or more importantly, if we'll even perceive the arguments to be what you perceived them to be? How about just telling us what you think? I bet you can do it in less words than a term paper, and with more originality.
Posts
Kind of a bad example, since it's self-defeating. You can't type a number that your brain is theoretically incapable of encoding, the scale just doesn't work out. You'll run out of time before you run out of neurons.
Right! So we've got 'picture' and 'understand' separated out here. Why is 'know' only 'picture' and not 'understand'?
Iunno. I can imagine/know something perfectly mathematically round (not composed of those annoying atoms), I don't think my mind's eye has the resolution for it, though.
Got to a number with more digits than leptons in your brain. Not a larger number than, so no that doesn't count. You could not store all of those digits in a computer, and it would take many times your life to type or read them, and you could not remember them all at once.
Just like you can not remember all of the digits of Pi at once, and beyond a point the numbers needed to calculate the next digit in Pi would be too large for your brain to work with even using external storage.(Pi has more digits than there is matter in the universe, to the extent that Pi has digits at all)
Why in the world would the base matter?
Why in the world would the base matter?
Well, no one is literally a platonist these days. So it's not as though I'm accepting the baggage that goes along with some of the crazier aspects of plato's metaphysics (the realm of the forms, the rememberance theory of knowledge, etc). It would probably derail the thread too much to go into why platonic universals aren't like religion really at all. I would suggest though that you start your reading with Bertrand Russell. A man who was not a fan of religion, yet argued quite persuasively for a form of platonism.
"We believe in the people and their 'wisdom' as if there was some special secret entrance to knowledge that barred to anyone who had ever learned anything." - Friedrich Nietzsche
Posh's point, or so I took it, is that there is an ordinary integer number greater than that corresponding to every particle in the universe, or the brain, or whatever other arbitrarily large collection of physical objects one chooses, and that this number is no more or less real, no more or less sensible or understood, than the number corresponding to the exact number of "whatever large number of things", or the number 23, for that matter.
This is unsatisfying for the reason I gave earlier: one can concede that one's beliefs about numbers are physical, but maintain that numbers themselves are not. The reductive naturalist has to not only explain how our beliefs can be physical, but how all of their objects can be as well. There are, as far as I know, two main ways of doing this for mathematical statements. The first is fictionalism: fictionalists claim that mathematical statements are literally false--they quantify over abstract objects, which do not actually exist--but that they nonetheless are useful for our purposes. They then have to give some explanation of why a categorically false area of discourse has this handy property of usefulness (as well as to explain why math certainly seems true). The second is nominalism: nominalists claim that mathematical statements are not about abstract objects per se, but rather are a more complicated way of saying things about everyday spatiotemporal objects. So math consists in true statements, they're just not of the form that their surface grammar seems to indicate. The nominalist then has to explain exactly how this paraphrase from math into ordinary object language is supposed to be carried out in a way that preserves at the very least most of the interesting fragments of mathematics.
These tasks are very hard. For instance, I was recently reading a book review of a recent nominalist which pointed out that the paraphrase she gave of math into physical object language ultimately descended into statements about geometric relations between spacetime points: but it's unclear how 'nominalist' this really is when it helps itself as 'physical object language' to the mathematical characterizations of geometry between points with real-valued coordinates and etc. And I think that the common view is that Hartry Field has the most worked-out fictionalist view, but that even his account struggles to explain why math has truth-preserving features and also to explain enough of it to ground its applications in science.
Also, you don't have to go to the large end of the number line to start getting perplexities for people who think that every truth is physically encoded in some straightforward way. There are already more real numbers between 0 and 1 than particles that have ever or will ever exist. There are more tautologies than thoughts: for instance, A->A is a tautology, and if you substitute every thought ever thought, in turn, for A, you will get a list just as long. If these are physically encoded, it is not in the straightforward way of being written down, or even thought about. Not to mention the straightforward point that 2 + 2 = 4 before anyone ever lived, and it will afterward as well.
