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Empiricism is False
MrMister
Jesus dying on the cross in pain? Morally better than us. One has to go "all in".Registered User regular
Jesus dying on the cross in pain? Morally better than us. One has to go "all in".Registered User regular
This thread inspired by some recent reading. It is about philosophy, particularly the philosophy of knowledge. Disclaimer: mistakes will almost certainly be made. Hopefully, it will be interesting anyhow.
1. Background: What Is Empiricism? What is Rationalism?
Traditional Empiricists believe that all knowledge ultimately stems from sense-experience. Their foils, Rationalists believe that Empiricism is false. They believe that there is other possible knowledge--perhaps obtained through a faculty of rational intuition, or (as they argued in the bad old days) through the grace of God.
Rationalists have often attacked Empiricists over forms of knowledge which they take to be inexplicable on the basis of sense-experience: for instance, mathematical knowledge, knowledge of right and wrong, and so on. The Rationalists have argued: if Empiricism were true, knowledge of these things would be impossible; but knowledge of these things is possible; therefore, Empiricism is false. Empiricists have countered by either trying to explain how knowledge of these subjects is, after all, possible on the basis of sense experience, or by denying that there can really be such knowledge at all. So, for instance, some traditional Empiricists have tried to explain mathematical knowledge on the basis of abstraction from concrete encounters with physical objects, thus deriving it from sense-experience, and some have rejected altogether the idea of ethical knowledge.
The prospects of a fully traditional Empiricism are, as far as I understand, fairly dire. Mathematical knowledge, particularly, is not plausibly reconstructed along Empiricist lines ('Nominalists,' who believe numbers are useful fictions that do not literally exist, despite their best efforts have not been able to give a reconstruction of mathematics in those terms capable of doing nearly what the Platonists can). But a more moderate Empiricist claim is still popular--even orthodox. This moderate Empiricism concedes that there may be knowledge which is independent of the deliverances of the senses, but restricts that knowledge to the necessary truths--things that could not have been otherwise (nothing is both a cat and not a cat; every bachelor is unmarried; 2+2 = 4; perhaps, causing needless suffering is wrong). However, they claim, knowledge of contingent truths--things which could have gone either way (I am a student; the oxygen theory of combustion is true)--is exclusively the province of the senses. So, in an important sense, we still have no a priori (i.e. independent of experience) knowledge of the particularities of the world.
Even this moderate Empiricism is false, though. There is a priori knowledge of contingent facts about the world. Or: so I will argue. The structure of the argument will be as follows. First, I will describe a particular view of the way perception provides justification for our beliefs, perceptual dogmatism, and then describe problems besetting that view. I will then argue that the features of perceptual dogmatism which generate the problems will be general to any non-skeptical Empiricist view, i.e. any Empiricist view which holds that knowledge is possible. Since knowledge is possible, we should thus reject Empiricism.
2. Perceptual Dogmatism and Bootstrapping
First, assume both that there is a separation between appearance and reality (sometimes things are not as they seem) and that it's possible to for the same appearance to correspond to multiple different arrangements of reality (the shimmering on the horizon could be either a mirage or a genuine oasis). These are, as the examples suggest, relatively uncontroversial.
These assumptions are natural, but they raise a worrying question. If appearance and reality are distinct, and a set of appearances do not necessitate any particular arrangement of reality, then what justifies us in drawing conclusions about reality on the basis of mere appearance? One answer is: we just are. Consider the following view:
Perceptual Dogmatism: if I have an experience with content P (say, that the book is on the table), then I am automatically defeasibly justified in believing P. That is to say: I am justified in believing P up until I come into some other evidence to the contrary (you tell me it was actually a brick cleverly painted to look like a book). I don't need a prior guarantee that my experience is veridical: I'm justified in believing it 'for free.'
This view is in many ways attractive. It seems to match our ordinary reasoning about our experience. And it acknowledges experience's fallibility, while avoiding full-on skepticism. However, recent authors have noticed a serious problem with it. Namely, it permits an intuitively abhorrent form of reasoning known as 'bootstrapping' (after 'pulling yourself up by your bootstraps,' which it illicitly allows you to do).
