Great lecture. One correction: at 7:45, you mention that Hume must have missed something regarding intuitive certainty, if he wants to say that all knowledge resolves into probability. Yet, Hume is well aware of this. In fact, in Part III of Book I, he says: "Three of these relations [resemblance, contrariety, and degrees of quality] are discoverable at first sight, and fall more properly under the province of intuition than demonstration" (T 1.3.1.2). A difficulty in interpreting the Treatise is the inconsistency between his commitments to intuitive knowledge (and relations of ideas, more generally) and Part IV of Book I that seems to skeptically undermine any attempt at justification, whether empirical or rational. One of the interesting things to note is that the late Hume of the Enquiries is much more conservative in his epistemology. The relations of ideas take on a definite role in the First Enquiry, while much of the radical skepticism of the Treatise is lost. And, still, the question remains as to why he changed his mind. It seems to me that his pursuit of a position at a university and the relationship between skepticism and atheism is the most likely reason. He never did obtain a teaching position. Unfortunately, I find many Hume scholars and many graduate students alike prefer his more conservative epistemological positions -- ones that don't undermine the sacred laws of logic and mathematics. Why, indeed, is his skepticism with regard to reason an understudied aspect of his corpus? Perhaps it is because the attachment to truth and certainty among philosophers is a similar type of attachment theists exhibit toward god -- like children who don't want to let go of the comfort of their parent. As Peter Unger said: "In philosophy, being a sceptic usually means walking a lonely road."
The argument against induction may even be strengthened by asking weather we even know past occurrences of some correlation have ever happened at all. All we have to do is apply a similar argument against the reliability of memory: I may be experiencing a memory now, but how to I know it actually matches up to a past occurrence/experience? Because I have memories of memories being accurate? Circular reasoning.
Sorry to be offtopic but does someone know of a method to get back into an Instagram account? I was stupid lost the password. I love any assistance you can give me.
Thanks to Uebermarginal, I found your channel, and I must say it is a pearl. I was going to get into reading Hume for several years now, and you just make it so much easier.
Thanks for this. The robot recommended this just as I got the solution to a critique of Cartesian rationalism I have been struggling with for years from a _Doctor Who_ video.
I have felt that Hume proposes that subjective confidence in an assessment may aid the desires in making better or more valuable judgements. Always thought that existentialists should pay greater regard to Hume, that the nature of skepticism in relation to the inescapability of judgement outlined here provides a very clear psychological foundation for existence.
This makes me think of Pyrrhonism, in which epistemic certainty is considered impossible due to things like the problem of the criterion or the Münchhausen trilemma, and epoché (suspension of judgement) is thought to be the appropriate frame of mind to achieve ataraxia, thereby supposedly leading to eudomonia. A criteria of action including sensation, compulsion of pathé (natural drives), and deference to social custom is then used to make decisions holding to appearances and perceptions without beliefs.
I believe that Intuition is the judgement of certainty of an outcome under a particular " set of conditions". The degree of fallacy of intuition is directly proportional to the degree of deviation from such set of conditions. For example - I failed in something multiple times in a particular period of time. Now after a gap of two years, my intuition says that I will fail again. But there is certain fallacy in such an intuition because after two years " set of conditions" have changed. Maybe my approach has changed, my skill levels have improved , my personality has changed slightly. So, the prevailing conditions are very different. Therefore, fallacy in intuition exists.
For a moment there I wondered if Hume came before or after Descarte in the philosophical discourse, which may be some evidence to Hume's point, as we all know Descartes was prior. But really, his approach here is interestingly misguided. The objections given are all relevant: meta-evaluations can reinforce or even increase the probability of one's epistemic performance; there is a significant distinction between the probability of the event and the probability of my epistemic efficacy (and my resultant confidence therein); and there is the problem the the self-defeating nature of the argument. But the third objection rests on the "skeptical regress" only in the way that it must come to some arbitrary end, the only motivation for which is custom informed by passion. Though that seems coherent, it rests on the assumption that this particular form of skeptical regress is the inevitable result of reason left to it's own devices, which is really what Hume supposes to demonstrate. I would take the third objection down another path. If my faculties for discerning the truth of something, even of matters such as 1+1 = 2, are probabilistic at best, then are not my evaluations of this very notion also probabilistic? How can I be confident in the probability either way? Can I not say with 100% certainty that I did not go to the store yesterday? Can I not know with absolutely certainty, for example, that I am uncertain, regardless of the degree of uncertainty? If not, then those counterclaims against my certainty also suffer from the same curse of dubiousness. If, in other words, reason would "entirely subvert itself", then I have, by acceptance of this principle, an instance of its self-subversion in the very principle of my skeptical thought process. Why shouldn't this attenuate itself into epistemic irrelevance just as quickly as it asserted itself? It is also a glaring problem to suggest that there are no non-arbirary stopping points in a process of reason which represent sufficient assurity to an epistemic chain of meta-evaluations. Besides this, the prior criticism applies here also. By what assurity does Hume assert that there is no non-arbitrary stopping points to a valid process of reason which has absolute certainty? Why does his principle of a self-subverting reason not apply here also?