That's not exiting physical closure by counterexample from within the physical.
Let me continue to assume an utterly physicalist position, with the understanding that I am not a champion of ontological minutiae: the numbers themselves, as discrete entities, don't have to exist in our brains as individual little nodes of meaning. Mathematics is a system of abstract rules, and it exists in any person's mind to whatever extent they understand that system. The number 0.2345 doesn't have to exist, itself, as a number in someone's brain - in fact, it could be argued based on cognitive observations that only a very limited array of numbers exist as fully formed, completely grasped, independent concepts of quantity in someone's mind, if they can do so at all. All that is required is the system of symbols and operations capable of generating that number. For the moment that we read and discuss a given number, or manipulate it or write it down or what have you, it likely has some kind of individual physical existence in a neurological sense, but this is likely not persistent. On the other hand, a number like pi probably has a permanent spot in many of our brains, even though we are unable to fully grasp the nature of the quantity it represents in the same sense that we fully grasp the nature of the quantity of, say, 3.
All this to say, the "object" of these thoughts is not necessarily separate from the thoughts themselves. The abstract system in question is self-contained and tautological. If you think about "2," you are not applying your thought to a non-physical, external entity; you are applying a system of abstraction that is physically extant in your brain.
Was 2+2=4 really true before anyone lived, and was "all bachelors are men but not all men are bachelors" true before our planet was more than a swirl of cosmic dust? I don't know if I would say so. Or rather, I don't know if I would say they are "true" in a way that is meaningfully related to temporal or spatial position, just as I would not necessarily say they "exist" in an abstract sense. If I create a completely meaningless but internally consistent system where hurgadurp equals flipadiggaboo, can that gibberish statement be described as "true" or "false" in a way that has any meaning outside of a description of that internal consistency? Was it true for all of time, before I even thought of it? Did it exist beforehand?
I think there are grounds for a physicalist to reject the notion that such an abstraction has some sort of timeless non-physical existence; the systems and rubrics that produce these statements and contain these logics do physically exist in our mind. Any statement of their independent truth or existence can only be made from within those systems.
Let's just go on assuming that it is the case when we are tasked with a physics problem and continue to not care at all other times, unless your are one of those religious folk who just assume that it is false at all times, in which case - carry on, crazy diamond!
try this
For our purposes, "actually" and "there" don't make a lot of sense. But yes, when you talk about an object in the world, you are specifically talking about your mental construct of that object, formed by your observations and ideas about it. Another person has different experiences with it, and thus a somewhat different mental construct, but you two are able to reach enough common ground on it to have a useful conversation.
If you did not have experiences and observations and memories in your head about the object, you would not know of any such object. Having them gives you something to talk about.
Suppose one time you saw a completely different object, but you thought it was the same object, and it did something weird. Later, when talking about the object, would you not actually be talking about a mental construct you have that mistakenly conflates two different objects? Would you not be talking about an object which also does that weird thing, even though the "actual" object does no such thing? Of course. You're always talking about your mental construct.
Surely you've been in enough threads with me by now that we can skip the part where you invite me to start my reading. I did AP ind. study projects in high school covering major philosophers, and I minored in philosophy at a pretty good university. I'm not saying that makes me right or anything, or even an expert, but just, you know, whatever. We don't need Russell, surely _J_ will come along soon enough to argue his own form of athiest platonism.
I believe this is on the right track, except then, as you point out, what exactly can be true? I would say that math is fiction, but not necessarily false. Link wields the Master Sword. Fiction, but not false. 2 + 2 = 4. Fiction, but not false. Quite useful, in fact, and thus quite likely to be revered as a pure form of truth. Fiction only equates to falsehood if physical/material reality equates to truth. And I'm not a fan of that latter part.