Suppose that I am being administered a color-vision test. I am presented a number of cards in order, and I tell the examiner the color I perceive each to be. So: I see what appears to be a red card, I say "that's a red card," I see what appears to be a green card, I say "that's a green card," and so on. Now it appears that the Perceptual Dogmatist has no way to block the following line of reasoning: I say to myself: well, the first card looked red. And it was red! (remember, perceptual dogmatism allows me to conclude 'is P' from 'looks P,' at least until I obtain evidence to the contrary). And the second card looks green. And it was green! And I can do the same for all the cards in the test. But this entails that I got the right answer every time; so, by simple logic, I can conclude that I got the right answer every time. And from that I can conclude by inference to the best explanation that I must have exceptionally reliable color vision.
Notice that I can do all of this reasoning before the examiner reveals the actual results to me. But this is absurd! I cannot, in advance of getting the results, know that my color vision is reliable in this way. I cannot go from having no opinion about the reliability of my color vision to knowing its accuracy merely by repeating to myself the colors a bunch of cards appear. But yet, the only inferences I used were: "seems X" to "is X;" inference to the best explanation; and basic deductive logic (and, on more complicated presentations, inference to the best explanation becomes dispensable--the problem is the combination of perceptual dogmatism and basic logic). Bad news for perceptual dogmatism.
Some authors have actually been willing to defend this sort of 'bootstrappy' reasoning (they see it as the only alternative to skepticism). They claim it is surprising, but nonetheless a reasonable way to gain confidence in your color vision. But this position is not defensible. For assume that bootstrapping arguments are reasonable: suppose I really can gain justified confidence in the reliability of my color vision that way. This yields an immediate problem when we notice that the above test was 'no-lose'--no matter what cards were shown, and what their real and apparent colors, at the end I was going to be able to justifiably claim the reliability of my color vision. But if there is ever a test where every result would justify a certain conclusion, then it is a test which you do not actually need to run. You can simply believe the conclusion right out. After all, you know that at the end of the test you will be justified in believing it, so why not start now? (Compare: I tell you that once I show you my bike, you will be justified in thinking it's blue; what color should you think it is now?). So, if the bootstrapping reasoning is reasonable, then I can, just by deploying the above reasoning, gain confidence in the reliability of my color vision without even having to run the tests at all.
In summary: Perceptual Dogmatism leads to bootstrapping. But if bootstrapping is permissible, then one need not actually go through the motions: one can, simply by thinking about it, come to the conclusion that one's color vision is reliable. But notice that the reliability of my color vision is most certainly a contingent fact about the world! I certainly could have had unreliable color vision. Hence, if bootstrapping is permissible, then it is possible for me to have a priori ('just by thinking about it') knowledge of a contingent fact (namely that my color vision is reliable).
In other words, if Perceptual Dogmatism is true, bootstrapping is possible; and if bootstrapping is possible, then Empiricism is false.
3. Conclusion: Empiricism is False
One might wonder: okay, Perceptual Dogmatism is committed both to bad reasoning, and ultimately, to the falsity of Empiricism. Why not think that this is just so much the worse for Perceptual Dogmatism? In other words, why can we not, as Empiricists, simply reject Perceptual Dogmatism and come up with some other theory of perception?
The reason is as follows: the only feature of Perceptual Dogmatism we needed to get the bootstrapping going, and subsequently to get the a priori knowledge of contingent facts, was just the fact that it licenses inferences from sense experience to worldly states of affairs that are not strictly entailed by the occurrence of that experience. But any non-skeptical Empiricist is going to have to license some inferences from sense experience that go beyond strict logical entailment, for the simple reason that the existence of our sense-experiences logically entails not much at all--certainly nothing like the range of facts we take ourselves to know about ourselves, the world, and the ordinary objects that populate it (it is not logically entailed by anyone's sense experiences, for instance, that trees exist; there could simply be a lot of clever tree-illusions). So any non-skeptical Empiricism will have the structural feature which leads to bootstrapping, and since bootstrapping leads to a priori knowledge of contingent facts (which contradicts Empiricism), it follows that any non-skeptical Empiricism entails its own falsity. Hence, there is no viable non-skeptical Empiricism. And if there is no viable non-skeptical Empiricism, then there is no viable Empiricism.
So, Empiricism is false.
1. Background: What Is Empiricism? What is Rationalism?
Traditional Empiricists believe that all knowledge ultimately stems from sense-experience. Their foils, Rationalists believe that Empiricism is false. They believe that there is other possible knowledge--perhaps obtained through a faculty of rational intuition, or (as they argued in the bad old days) through the grace of God.