It seems the mathematical examples are not all of a kind. One might easily say that my knowing that 1+1=2 (considering just the fact for present purposes - not the proposition) is different from my knowing 12+22=34, because there are no "steps" of calculation carried out in applying the +1 function, or at least not in adding one to itself. Also, the objection about inability to keep applying the "how good am I at evaluating the previous level type of judgment" function is very much to the point. First, it seems that with 1+1=2 there is no doubt at all, because no process in which error may enter. That is, I have never actually doubted (never been able to doubt?) 1+1=2, unlike the case with 12+22, or something involving more difficult calculation, which I may have applied and then remembered for awhile, but then forgot, as it were, so that a new calculation needed to eventually be applied. But even if the question is 12+22, and I recognize that I had forgotten it for awhile, it seems that to go to the next evaluation level and ask, "How good have I been at correctly calculating this kind of problem?" I am at a loss as to just what "this kind of problem" is, and if I try to ascend to another level of evaluation, it seems the subject matter of the attempted question has quite disappeared. So with 1+1=2, the first evaluation results in no diminution of the probability from a perfect 1. And with larger number calculations the question posed at each higher level of evaluation looks like it may be just the very same question as was posed in the previous level evaluation, which in fact may seem actually to be a nullity, a mere attempt at asking an evaluative question without quite knowing how to go about it.
"But even if the question is 12+22, and I recognize that I had forgotten it for awhile, it seems that to go to the next evaluation level and ask, "How good have I been at correctly calculating this kind of problem?" I am at a loss as to just what "this kind of problem" is" I'm confused about what the objection is here. "This kind of problem" would be something like "addition involving small numbers." Further, it seems to me that it's perfectly sensible to ask, "how reliable have I been at performing additions involving small numbers?", and that the answer to this question will bear on my degree of confidence in an addition I've just performed. In fact, this happened to me when I was writing the script to the video. I initially wrote down "22+12=34", almost automatically - it took me less than a second to work it out. But then I remembered that automatic judgements such as this are sometimes wrong, and I checked the equation again. My degree of confidence in my initial judgement declined, partly because I recalled similar judgements being mistaken in the past. Of course, there is a serious problem about taxonomizing "kinds of problems". Is "22+12=34" the same kind of problem as "101+51=152"? When I remembered certain judgements in the past being mistaken, am I comparing the current problem to relevantly similar problems? Etc. There isn't really an objective answer to questions such as these. But it doesn't this point support Hume's argument? It leaves us unsure of how to work out the probability of error, and so increasingly unsure of what our degree of confidence in the initial judgement should be.
"It seems that with 1+1=2 there is no doubt at all, because no process in which error may enter." If there is no process, then doesn't that give us reason for doubt? One can construct a deductive proof for 1+1=2 by using something like the axioms of Peano arithmetic, but that would be a process. If we haven't gone through that process, then what is our justification for believing that 1+1=2? Is it just what we've always been taught since elementary school? Surely we're not automatically justified in believing a thing just because the people around us claim that it is true. If people believe everything they're told, then people will believe anything.
I think the psychology paper on working memory is called something like "Remembering 7 items plus or minus two" - Edit: found it -> www2.psych.utoronto.ca/users/peterson/psy430s2001/Miller%20GA%20Magical%20Seven%20Psych%20Review%201955.pdf
This is why it's important to divide skepticism by topics and consider each topic individually. In the case of 1 + 1 = 2, we have at least two interesting questions. For one, is it possible to know that 1 + 1 = 2? The answer seems to be yes, that is easily possible just by logically proving that 1 + 1 = 2 based on the definitions of arithmetic operations. Such a proof seems to be possible, and if we have such a proof then it would guarantee the truth of 1 + 1 = 2 as well as justifying our belief. We run into a different issue when we ask whether we could be wrong about 1 + 1 = 2. In other words, can we know that we know 1 + 1 = 2? This is no longer a question about arithmetic, and now it's a question about ourselves and our capabilities at logical reasoning. We believe that we have a sound proof of 1 + 1 = 2, but how do we justify that belief in the face of the fact that we sometimes make errors in reasoning? It would be arrogant to suppose that just because 1 + 1 = 2 seems extremely obvious, therefore we are infallible in this judgement. We should admit that our best justification for believing that we know 1 + 1 = 2 is our personal evaluation of the reasoning, and that is really no justification at all. There are plenty of people in this world who believe very silly things with total confidence. In short, there's no cause for skepticism about mathematical facts which can be deductively proven, but there is cause for skepticism about our own personal judgements about which propositions are deductively proven mathematical facts. In general we can know mathematical facts, and it seems likely that we know 1 + 1 = 2, but we don't know that we know 1 + 1 = 2.
Haha, this only follows if math can be disentangled from the psychologies in which the math is performed. Even math done by a computer is ultimately interpreted by a human mind at some point and is itself a computer designed by a human mind, even if it operates in the background, the appropriate functionality is ultimately judged by a human, they simply cannot be disconnected... Math has always and will always be experienced within the imaginations of those utilizing it.. the idea that mathematical axioms don't bump into the human psychologies that arrange them is nonsense.. also if the psychologies that design mathematical axioms are faulty than the reliability of math and the idea of relating it to some greater truth or reality is suspect.