This is a tough problem, and IMO is very similar to the qualia dilemma. But I don't think fictionalism necessarily requires that one answer why math is so useful. It only requires a good argument for why it is fiction. My personal philosophy, that I came up with years ago in a fever-induced hallucination and have struggled to fully recall and conceive ever since, is actually very similar to the nominalist explanation you gave, except that it relates to the thought process and the connections between neurons, not mathematically defined points in space. In general, that mathematics is an abstract model of one key aspect of how our brains are wired to make sense of and operate within our observations of the universe, one we can isolate and work wonders with, and then reapply to our interactions with the universe to make even better sense of observations of it. Sort of like how math and logic can be represented by simple circuitry, passing currents. In fact, that's the most fundamental mechanism we'ver ever developed for representing it.
Srsly. I'd suggest that even for "2" to be a valid concept, you'd need to have two obects which are entirely indistinguishable from one another. Which is sort of a contradiction.
So when I refer to the blue ball over there, I am in fact really referring to a particular group of cells in my brain? But there is actually an object out there.
What if I point at the blue ball? And say something like "that blue ball is over there." Am I still referring to a group of cells in my brain? What am I pointing at?
I really don't want to offend J here. But I'll take Russell's position over his.
I'm glad that we can skip all reading then. What do you think is a good rejoinder to Russell's objection to Price's resemblance theory of nominalism? Do you think that there is a good way to respond to the objection that Quine's update to nominalism fails because of the empty set?
"We believe in the people and their 'wisdom' as if there was some special secret entrance to knowledge that barred to anyone who had ever learned anything." - Friedrich Nietzsche
Not so. Numbers are non-physical, but do not causally interact with anything physical. Hence, the physical is stil causally closed. If they don't causally interact with anything physical, how do we know about them? That's what I answer in the last two sections of the OP.
This is a less straightforward, and hence more plausible, way to try to reduce math to people's thoughts about it. It is not that individual token mathematical statements are physical by virtue of being physically thought (a view I think is hopeless, for the reasons above), but that all mathematical statements are physical in virtue of enough of the central elements of math as a whole being physically thought. But I still think you are underestimating the difficulties here.
To start, just consider my belief that the sun is round. This belief has a straightforward predicative form: is ascribes a property (roundness) to a thing (the sun). We can say that the belief refers to the sun, and that it is true if and only if the sun has that property, roundness. Notice that my belief that 2 is prime has the exact same surface syntax: it appears to be ascribing a property (primeness) to a thing (the number 2). If it functioned as a regular descriptive sentence, we would say that it refers to the number 2, and is true if and only if the number 2 has the property, primeness. But we can't say this, at least if we don't think that the number 2 and the property of primeness literally exist.
It's okay if two sentences with the same surface grammar nevertheless have different deep logical structures: for instance, 'nothing is bigger than itself' has the same surface grammar as 'the sun is round' and '2 is prime'--that of a predication onto 'nothing'--but that is not its deep form (if it were really predicative, nothing would have to be a thing--ew). So maybe statements about math, like that statement about nothing, only appear to have a standard descriptive form. But if we want to make this claim, then we should be able to say what the real deep logical form actually is, and whatever form we claim should be able to explain the central features of mathematics. And it's not clear anyone has managed to do this in an anti-realist way.
For instance, the straightforward reading of math makes it easy to see how mathematical statements can be true: '2 is prime' is true if 2 has the property of being prime, just like 'the sun is round' is true if the sun has the property of being round. But on your proposal, the object of a mathematical thought is the thought itself. But then it is very hard to see how they can be true. For one thing, self-referential sentences are fraught with paradox, and considered meaningless on standard solutions to the liar paradox. For another, although some beliefs might be self-fulfilling, e.g. "I have at least one belief" can make itself true by being held, it is difficult to see how mathematical beliefs have anything like that character. It also seems to imply that, by destroying or altering your brain I could destroy or alter mathematical truths--after all, by destroying or altering the objects of ordinary beliefs I can make them false. Finally, it certainly seems that when we both consider whether Goldbach's conjecture is true, we think about the same thing; but if our mathematical beliefs are actually about our own brains then we are not thinking about the same thing. We are each actually thinking about our own brain. This threatens ugly consequences: if we aren't actually thinking about the same thing, then are we even disagreeing when I say "Goldbach's conjecture is true" and you say "Goldbach's conjecture is false"? If our beliefs have different objects, which we merely use the same words to express, how can they contradict each other? After all, when I say "the bank is closed" and you say "the bank is open" we only disagree if we're talking about the same bank. So it seems we could not. But isn't that wrong--don't we actually contradict each other when we take differing stands on Goldbach's conjecture?