Rationalists have often attacked Empiricists over forms of knowledge which they take to be inexplicable on the basis of sense-experience: for instance, mathematical knowledge, knowledge of right and wrong, and so on. The Rationalists have argued: if Empiricism were true, knowledge of these things would be impossible; but knowledge of these things is possible; therefore, Empiricism is false. Empiricists have countered by either trying to explain how knowledge of these subjects is, after all, possible on the basis of sense experience, or by denying that there can really be such knowledge at all. So, for instance, some traditional Empiricists have tried to explain mathematical knowledge on the basis of abstraction from concrete encounters with physical objects, thus deriving it from sense-experience, and some have rejected altogether the idea of ethical knowledge.
The prospects of a fully traditional Empiricism are, as far as I understand, fairly dire. Mathematical knowledge, particularly, is not plausibly reconstructed along Empiricist lines ('Nominalists,' who believe numbers are useful fictions that do not literally exist, despite their best efforts have not been able to give a reconstruction of mathematics in those terms capable of doing nearly what the Platonists can). But a more moderate Empiricist claim is still popular--even orthodox. This moderate Empiricism concedes that there may be knowledge which is independent of the deliverances of the senses, but restricts that knowledge to the necessary truths--things that could not have been otherwise (nothing is both a cat and not a cat; every bachelor is unmarried; 2+2 = 4; perhaps, causing needless suffering is wrong). However, they claim, knowledge of contingent truths--things which could have gone either way (I am a student; the oxygen theory of combustion is true)--is exclusively the province of the senses. So, in an important sense, we still have no a priori (i.e. independent of experience) knowledge of the particularities of the world.
Even this moderate Empiricism is false, though. There is a priori knowledge of contingent facts about the world. Or: so I will argue. The structure of the argument will be as follows. First, I will describe a particular view of the way perception provides justification for our beliefs, perceptual dogmatism, and then describe problems besetting that view. I will then argue that the features of perceptual dogmatism which generate the problems will be general to any non-skeptical Empiricist view, i.e. any Empiricist view which holds that knowledge is possible. Since knowledge is possible, we should thus reject Empiricism.
2. Perceptual Dogmatism and Bootstrapping
First, assume both that there is a separation between appearance and reality (sometimes things are not as they seem) and that it's possible to for the same appearance to correspond to multiple different arrangements of reality (the shimmering on the horizon could be either a mirage or a genuine oasis). These are, as the examples suggest, relatively uncontroversial.
These assumptions are natural, but they raise a worrying question. If appearance and reality are distinct, and a set of appearances do not necessitate any particular arrangement of reality, then what justifies us in drawing conclusions about reality on the basis of mere appearance? One answer is: we just are. Consider the following view:
Perceptual Dogmatism: if I have an experience with content P (say, that the book is on the table), then I am automatically defeasibly justified in believing P. That is to say: I am justified in believing P up until I come into some other evidence to the contrary (you tell me it was actually a brick cleverly painted to look like a book). I don't need a prior guarantee that my experience is veridical: I'm justified in believing it 'for free.'
This view is in many ways attractive. It seems to match our ordinary reasoning about our experience. And it acknowledges experience's fallibility, while avoiding full-on skepticism. However, recent authors have noticed a serious problem with it. Namely, it permits an intuitively abhorrent form of reasoning known as 'bootstrapping' (after 'pulling yourself up by your bootstraps,' which it illicitly allows you to do).
Suppose that I am being administered a color-vision test. I am presented a number of cards in order, and I tell the examiner the color I perceive each to be. So: I see what appears to be a red card, I say "that's a red card," I see what appears to be a green card, I say "that's a green card," and so on. Now it appears that the Perceptual Dogmatist has no way to block the following line of reasoning: I say to myself: well, the first card looked red. And it was red! (remember, perceptual dogmatism allows me to conclude 'is P' from 'looks P,' at least until I obtain evidence to the contrary). And the second card looks green. And it was green! And I can do the same for all the cards in the test. But this entails that I got the right answer every time; so, by simple logic, I can conclude that I got the right answer every time. And from that I can conclude by inference to the best explanation that I must have exceptionally reliable color vision.