The fact that the incertantity build up as we go through the verticals verification doesn't imply that the margin of error will necessarely get ridicoulously big, mathematically speaking. Suppose a physicist made a calculation and found x as result, with margin a. If for every n, at the n-th level of verification the margin increase by a/2^n,then the final margin will only 2a at the end because 1+1/2+1/4+1/8... = 2.
Was always sensitive to the distinction Hume makes between what we can call relations of ideas as opposed to matters of facts. We construct the idea of a rectangle based on relations of ideas that constitute this object. That is different from our assessment of other ideas that we have in terms of our investigations related to objects. As a result the object generated from relations of ideas is the definition of the object, and must be present for that object to exist, however induction will be inseparable from the possibility of error, since we are not proceeding from a definition of an object, but an assessment of a combination of objects. In addition the idea of regularity of matters of fact such as natural law assume that we can understand or even anticipate all potential variations within these matters.
I knew little of hume's skepticism before encountering this-and I was in doubt about everything itself, including the very system I use to doubt things-logic, his argument seems to be using a different basis however, and not trying to do the same thing
I have not watched the full video, but just my initial thoughts on the very first argument of the addition chain, to me seems meaningless, because wouldn't we say that the point of reason here is to make a certain claim of relation, that claim in abstract is seperate from the notation on the paper, the certainty of the veracity of the claim is independent of whether you made a mistake reading it caues the mistake in reading, say the number of ones that is being added simply leads to a different abstracted claim that you are considering
Regarding the difficulty or impossibility of higher level evaluations of judgment ability, it seems there is a type/token difference, in which the first level meta-judgment is a judgment about a judgment type, but after that it is, or quickly becomes, judgment about nothing but individual token judgments, which, if true, seems to spoil Hume's claim.
@Giannis Polychronopoulos It was truly shocking to learn that a Scottish man born over 300 years ago was racist. What will they tell us next, that he was prejudiced against homosexuals?!
@Giannis Polychronopoulos That's not shocking to me - I knew that's what you were doing. I just found it a little silly. Yeah, Hume was racist. He was also affable. Those features are compatible, especially given the time he was around.
@Giannis Polychronopoulos It may be that most people find racism disgusting (actually I'm skeptical about that, but hopefully it's true), but I doubt it would significantly change their judgements concerning the personality traits of a politically conservative Scotsman from 300 years ago. Most people are capable of evaluating past figures within the context of their time. I agree that this conversation is boring. You're the one who brought up this topic though. As for the mind-(in)dependence affability, it depends on how we're using the term. We can specify facts about people's behaviour, and about how others react to that behaviour, including social conventions for what counts as affability, etc.
@Giannis Polychronopoulos Yeah, it's "too boring" to explain what's wrong with my totally uncontroversial statement, in the context of a topic that you chose to raise. Lol.
@@parkermoss9518 I do not understand why that implies it diverges. I will give a counterexample. Since infinite products are less familiar to me, I will take the logarithm of both sides and since each multiplicand is less than 1, its logarithm will be negative. So then the question is if the sum of strictly negative numbers necessarily has to diverge (to negative infinity), or multiplying by a minus 1 on each side, that an infinite sum of strictly positive (non-zero and non-negative) numbers necessarily diverges to infinity. Geometric sums with a term-to-term ratio is between 0 and 1 (exclusive) are examples of this. For example, take 1 + 1/2 + 1/4 + ... = 2. If we take f(x) = 10^(-x) on both sides, we get 10^-1 * 10^(-1/2)^(10^-1/4) ... = 10^-2 = 0.01. Thus an infinite smaller-than-one product has converged to a non zero number. The fact that this number is quite small, 1%, is of no consequence since we can simply take both sides to some small power, say 0.0001. Thus we have 10^-0.0001 * 10^-0.00005 ... = 10^-0.0002, which is (checking with a calculator) 0.999539589003, i.e more than 99.9%. Sorry if I have misunderstood something.
@@parkermoss9518 However if, as the video talks about, each subsequent probability decreases, then this corresponds to an infinite sum of strictly positive numbers where the next is always greater than (or equal to) the other. This necessarily diverges. The proof of this being that we could take a series with the first term repeating, and lim a*n will diverge, and since it is termwise smaller it is smaller on the whole, and if a smaller series diverges then the larger does as well. Sorry for commenting without finishing the video.
the way you presented the argument initially (we can't ever know anything for certain, based on pure reason) made it sound like Hume was just objectively wrong - "i think, therefore i am." - there you go. pure reason arriving at absolute objective truth that we can be 100% certain of. case closed. but then, as you describe his argument further, it becomes clear that he agrees that the way you initially presented his argument is wrong by granting that it isn't logic he's skeptical of, but human application of infallible logical systems (empirical measurements, for instance) so he's asserting the objective truth of conclusions arrived at by pure reason, in that admission ( the IDEA of "2+2=4 in a system with a base of 4 or more", for instance), but he's pointing out the human tendency for mistakes (the fact that i may have made an error in expressing or understanding the objectively true concept of the aforementioned "2+2" equation). this is really just a common, and uncontroversial position that you're presenting as if he said something insane and objectively wrong. he basically just said "hey we make mistakes sometimes, so we always have to be skeptical of things like science" - and that idea is the backbone of science. nothing controversial here at all.