This particular post was addressed to you, but many of these objections would apply just as well to the anti-realist theories other posters are putting forward about math. I think it is under-appreciated how much difficulty there is in trying to actually give a precise, adequate characterization of math on non-realist grounds.
Math would still be math even if we used silly names, and if you offer rigorous definitions of your terms then they no longer count as gibberish.
A final question: if I read you correctly, you take the systems of the brain to be explanatorily prior to the truth or falsity of individual mathematical judgments (sometimes people say the same, but for systems of social enforcement: 2+2 = 4 because your teacher will slap your knuckles if you say anything else). Individual judgements are mathematically correct or incorrect insofar as they follow from the beliefs encoded in certain neural systems. But there seems to be a dilemma in regard to how we read 'follow from.' If 'follow from' is read as 'mathematically follows from by way of valid proof,' then we are presupposing a notion of mathematical correctness in our definition of mathematical correctness, and hence have actually done nothing to show how to define it away in terms of physical systems. But if we read 'follows from' as 'is a causal result of' then it is impossible for anyone to ever have a false mathematical belief (so long as it was the causal result of their relevant neural system). But surely some people do have false mathematical beliefs (that are causal results of their relevant neural system)--for some years before it was proved to generate paradox, the naive axiom of comprehension was held true. This was a mistake, but I cannot see how to say why without adverting to an abstract fact of the matter which existed before, and independently of, anyone's thought about it.
I think that you're off the mark about some things (like the relation of positivism to odious politics--the Vienna Circle philosophers were actually, by and large, radical leftists, a political orientation is find not odious at all); however, I don't think you're off the mark about the "reductive naturalists think everything is best explained by physics bit." They do, at least as I've set things up. And reductivism can be just as much an attack on the autonomy of the special sciences (like economics, biology, psychology, etc.) as it is an attack on realist theories of math, ethics, or whatnot.
On which note:
Ask and ye shall receive:
For a sense of the difficulty: try asking how one would go about translating true generalizations in economics into the language of physics given that cowrie shells, dollar bills, gold coins, feathers, franc notes, and pennies can all count as ‘money;’ that factories, cows, human slaves, shovels, and tractors can all count as ‘capital,’ etc. What are the physical characterizations of 'supply' and 'demand?' If we require that our laws of science take a simple unified form, then the relation between supply and demand will be so characterizable in economic terms but not physical ones--where the best you'll get is that physical laws entail that:
{incredibly complicated physical description A --> incredibly complicated physical description B}
{incredibly complicated physical description C --> incredibly complicated physical description D}
.
.
.
and that some effect in supply is defined as {A or C or .... }
and some resultant economic effect is defined as {B or D or ...}
This prima facie looks like a worse candidate for a law than "supply bears such-and-such relation to demand." The latter seems simple and unified, rather than gerrymandered. And it seems to be a better explanation. It contains all of the relevant information and none of the irrelevant information, and it explains why and how that information relates to produce the outcomes it does. This is the classic argument for the autonomy (and non-reducibility) of the special sciences to physics.