Notice that I can do all of this reasoning before the examiner reveals the actual results to me. But this is absurd! I cannot, in advance of getting the results, know that my color vision is reliable in this way. I cannot go from having no opinion about the reliability of my color vision to knowing its accuracy merely by repeating to myself the colors a bunch of cards appear. But yet, the only inferences I used were: "seems X" to "is X;" inference to the best explanation; and basic deductive logic (and, on more complicated presentations, inference to the best explanation becomes dispensable--the problem is the combination of perceptual dogmatism and basic logic). Bad news for perceptual dogmatism.
Some authors have actually been willing to defend this sort of 'bootstrappy' reasoning (they see it as the only alternative to skepticism). They claim it is surprising, but nonetheless a reasonable way to gain confidence in your color vision. But this position is not defensible. For assume that bootstrapping arguments are reasonable: suppose I really can gain justified confidence in the reliability of my color vision that way. This yields an immediate problem when we notice that the above test was 'no-lose'--no matter what cards were shown, and what their real and apparent colors, at the end I was going to be able to justifiably claim the reliability of my color vision. But if there is ever a test where every result would justify a certain conclusion, then it is a test which you do not actually need to run. You can simply believe the conclusion right out. After all, you know that at the end of the test you will be justified in believing it, so why not start now? (Compare: I tell you that once I show you my bike, you will be justified in thinking it's blue; what color should you think it is now?). So, if the bootstrapping reasoning is reasonable, then I can, just by deploying the above reasoning, gain confidence in the reliability of my color vision without even having to run the tests at all.
In summary: Perceptual Dogmatism leads to bootstrapping. But if bootstrapping is permissible, then one need not actually go through the motions: one can, simply by thinking about it, come to the conclusion that one's color vision is reliable. But notice that the reliability of my color vision is most certainly a contingent fact about the world! I certainly could have had unreliable color vision. Hence, if bootstrapping is permissible, then it is possible for me to have a priori ('just by thinking about it') knowledge of a contingent fact (namely that my color vision is reliable).
In other words, if Perceptual Dogmatism is true, bootstrapping is possible; and if bootstrapping is possible, then Empiricism is false.
3. Conclusion: Empiricism is False
One might wonder: okay, Perceptual Dogmatism is committed both to bad reasoning, and ultimately, to the falsity of Empiricism. Why not think that this is just so much the worse for Perceptual Dogmatism? In other words, why can we not, as Empiricists, simply reject Perceptual Dogmatism and come up with some other theory of perception?
The reason is as follows: the only feature of Perceptual Dogmatism we needed to get the bootstrapping going, and subsequently to get the a priori knowledge of contingent facts, was just the fact that it licenses inferences from sense experience to worldly states of affairs that are not strictly entailed by the occurrence of that experience. But any non-skeptical Empiricist is going to have to license some inferences from sense experience that go beyond strict logical entailment, for the simple reason that the existence of our sense-experiences logically entails not much at all--certainly nothing like the range of facts we take ourselves to know about ourselves, the world, and the ordinary objects that populate it (it is not logically entailed by anyone's sense experiences, for instance, that trees exist; there could simply be a lot of clever tree-illusions). So any non-skeptical Empiricism will have the structural feature which leads to bootstrapping, and since bootstrapping leads to a priori knowledge of contingent facts (which contradicts Empiricism), it follows that any non-skeptical Empiricism entails its own falsity. Hence, there is no viable non-skeptical Empiricism. And if there is no viable non-skeptical Empiricism, then there is no viable Empiricism.
So, Empiricism is false.
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But my first reaction is that some form of empiricism seems to work pretty well. And I wonder if a philosophical rejection of Empiricism shouldn't take that into account. Or is this 'empiricism' different from trusting my senses so I don't get eaten by sabretooth tigers?
Doesn't this just lead to solipsism? And if so, what do you think of the private language argument, which was my rescue from teenage solipsism?
It's worth noting that the Rationalist view which I accept (unlike, say, the Rationalist view _J_ accepts) does not reject the natural sciences and their deliverances. Nor does it deny that our senses are reliable or that they play a primary role in our knowledge of the world. So I still agree that sorts of investigations that you allude to certainly work, and we ought to keep them up.
What my view rejects is that we can explain the totality of what we know merely in terms of the deliverances of the senses. There are things we know which cannot be explained on that basis--for instance, quite a few things having to do with how we ought to interpret or understand what our senses are telling us. We cannot learn those very facts on the basis of our senses, on pain of all sorts of bad stuff. The case above is a case like that. I think we do in fact know that our senses are reliable, but that we do not know that on the basis of our senses. We know it a priori by something like the faculty of rational intuition.