I believe hume has to proove that the probability converges to 0. That it does not deverge. Most series of multiplication are unknown but we should assume that it converges to a value greater than zero since we can come to beliefes.
Theres an interesting solution the the regress. Imagine you assess a some claim, and if you assume you made no mistake, you are certain it is true. Now consider you could uave made a mistake by assessing the accuracy of your reasoning, which we will call metareasoning level 1. Lets say you come to the conclusion that, assuming you didnt make a mistake with this metareasoning, that your reasoning on these kinds of problems has is has a 3/4 chance of being airtight. You then asses the chance you are right made a mistake in metareasoning level 1, and come to the conlusion that, assuming you made no mistake in your metametareasoning ( metareasoning level 2) has a 15/16 chance of begin right. You assess level 3 to be 35/36, and so on where the nth level of metareasoning turns out to be 1-1/(4n^2). It turns out that the infinite product of all these, that is to say the probability that all of this infinite regress is independently and silmultaneously true, coverges to 2/Pi, about 63%. That means that when a claim seems, from plain reasoning, to be basically certain (such as in the case that you have what you believe to be a formal logical proof), you can metaevaluate the whole regress to learn that it is actually 63% likely to be true. Neat, right? Infinite regress solved without indeterminism. You just need to be convinced that your meta reasoning abilites increasingly appraise the preceding level to be more and more likely to be accurate, which, actually seems reasonable. Obvious the specific 2/pi formula isnt true for human reasoning, its just an particular example of a convergent product for illustrative purposes.
If you want to pick post-regress probability p that your certain beliefs should have, you should appraise at level n that, assuming you haven't made a mistake is your assessment, if you indeed made a mistake in level (n-2), level n-1 has a 100(1+[1-1/p])^(2^n)% likelyhood to identify that
Respecting skepticism about reason, it seems one might well believe there are 3 beliefs about which I am not pushed to skepticism: 1) I exist; 2) My mental state of the present instant is as I believe it to be (whether I am a deceived brain in a vat or otherwise); 3) Mathematical truths, given the assumption of our theory of arithmetic. So very simple (or primitive) beliefs, which involve neither the consideration of part or all of a chain of facts, nor a manifold of concurrent facts, would seem to be unassailed by skepticism regarding a vast number of beliefs requiring a (or a longer) reasoning process.
"it seems one might well believe there are 3 beliefs about which I am not pushed to skepticism: 1) I exist" Hume might have the resources for giving you a push on that first one 😉: davidhume.org/texts/t/1/4/6
When Hume uses the terms "Reason" and "The Understanding" he's being critical of the Scholastic a priori reasoning that was still being taught in the Universities. He writes of the peripatetic philosophy (Aristotle) that St. Thomas had incorporated into Christian Theology/Natural Science/Metaphysics. The empiricists (Newton, Locke, Hume, etc.) rejected Aristotle's metaphysics which made ZERO appeal to sensory based evidence - but were still very much in vogue in the seminaries and Universities. Hume was only a sceptic wrt the scholastics.
@@JulioCSilvaPhilosophy Just to clarify, I have pretty serious death anxiety (about my own death, not about the death of others). The only thing that really works for me is to just not think about it. So it's unlikely that I'll ever do a video on philosophy of death, or even study it. I've mentioned this before, which is what Trynottoblink's joke was about.
@@KaneB : People tend to fear that which they do not understand. I don't know if studying the philosophy of death could really help with anxiety, but it wouldn't be greatly surprising if it did. As an analogy, some people find that doubt gives them anxiety, but one wouldn't expect that in a skeptic. Maybe skeptics are skeptical due to their lack of anxiety over doubt, but maybe studying skepticism could be a cure for anxiety over doubt. Spend enough time with a thing and it becomes like an old friend. Or maybe it makes anxiety a hundred times worse; do not take this as medical advice.
Not as far as I'm aware. There's nowhere near as much literature on this particular argument as there is on the classics like induction, causality, selves, etc.
couldn't there be another objection, that each increase in uncertainty in a chain is so small, and all chains of reasoning are in the practice of course finite, so the extra uncertainty from chains of reasoning does not lead to never believing anything, but simply acting on beliefs probabilistically?