This sort of non-reductive view faces a challenge, though. Return to the case where I say ‘duck!’ and you duck. It seems simply true to say that the vibrations in the air caused you to duck. But if the linguistic facts are not reducible to, or not identical to, those very same vibrations, how could the linguistic fact that ‘duck’ means duck also have caused you to duck? There is a threat of causal exclusion here--once we have described the micro-physical causal chain leading to your act of ducking, anything else we add over and above would seem to be extraneous. Few accept the view that every linguistic utterance involves a perfectly overlapping set of overdetermined causes (whether there are ever overdetermined causes is already controversial). The exclusion argument threatens to show that if the special sciences really are irreducible to physics, then as a consequence they must also be causally irrelevant--bad news for economics, say, which at least ostensibly is trying to describe causal interactions between market forces.
or is gravitation itself considered a physical thing?
No, and yes.
Gravity falls under the banner of physics.
Well, physicists talk about the curvature of space-time, but then other physicists go into detail so great that I can't understand the science myself. So yes, physicists do provide a physical mechanism. Several, really.
But then, whether anyone understands gravity is separate from whether it is physical or not. 'Physical' includes fields and waves and rays and so on. Not just matter.
No need to extend as far as economics. The study of multiple atoms alone already involves substantial amounts of handwaving with regards to what exactly the constituent subatomic entities are doing; it is simply too difficult to tractably manipulate save in special cases.
But the strength of reductive science is in generality - in conservation laws and the like, where we assert very little about specific entities but make strong statements about their aggregates. There is no point in economics or any apparently irreducible science at which one overturns the Laws of Thermodynamics. And if there appears to be a conflict - if we, e.g., hypothetically try to drag Solow growth theory into geologic time scales - it seems reasonable to defer to the 'more fundamental' science.
The reductionism is not absent, but buried; the economic laws are but a map to the territory that is the intractably complicated set of physical laws, and really only the physics of fundamental forces and particles tries to say that their map is too the territory. Does any other science forward that claim, in the halls of respectable academia? Peculiarly aggressive natural philosophers of mind, perhaps?
It depends on what you mean by 'too far wrong.' I am not trying to give a theory which renders paranoid schizophrenia a priori impossible; that would be a bad plan, given that it actually exists and what actually exists cannot be a priori impossible. Instead I'm trying to give a reason to think that it is part of what it is to possess concepts, and to be a mind, that one be rational. And, on some descriptions, the paranoid schizophrenic is not a counterexample to my claim, because the paranoid schizophrenic, although they get some important things wrong, nonetheless gets a great deal of things right in the routine course of concept application.
The importance of 'rationality as a default for minds' is supposed to be providing an explanatory connection between our beliefs in, say, mathematical propositions, and the truth of those propositions. Since mathematical propositions are non-physical that explanation can't go by way of the propositions themselves, or their physical bases, causing the corresponding beliefs in us by way of perception. So instead we secure a connection by saying: our beliefs in mathematical propositions are non-accidentally true because it is in the nature of those beliefs to be rational--because if they were sufficiently irrational, they wouldn't be beliefs at all. The goal is to render non-mysterious how, in absence of any causal interchange, our beliefs about non-physical propositions could be any better than random guesses.
It's worth noting that, if this works, it gives us a lot. Realists traditionally have a problem explaining how we could know about the relevant subject matter, but are good at explaining both why we should care about it once we do and how the semantics works. Anti-realists traditionally are very good at explaining how we could know about the subject matter, but terrible at explaining why we should care about it and how the semantics works. So: if the story I've told works out, then Realism will have a good explanation on all fronts--knowledge, importance, and semantics--ergo, we'll have an available view with no glaring flaws. That doesn't come along all that often! Of course, 'it would be nice if this were true, ergo this is true' is a bad argument. But at least it explains why this is a view worth fully investigating, even if it initially seems implausible.
Once again, I have the very rare but very Kyrie Eleison (geddit?)experience of having someone else being able to articulate the half-formed things I am failing to think.
I can't help thinking that the definition of rationality is important here. Some people seem to view it as a kind of property of the universe, others as a property of our minds. When I was young and loved Zen and The Art of Motorcycle Maintenance, I started thinking of it as an intellectual tool developed to be able to handle things we couldn't perceive - whether that is the future, metaphysics, or something far away. Research on language development has made me start to think of language as something we have an innate aptitude for. So perhaps rationality is something we have a natural aptitude for too?