Why does that matter? Well, once we admit that there is such thing as rational intuition, and that it generates crucial knowledge in this case, it becomes ad hoc to object to its use elsewhere. So, for instance, my story of how we know that certain ethical principles are true will involve rational intuition.
I think that the problem for the empiricist here is very much that if one restricts oneself to sense-data and logical consequences thereof, it is very difficult to avoid solipsism. The private language argument I have less to say about. I reject it, but am not a Wittgenstein expert so can't give a great treatment of it offhand (it is famously difficult to do justice to).
I'd say a lot of that 'rational intuition' is really evolved structures in the brain, but I have no idea how to mix science and philosophy, and whether it should ever be allowed, like fish with red wine (which can be great, actually).
I agree with the private language argument myself, though I think my idea of it is based more on modern linguistics and semiotics than Wittgenstein, coz, y'know, I have no idea what the fuck he's talking about half the time, but by golly isn't it impressive.
Figured that was what you were thinking about. You.
Both are flawed, and neither is sufficient on their own to treat as dogma.
A practical approach dictates using a mix of the two to under stand the universe, and even that is probably insufficient since there is no way to verify that the universe is completely observable, nor much convincing reason to believe that it is completely rational or consistent.
try this
This, I believe completely misses the point. I think, when mrmr speaks of knowledge he is talking about where ideas and beliefs come from, without any particular regard for their truth. This is sort of intertwined with his bootstraping example.
Honestly, I am not sure about this. His argument seems to beg not only the question of the existence of knowledge, but its definition as well. I am not in any meaningful way versed in philosophy and thus am probably not using the same, probably highly codified, definition of the term.
Edit: knowledge as something someone believes that is true and warranted? Meh.
Metzinger may be a good place to start if you're interested in philosophy of mind/neuroscience. He authored a decent book intended for the layperson titled 'The Ego Tunnel', dealing with phenomenological self models.
What is the history of mathematics? I have a sneaking suspicion that the first mathematicians did not awake one day and, poof, the concept magically manifest itself.
Far more likely that math was initially tied to physical units of some sort (crops, perhaps? It seems like math becomes particularly useful once you've set-up community agriculture), then abstracted from there & spread via verbal and / or written memes that eventually evolved to what we know today.
I hang out on a forum of rationalists who spend most of their time philosophizing. The OP uses a definition of rationalism and empiricism that I have never heard of before. I also don't see an inherent contradiction between rationalism and empiricism and have always heard of them being closely linked.
^ This ^
That may be one of the most aggressive instances of pretending science doesn't exist that I've ever read.
And this is definitely the most aggressive instance of pretending philosophy has never existed that I've ever read.
And pure Rationalism shutupshutupshutupdontarguewithmemrillusion doesn't work either.
Sense data mixed with some a-thinkin' works just fine.
Which is sort of a conventional view outside philosophy, but I'm guessing given his job, within philosophy that's not?
Is 2+2=4 true?
Heh, I stupidly didn't register that obviously skeptical Empiricism would merely state that we can't have any knowledge about the world. i.e. empiricism would be the only viable path to knowledge, but it is impossible. We can't use it so we can't really have any knowledge.
I don't think MrMr is advocating just that Empiricism is true for just some fields of knowledge though.
Hmm? I'm talking about how it doesn't even deign to mention the idea of structurally instinctive reasoning, while devoting time to Plato. We do have brains, and we do use them to think.
It's true that I assume the possibility of knowledge. But that is a reasonable assumption (Try assuming the contrary: that knowledge is impossible. Do you know that? These and other questions do have consistent answers, I think--they do not show the view inconsistent--but the ultimate picture that results is extremely unattractive).
How so?
Yes, but you'll note that this type of mathematical function / model is just a human construct. '2' is not an actual thing - it's just an abstraction we can use for the purpose of building models & quantifying what we see.
You can imagine the scenario in such a way that this isn't so--an eccentric billionaire sponsors color-vision tests for everyone! Indeed, the very narrative idea of the independently administered test can be dispensed with. You can simply show yourself a bunch of colored cards, and still get the bootstrapping reasoning going. So, the fact that we typically only administer color tests to people whose vision we have reason to doubt does not undermine the argument.