I think I'm with Hume here on 1+1=2. It may seem inconceivable, but the mind is plenty capable of experiencing even the most patent and direct of incoherencies as undeniably coherent, and vise-versa. This is probably easier to accept if you've witnessed it, and especially if you've experienced it yourself. One of the ways of potentially experiencing this is through the use of certain substances, like psilocybin mushrooms. It's not impossible for that sort of experience you have of just directly "seeing" the necessary truth of something like 1+1=2, to be experienced in regard to something like 1+1=1. That sense of rational coherency/incoherency isn't derived directly from the concepts in question; it's produced in your mind, in response to the coherent/incoherent content, but it doesn't necessarily need to do so accurately. One can *experience* a direct contradiction as inarguably coherent
Skeptics still believe in the standard of absolute truth. They judge everything by it when they make their arguments. You can go further and reject the notion of absolute truth. I even suspect that absolute truth is a religious artefact in culture. It's supposed to be eternal, immutable and transcendent. Of course it's an impossible standard then.
Great lecture. One correction: at 7:45, you mention that Hume must have missed something regarding intuitive certainty, if he wants to say that all knowledge resolves into probability. Yet, Hume is well aware of this. In fact, in Part III of Book I, he says: "Three of these relations [resemblance, contrariety, and degrees of quality] are discoverable at first sight, and fall more properly under the province of intuition than demonstration" (T 1.3.1.2).
A difficulty in interpreting the Treatise is the inconsistency between his commitments to intuitive knowledge (and relations of ideas, more generally) and Part IV of Book I that seems to skeptically undermine any attempt at justification, whether empirical or rational.
One of the interesting things to note is that the late Hume of the Enquiries is much more conservative in his epistemology. The relations of ideas take on a definite role in the First Enquiry, while much of the radical skepticism of the Treatise is lost. And, still, the question remains as to why he changed his mind. It seems to me that his pursuit of a position at a university and the relationship between skepticism and atheism is the most likely reason. He never did obtain a teaching position.
Unfortunately, I find many Hume scholars and many graduate students alike prefer his more conservative epistemological positions -- ones that don't undermine the sacred laws of logic and mathematics. Why, indeed, is his skepticism with regard to reason an understudied aspect of his corpus? Perhaps it is because the attachment to truth and certainty among philosophers is a similar type of attachment theists exhibit toward god -- like children who don't want to let go of the comfort of their parent. As Peter Unger said: "In philosophy, being a sceptic usually means walking a lonely road."
The argument against induction may even be strengthened by asking weather we even know past occurrences of some correlation have ever happened at all. All we have to do is apply a similar argument against the reliability of memory:
I may be experiencing a memory now, but how to I know it actually matches up to a past occurrence/experience? Because I have memories of memories being accurate? Circular reasoning.
Great thumbnail image for this video. Really catches the eye; it’ll definitely get you more views.
So true haha it was probably why i clicked this on particular instead of other thumbnails besides loving Hume.
Sorry to be offtopic but does someone know of a method to get back into an Instagram account?
I was stupid lost the password. I love any assistance you can give me.
@Aiden Camden Instablaster :)
Thanks to Uebermarginal, I found your channel, and I must say it is a pearl. I was going to get into reading Hume for several years now, and you just make it so much easier.
Thanks for this. The robot recommended this just as I got the solution to a critique of Cartesian rationalism I have been struggling with for years from a _Doctor Who_ video.
I have felt that Hume proposes that subjective confidence in an assessment may aid the desires in making better or more valuable judgements. Always thought that existentialists should pay greater regard to Hume, that the nature of skepticism in relation to the inescapability of judgement outlined here provides a very clear psychological foundation for existence.
Internet Skeptic:I am the biggest skeptic there is
Hume and Descartes:Hold my epistemology
Yes nice video on skepticism it has been one of those things that I could never overcome
This makes me think of Pyrrhonism, in which epistemic certainty is considered impossible due to things like the problem of the criterion or the Münchhausen trilemma, and epoché (suspension of judgement) is thought to be the appropriate frame of mind to achieve ataraxia, thereby supposedly leading to eudomonia. A criteria of action including sensation, compulsion of pathé (natural drives), and deference to social custom is then used to make decisions holding to appearances and perceptions without beliefs.
10:02 Miller: 7 +or- 2 bits of information is the working limit of human memory.
I believe that Intuition is the judgement of certainty of an outcome under a particular " set of conditions".
The degree of fallacy of intuition is directly proportional to the degree of deviation from such set of conditions.
For example - I failed in something multiple times in a particular period of time. Now after a gap of two years, my intuition says that I will fail again. But there is certain fallacy in such an intuition because after two years " set of conditions" have changed. Maybe my approach has changed, my skill levels have improved , my personality has changed slightly. So, the prevailing conditions are very different. Therefore, fallacy in intuition exists.