When I start to think about things like this I really feel the limits of language - like I want to say maybe that rationality is the kind of thinking that humans are good at, and that there could be other forms of... useful cognition?... that other entities might be good at instead of maths. But I can't even manage to write what that might be.
Apparently my elders were wrong and I should have been taking more drugs when young, not less.
It seems quite possible to hypothesize causal interchange. What kind of physical minds would tend to exist, in a universe with Unreasonably Effective mathematics...? Anthropic-principle style, if you will.
I just can't bring myself to buy the premise that any information can be "non-physical". Several of the examples provided - democracy, the prudency of running from bears - are really just complex sets of information regarding the physical (Running from bears for instance, is only prudent if bears pose a threat to ones survival or if ones survival is considered a priority. The former depends on physical facts and the latter is survival instinct, which is not an abstract concept, it's physical hardcoding) and refering to them as non-physical occurs only because it's complex to explain in terms of information regarding the physical.
Mathematics is less obvious because its information about how classify sets rather than classifications in their own right, but I don't think there's anything to suggest they would have a non-physical existance.
To pose an example, there is only a difference in complexity between storing and treating numbers in our minds, and them having a non-physical existance, and storing/treating any and all computer software, which would then too have a non-physical existance.
Which seems like a very weird result.
(As a sort of preemptive aside; We have to allow the definition of sets without requiring the enumeration of all elements of that set. In other words if a number can be uniquely defined in words, then the number is uniquely defined , period. The reason why is that otherwise we would lose the ability to call something an apple, because an apple is just a set of cells which is a set of molecules which is a set of atoms which is a set of... If we required the enumeration of every element within a set to define a set, rather than the "rule" by which we can identify the set, it would be impossible to call a set-of-sets an apple because I'm pretty sure none of us actually could characterize every single sub-atomic particle in an apple.
Hence, the definition of a large number - or any of the irrational or surreal numbers - must be allowed, without requiring us to wallow through all the elements of such sets. If you actually required that, you couldn't tell me what an apple was)
You jumped from "physical" to "regarding the physical". The two are different concepts.
edit: As in, give me the criteria for what constitutes non-physical objects. Refering to information that is stored/transmitted physically and is about the operation of physical systems - however complex those systems may be - as non-physical strikes me as completely arbitrary
A group of brain cells is telling your arm to position in a way that your brain logically relates to another group of cells storing an observation of what another group of cells consider a blue ball. This is all kind of silly. Forget the "groups of cells," I think you're focusing on that in an attempt to avoid the more intuitive thrust of what I said. You are, of course, referring to what you think is a blue ball and where you think it is. And some of what you think about it is likely different from what others think about it. Like I said, for all we know you are also confusing it with a completely different blue sphere you saw another time. You can't possibly know if that's the case or not. It's all a matter of what you're thinking, and trying to communicate.
Lol, maybe next we'll start responding to each other with [cite]. Instead of vague name-dropping in an attempt to out-authority me, why don't you explain LoserForHireX's stance on the matter? Russell and Price and Quine aren't here to defend themselves, and I think most people would rather read the thread and read forumer's arguments.
Well, "information," by its nature, is that which informs. It is a matter of mind, and is entangled in the paradox of qualia. Other than the "cluster of brain cells" connection, information is quite separated from the physical. It is decidedly mental. Though, I don't completely disagree with your stance that information necessarily emerges from sense data.
I'm just trying to understand whether or not there are objects out there. But your position isn't terribly clear on whether there is or not. You are really trying hard to push for some sort of epistemic argument, when I'm asking a metaphysical question. What manner of objects exist? Is there a thing out there? Regardless of what it is that we can know about it, is there are a thing out there to know about? And you seem to waffle in between trying to deny that there is, and using language that indicates that you believe that there is an object there.