Alternatively: what you might be thinking is something like 'as soon as you start thinking of what you're doing as being a test you entertain the possibility of systematic error; as soon as you entertain the possibility of systematic error, it undermines your previous default justification.' Some people say that knowledge and justification can be contextual in this way--they are the contextualists. I find this ultimately unsatisfying: it does a relatively good job of tracking how we assert and deny claims to knowledge in different conversational contexts, but does not, I think, do much to help us understand the fundamental rationality of what we are doing when we do so.
(This is, incidentally, an area where there is substantial crossover between philosophy of knowledge and philosophy of language: a great deal of effort has gone into understanding the general semantics of context-sensitive terms like 'flat' and 'tall'--terms which naturally raise the question 'relative to what?'--in the hopes that, among other things, it could be fruitfully applied to 'is justified' and 'knows').
If and only if you accept the unproven postulates that underly the space of numbers you are using.
not enough information to answer the question. Are those in the space of Rational Numbers, Real Numbers, Complex Numbers? There's an uncountable infinity of different spaces of numbers.
But once you nail down what kind of numbers you are talking about it will always come down to: It is true if and only if you accept the unproven postulates on which it relies.
1) Subjective consciousness - how individuals process information like colors, sounds, etc, and how similar or different this process is from person to person - is not yet a well understood science. I'd say this example is flawed on that basis, in that it uses a topic that there is still a lot of ignorance of as a springboard.
2) Just because you think you got the answer does not mean you actually, empirically, got the right answer. I don't see what point you're trying to make here? If I bite into a sandwich and remark that it tastes like it has mustard on it, and then it's revealed that it has no mustard on it, that's not some terrible paradox: it just means I was wrong. Human beings do tend to get things wrong.
Ronya is correct. I was unaware that the term had been taken up in common use elsewhere, or I would have clarified that my intent was to draw the traditional philosophical distinction.
I do find it unfortunate that the term has been taken up in this way, though, as it is totally inconsistent with the entrenched philosophical use (Rationalwiki says: "From the strict philosophical standpoint, rationalism is the view blah blah blah... [but] The term is more commonly used blah blah blah..." Well, let me say that philosophers never use the term to mean the 'more common' thing.)
Actually, that article does mention, albeit in passing, that "The second thesis associated with rationalism is the Innate Knowledge thesis... According to some rationalists, we gained the knowledge in an earlier existence. According to others, God provided us with it at creation. Still others say it is part of our nature through natural selection." The last option sounds like what you're talking about. (I have heard some allege that Chomsky definitively proved Rationalism by way of definitively proving an innate capacity for language mastery; what to make of this I am less than sure).
It is also a little unfair to attack the article for discussing Plato, when it explicitly states: "Contemporary supporters of Plato's position are scarce," before going on to list a number of damning objections to his view.
What is "balls to the walls empiricism"?
The traditional argument for mathematical Platonism is: the sentences of mathematics are literally true. The sentences of mathematics ascribe properties to and quantify over the numbers ('3' is prime; no number is the largest prime). Sentences of that form cannot be literally true unless they refer to and quantify over actual entities. Hence, numbers are actual entities.
Since numbers are, additionally, typically taken to be non-spatial, non-causal, abstract, constitutively independent of our thought about them, and so on, it is then a problem to explain how we could actually know those sentences about them. It is particularly a problem for hardcore empiricists, who have the special challenge of explaining how sense-data could be the foundation for knowledge of abstracta with these properties.
Some (nominalists, fictionalists) have tried to give interpretations of mathematics where it is not committed to quantifying over and referring to genuine entities. As far as I understand, they have succeeded at best partially. Particularly, they have not succeeded in giving a mathematics that is both 1) uncommitted to abstract entities and 2) fully adequate to the purposes to which mathematics is employed in and presupposed by our best physical sciences. Hartry Field's Science Without Numbers was as early systematic attempt, but from what I understand both it and what has come after it has ultimately failed.
This is, however, not my area of expertise (which is why I did not make the Rationalist critique from knowledge of mathematics my main line of argument).
...Platonism? Like, you're defending the ideas of the Greek philosopher who was 100% incorrect about the solar system, who decried experimentation as heretical because otherwise he'd be proven to be hack, who posited the idea of the 'perfect solids' and conspired to censor geometric knowledge from the public as he felt that some shapes were evil, etc?
You don't have a more up to date source than Plato?
EDIT:
It's not a 'problem' at all. Humans invented the abstractions in order to deal with physical problems (for example, tabulating crop yields). We know (or can reasonably assert) that they're abstractions & human inventions because they're strictly tied to human culture & history.