I love daddy Hume
For a moment there I wondered if Hume came before or after Descarte in the philosophical discourse, which may be some evidence to Hume's point, as we all know Descartes was prior. But really, his approach here is interestingly misguided. The objections given are all relevant: meta-evaluations can reinforce or even increase the probability of one's epistemic performance; there is a significant distinction between the probability of the event and the probability of my epistemic efficacy (and my resultant confidence therein); and there is the problem the the self-defeating nature of the argument. But the third objection rests on the "skeptical regress" only in the way that it must come to some arbitrary end, the only motivation for which is custom informed by passion. Though that seems coherent, it rests on the assumption that this particular form of skeptical regress is the inevitable result of reason left to it's own devices, which is really what Hume supposes to demonstrate. I would take the third objection down another path. If my faculties for discerning the truth of something, even of matters such as 1+1 = 2, are probabilistic at best, then are not my evaluations of this very notion also probabilistic? How can I be confident in the probability either way? Can I not say with 100% certainty that I did not go to the store yesterday? Can I not know with absolutely certainty, for example, that I am uncertain, regardless of the degree of uncertainty? If not, then those counterclaims against my certainty also suffer from the same curse of dubiousness. If, in other words, reason would "entirely subvert itself", then I have, by acceptance of this principle, an instance of its self-subversion in the very principle of my skeptical thought process. Why shouldn't this attenuate itself into epistemic irrelevance just as quickly as it asserted itself? It is also a glaring problem to suggest that there are no non-arbirary stopping points in a process of reason which represent sufficient assurity to an epistemic chain of meta-evaluations. Besides this, the prior criticism applies here also. By what assurity does Hume assert that there is no non-arbitrary stopping points to a valid process of reason which has absolute certainty? Why does his principle of a self-subverting reason not apply here also?
It seems the mathematical examples are not all of a kind. One might easily say that my knowing that 1+1=2 (considering just the fact for present purposes - not the proposition) is different from my knowing 12+22=34, because there are no "steps" of calculation carried out in applying the +1 function, or at least not in adding one to itself. Also, the objection about inability to keep applying the "how good am I at evaluating the previous level type of judgment" function is very much to the point. First, it seems that with 1+1=2 there is no doubt at all, because no process in which error may enter. That is, I have never actually doubted (never been able to doubt?) 1+1=2, unlike the case with 12+22, or something involving more difficult calculation, which I may have applied and then remembered for awhile, but then forgot, as it were, so that a new calculation needed to eventually be applied. But even if the question is 12+22, and I recognize that I had forgotten it for awhile, it seems that to go to the next evaluation level and ask, "How good have I been at correctly calculating this kind of problem?" I am at a loss as to just what "this kind of problem" is, and if I try to ascend to another level of evaluation, it seems the subject matter of the attempted question has quite disappeared. So with 1+1=2, the first evaluation results in no diminution of the probability from a perfect 1. And with larger number calculations the question posed at each higher level of evaluation looks like it may be just the very same question as was posed in the previous level evaluation, which in fact may seem actually to be a nullity, a mere attempt at asking an evaluative question without quite knowing how to go about it.
"But even if the question is 12+22, and I recognize that I had forgotten it for awhile, it seems that to go to the next evaluation level and ask, "How good have I been at correctly calculating this kind of problem?" I am at a loss as to just what "this kind of problem" is"
I'm confused about what the objection is here. "This kind of problem" would be something like "addition involving small numbers." Further, it seems to me that it's perfectly sensible to ask, "how reliable have I been at performing additions involving small numbers?", and that the answer to this question will bear on my degree of confidence in an addition I've just performed. In fact, this happened to me when I was writing the script to the video. I initially wrote down "22+12=34", almost automatically - it took me less than a second to work it out. But then I remembered that automatic judgements such as this are sometimes wrong, and I checked the equation again. My degree of confidence in my initial judgement declined, partly because I recalled similar judgements being mistaken in the past.
Of course, there is a serious problem about taxonomizing "kinds of problems". Is "22+12=34" the same kind of problem as "101+51=152"? When I remembered certain judgements in the past being mistaken, am I comparing the current problem to relevantly similar problems? Etc. There isn't really an objective answer to questions such as these. But it doesn't this point support Hume's argument? It leaves us unsure of how to work out the probability of error, and so increasingly unsure of what our degree of confidence in the initial judgement should be.
"It seems that with 1+1=2 there is no doubt at all, because no process in which error may enter."
If there is no process, then doesn't that give us reason for doubt? One can construct a deductive proof for 1+1=2 by using something like the axioms of Peano arithmetic, but that would be a process. If we haven't gone through that process, then what is our justification for believing that 1+1=2? Is it just what we've always been taught since elementary school? Surely we're not automatically justified in believing a thing just because the people around us claim that it is true. If people believe everything they're told, then people will believe anything.
I think the psychology paper on working memory is called something like "Remembering 7 items plus or minus two" -
Edit: found it -> www2.psych.utoronto.ca/users/peterson/psy430s2001/Miller%20GA%20Magical%20Seven%20Psych%20Review%201955.pdf
Thanks for the link!
This is why it's important to divide skepticism by topics and consider each topic individually. In the case of 1 + 1 = 2, we have at least two interesting questions. For one, is it possible to know that 1 + 1 = 2? The answer seems to be yes, that is easily possible just by logically proving that 1 + 1 = 2 based on the definitions of arithmetic operations. Such a proof seems to be possible, and if we have such a proof then it would guarantee the truth of 1 + 1 = 2 as well as justifying our belief.