I'm doing all of this of course to try to tease out whether or not when I refer to "democracy" I'm referring to an object. If I am referring to an object, is it a physical object like the blue ball? How is it when it appears to share no properties in common with the blue ball (it doesn't have mass, color, shape, etc)?
I'm not trying to out authority you, Yar. Also, that's not vague name dropping. That's legitimate reference to well thought out and detailed arguments concerning the very subject that we're talking about.
As for my stance, I'm convinced by Russell's counter to Price's resemblance nominalism (that it fails to account for resemblance itself). I also think that Quine's failure concerning the empty set is pretty damning (that it creates false equivalencies for uninstantiated universals), and it extends to any nominalism that attempts to use sets (including trope theory). So there, that's my position. If you want a fuller argument I have a paper I wrote on trope theory and the empty set weakness that I'd be happy to email you.
"We believe in the people and their 'wisdom' as if there was some special secret entrance to knowledge that barred to anyone who had ever learned anything." - Friedrich Nietzsche
Well it doesn't help that a blue ball doesn't have any of those properties save as a enumerated list of components (molecules, atoms, quarks). All solids have a vapor pressure (in addition to the stress and ablation of bouncing such a ball) so the mass, shape, and composition of the ball will be in flux as well. The ball will likely have dye molecules that are the major contribution to the color as apposed to the polymer substrate so the ball doesn't have just one color.
But that's kind of besides the point. I would say that neither the ball nor democracy are physical objects, but concepts/labels that are reducible to physical objects (molecules/atoms/quarks/atomic forces/etc). But for tractability we still refer to them as "objects". Ball as a collection of atoms that share some features. Democracy as a collection of atoms that exist in people's brains and our aural and written languages. Each can be considered on any level of abstraction but have levels of extraction that is practical for each. The ball, classical and statistical mechanics. Democracy, social science (and neuroscience eventually).
Right, back on target. As I hinted at before, you are confusing degrees of certainty for actual certainty. What if we agreed that the mass of Democracy was the sum of all the masses of all the humans who are alive and who have ever voted? Or perhaps the total mass of all property owned by a Democractic government? Would Democracy not then have mass? Of course, you could argue that such things aren't really democracy, that they are arbitrary masses that are only minimally or nominally related to decmocracy. I could also argue that your measurement of the mass of a blue ball is arbitrary, because in 1,000 years it will have a very different mass, or because you're actually also measuring the mass of all the bacteria and dust on the surface of the ball. And don't even get me started on whether or not the air inside the ball counts towards its mass or not.
The difference is that despite a lack of absolute certainty, an object like a blue ball is simple enough, objective enough, that we can pretty easily come to an agreement, even come to an internationally agreed upon standard, for how we measure its mass and we can use such measurements to communicate usefully. Democracy, on the other hand, is far more subjective, and thus while we certainly could come up with a way to measure its mass, it would be far harder or perhaps impossible to come to any standard agreement on a useful measurement of the mass of Democracy. But these are not a hard and fast distinction; they are degrees.
I say one concept is more objective than the other. Enough so that for the sake of simplicity and usefulness, we can thus say that one is an object and the other only a subject. But if we're getting hardcore about it and looking for ontological truth, the distinction eventually disappears, and they are both simply on a continuum of objectivity and subjectivity. Even the blue ball is still a somewhat different collection of thoughts in each individual person's mind, and will always have a slightly different mass each time you measure it. More importantly, even the ball is ultimately open to an infinite number of attacks as to what it "really" is or isn't, attacks that can make even its being seem subjective.
Sorry if I didn't make it clear, but what I'm interested in, if it's possible, is a succinct summary of your thoughts to replace phrases like "Russell's counter" and "resemblance" and "Quine's failure" and "uninstantiated universals." We can all go look these up, but who knows if we'll even read the same parts you're referring to, or more importantly, if we'll even perceive the arguments to be what you perceived them to be? How about just telling us what you think? I bet you can do it in less words than a term paper, and with more originality.