It seems reasonable to disbelieve the existence of secretive eccentric billionaires, so to speak.
There is an assumption common to scientific reasoning which goes as follows: we assume that the universe is structured in a way that is reasonable to study. Here is one example, but there are plenty of areas of science which are subject to 'tractability', 'simplicity', etc. concerns. There we generally accept what you seem to describe as abhorrent bootstrapping.
By analogy, the 'discovery' that I have exceptionally reliable color vision is simply a reflection of the a priori belief in the constancy of color over time plus experiential knowledge.
It is an audience that seems most suitable for a study of philosophy at a rigorous level, but it is also a demographic unusually hostile to philosophy as she is practiced. I blame bad pedagogy.
Empiricists pretty much all accept (and have always accepted) that there is some role for a-thinkin' which is, at least in some sense, independent. For instance, they never deny that deductive logic is valid. And most Rationalists have (as far as I know) never held that sense experience is not an important source of knowledge--for example, arch-Rationalist Descartes thought that our senses were trustworthy and important ways to know about the world; he just thought this on the basis of an a priori proof that there exists a benevolent God who would not allow us to be systematically deceived.
So: what's the big kerfuffle, then? There are two main motivations for Empiricism (as I see it): first, it gives you a nifty hammer you can use against the bad guys. Leibniz says that he apprehends by the light of pure reason that everything must have an explanation, and from that infers that space must be relative rather than absolute? You can say: shut up, Leibniz, there's no light of pure reason. Leibniz says that he apprehends by the light of pure reason that God exists, and hence, that we live in the best of all possible worlds? You can say: shut up, Leibniz, etc. etc. This is nice. It's an all-purpose argument against people being annoying. Second, it can, in fact, be genuinely puzzling how we could have substantial a priori knowledge. The 'faculty of rational intuition' is famously mysterious. It is easy to want to consign all of that to the flames.
But, it turns out, the Empiricist hammer is a little too strong. Empiricists have recognized its strength, and have indeed been willing to give some things up in order to keep it (knowledge of ethics, knowledge of mathematical abstracta, even knowledge of mind-independent physical objects). But, I think, the result of arguments like those I gave in the OP is that, to really keep the hammer, you'd have to give everything up. Since this is untenable, so is Empiricism. It turns out, we have to believe in some of those spooky, rationally-aprehended substantial a priori facts, at least if we are to believe anything at all. So we had better come up with a theory that can accomodate that. And, unfortunately, it means we have to argue against the stupid things Leibniz says on a more case-by-case basis; we cannot simply shut him up at the outset by way of applying of our nifty Empiricist hammer.
No doubt that Plato felt his numbers were special, being assigned special symbols by the Greek authority, and who better to decide what numbers really meant than the Greeks, right, given that all other cultures were just savages anyway (according to Platonic philosophy)?
This is silly. Platonism is just the name of the view that numbers are both abstracta and in a strong sense real. It has been defended by: not only Plato, but also Frege (1884, 1893–1903, 1919), Gödel (1964), and in some of their writings, Russell (1912) and Quine (1948, 1951), not to mention numerous more recent philosophers of mathematics, e.g., Putnam (1971), Parsons (1971), Steiner (1975), Resnik (1997), Shapiro (1997), Hale (1987), Wright (1983), Katz (1998), Zalta (1988), and Colyvan (2001). It is also typically described as the dominant view among practicing mathematicians, although I recall reading some questioning that as of late.
No one questions that math is related to objects in the real world. One of the Platonist arguments, in fact, is that the fact that math works (and is indispensable to our best science) demands an explanation, and that the only available explanation is its literal truth.
Justifying these methodological principles of science--particularly, the favoring of simpler hypotheses--is very much a problem for hard-line Empiricists. After all, Hume, the father of Empiricists, also had a devil of a time with induction. And it is very much part and parcel with the problem I gave above.
I (and the Rationalist) would say that what we do is not bootstrapping, because our justification for Simplicity and etc. is strictly a priori. Hence, we do not 'pull ourselves up' with the senses into the possession of anything that we did not, by a priori reasoning, already have.
To be precise, either via some discovered conflict or via some discovered coherent alternative that later turns out to be more 'productive' in some vaguely-defined way. It is possible to be a coherentist or non-coherentist empiricist though, and I am sensing we are conflating closely-related philosophical problems here.