We run into a different issue when we ask whether we could be wrong about 1 + 1 = 2. In other words, can we know that we know 1 + 1 = 2? This is no longer a question about arithmetic, and now it's a question about ourselves and our capabilities at logical reasoning. We believe that we have a sound proof of 1 + 1 = 2, but how do we justify that belief in the face of the fact that we sometimes make errors in reasoning? It would be arrogant to suppose that just because 1 + 1 = 2 seems extremely obvious, therefore we are infallible in this judgement. We should admit that our best justification for believing that we know 1 + 1 = 2 is our personal evaluation of the reasoning, and that is really no justification at all. There are plenty of people in this world who believe very silly things with total confidence.
In short, there's no cause for skepticism about mathematical facts which can be deductively proven, but there is cause for skepticism about our own personal judgements about which propositions are deductively proven mathematical facts. In general we can know mathematical facts, and it seems likely that we know 1 + 1 = 2, but we don't know that we know 1 + 1 = 2.
Haha, this only follows if math can be disentangled from the psychologies in which the math is performed. Even math done by a computer is ultimately interpreted by a human mind at some point and is itself a computer designed by a human mind, even if it operates in the background, the appropriate functionality is ultimately judged by a human, they simply cannot be disconnected... Math has always and will always be experienced within the imaginations of those utilizing it.. the idea that mathematical axioms don't bump into the human psychologies that arrange them is nonsense.. also if the psychologies that design mathematical axioms are faulty than the reliability of math and the idea of relating it to some greater truth or reality is suspect.
The fact that the incertantity build up as we go through the verticals verification doesn't imply that the margin of error will necessarely get ridicoulously big, mathematically speaking. Suppose a physicist made a calculation and found x as result, with margin a. If for every n, at the n-th level of verification the margin increase by a/2^n,then the final margin will only 2a at the end because 1+1/2+1/4+1/8... = 2.
Was always sensitive to the distinction Hume makes between what we can call relations of ideas as opposed to matters of facts. We construct the idea of a rectangle based on relations of ideas that constitute this object. That is different from our assessment of other ideas that we have in terms of our investigations related to objects. As a result the object generated from relations of ideas is the definition of the object, and must be present for that object to exist, however induction will be inseparable from the possibility of error, since we are not proceeding from a definition of an object, but an assessment of a combination of objects. In addition the idea of regularity of matters of fact such as natural law assume that we can understand or even anticipate all potential variations within these matters.
I knew little of hume's skepticism before encountering this-and I was in doubt about everything itself, including the very system I use to doubt things-logic, his argument seems to be using a different basis however, and not trying to do the same thing
I have not watched the full video, but just my initial thoughts on the very first argument of the addition chain, to me seems meaningless, because wouldn't we say that the point of reason here is to make a certain claim of relation, that claim in abstract is seperate from the notation on the paper, the certainty of the veracity of the claim is independent of whether you made a mistake reading it caues the mistake in reading, say the number of ones that is being added simply leads to a different abstracted claim that you are considering
exactly my thoughts, i think
Regarding the difficulty or impossibility of higher level evaluations of judgment ability, it seems there is a type/token difference, in which the first level meta-judgment is a judgment about a judgment type, but after that it is, or quickly becomes, judgment about nothing but individual token judgments, which, if true, seems to spoil Hume's claim.
Hume and others like him scare me lol.....just let me be ignorant....don't ruin my reality please
By all accounts he was a fairly affable chap. Nothing to be afraid of!
@Giannis Polychronopoulos It was truly shocking to learn that a Scottish man born over 300 years ago was racist. What will they tell us next, that he was prejudiced against homosexuals?!
@Giannis Polychronopoulos That's not shocking to me - I knew that's what you were doing. I just found it a little silly. Yeah, Hume was racist. He was also affable. Those features are compatible, especially given the time he was around.
@Giannis Polychronopoulos It may be that most people find racism disgusting (actually I'm skeptical about that, but hopefully it's true), but I doubt it would significantly change their judgements concerning the personality traits of a politically conservative Scotsman from 300 years ago. Most people are capable of evaluating past figures within the context of their time. I agree that this conversation is boring. You're the one who brought up this topic though.
As for the mind-(in)dependence affability, it depends on how we're using the term. We can specify facts about people's behaviour, and about how others react to that behaviour, including social conventions for what counts as affability, etc.
@Giannis Polychronopoulos Yeah, it's "too boring" to explain what's wrong with my totally uncontroversial statement, in the context of a topic that you chose to raise. Lol.
Well done sir
I enjoyed very much the video and it reminded me to Kripkenstein somehow. By the way, can you please source the original argument of Hume?
I give the source right at the beginning. It's in the Treatise, the section "Of skepticism with regard to reason". That's book 1, part 4, section 1.
You can access it online here: davidhume.org/texts/t/1/4/1
@@KaneB Thank you very much. I just missed the source so I guess I am aligned with Hume's argument lol
however, limits in math don't always go to infinity. therefore, the limit of the iteration of our uncertainty does not necessarily go to 0.
@@parkermoss9518 I do not understand why that implies it diverges. I will give a counterexample. Since infinite products are less familiar to me, I will take the logarithm of both sides and since each multiplicand is less than 1, its logarithm will be negative. So then the question is if the sum of strictly negative numbers necessarily has to diverge (to negative infinity), or multiplying by a minus 1 on each side, that an infinite sum of strictly positive (non-zero and non-negative) numbers necessarily diverges to infinity. Geometric sums with a term-to-term ratio is between 0 and 1 (exclusive) are examples of this. For example, take 1 + 1/2 + 1/4 + ... = 2. If we take f(x) = 10^(-x) on both sides, we get 10^-1 * 10^(-1/2)^(10^-1/4) ... = 10^-2 = 0.01. Thus an infinite smaller-than-one product has converged to a non zero number.
The fact that this number is quite small, 1%, is of no consequence since we can simply take both sides to some small power, say 0.0001. Thus we have 10^-0.0001 * 10^-0.00005 ... = 10^-0.0002, which is (checking with a calculator) 0.999539589003, i.e more than 99.9%. Sorry if I have misunderstood something.
@@parkermoss9518 However if, as the video talks about, each subsequent probability decreases, then this corresponds to an infinite sum of strictly positive numbers where the next is always greater than (or equal to) the other. This necessarily diverges. The proof of this being that we could take a series with the first term repeating, and lim a*n will diverge, and since it is termwise smaller it is smaller on the whole, and if a smaller series diverges then the larger does as well. Sorry for commenting without finishing the video.
the way you presented the argument initially (we can't ever know anything for certain, based on pure reason) made it sound like Hume was just objectively wrong - "i think, therefore i am." - there you go. pure reason arriving at absolute objective truth that we can be 100% certain of. case closed. but then, as you describe his argument further, it becomes clear that he agrees that the way you initially presented his argument is wrong by granting that it isn't logic he's skeptical of, but human application of infallible logical systems (empirical measurements, for instance) so he's asserting the objective truth of conclusions arrived at by pure reason, in that admission ( the IDEA of "2+2=4 in a system with a base of 4 or more", for instance), but he's pointing out the human tendency for mistakes (the fact that i may have made an error in expressing or understanding the objectively true concept of the aforementioned "2+2" equation). this is really just a common, and uncontroversial position that you're presenting as if he said something insane and objectively wrong.
he basically just said "hey we make mistakes sometimes, so we always have to be skeptical of things like science" - and that idea is the backbone of science. nothing controversial here at all.
Great video
I believe hume has to proove that the probability converges to 0. That it does not deverge. Most series of multiplication are unknown but we should assume that it converges to a value greater than zero since we can come to beliefes.
Theres an interesting solution the the regress. Imagine you assess a some claim, and if you assume you made no mistake, you are certain it is true. Now consider you could uave made a mistake by assessing the accuracy of your reasoning, which we will call metareasoning level 1. Lets say you come to the conclusion that, assuming you didnt make a mistake with this metareasoning, that your reasoning on these kinds of problems has is has a 3/4 chance of being airtight. You then asses the chance you are right made a mistake in metareasoning level 1, and come to the conlusion that, assuming you made no mistake in your metametareasoning ( metareasoning level 2) has a 15/16 chance of begin right. You assess level 3 to be 35/36, and so on where the nth level of metareasoning turns out to be 1-1/(4n^2). It turns out that the infinite product of all these, that is to say the probability that all of this infinite regress is independently and silmultaneously true, coverges to 2/Pi, about 63%. That means that when a claim seems, from plain reasoning, to be basically certain (such as in the case that you have what you believe to be a formal logical proof), you can metaevaluate the whole regress to learn that it is actually 63% likely to be true. Neat, right? Infinite regress solved without indeterminism. You just need to be convinced that your meta reasoning abilites increasingly appraise the preceding level to be more and more likely to be accurate, which, actually seems reasonable. Obvious the specific 2/pi formula isnt true for human reasoning, its just an particular example of a convergent product for illustrative purposes.
If you want to pick post-regress probability p that your certain beliefs should have, you should appraise at level n that, assuming you haven't made a mistake is your assessment, if you indeed made a mistake in level (n-2), level n-1 has a 100(1+[1-1/p])^(2^n)% likelyhood to identify that
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Please make a video on HUME''s aesthetic theory.
interesting episode
Respecting skepticism about reason, it seems one might well believe there are 3 beliefs about which I am not pushed to skepticism:
1) I exist;
2) My mental state of the present instant is as I believe it to be (whether I am a deceived brain in a vat or otherwise);
3) Mathematical truths, given the assumption of our theory of arithmetic.
So very simple (or primitive) beliefs, which involve neither the consideration of part or all of a chain of facts, nor a manifold of concurrent facts, would seem to be unassailed by skepticism regarding a vast number of beliefs requiring a (or a longer) reasoning process.
"it seems one might well believe there are 3 beliefs about which I am not pushed to skepticism:
1) I exist"
Hume might have the resources for giving you a push on that first one 😉: davidhume.org/texts/t/1/4/6
1. You don't know you're you with certainty
When Hume uses the terms "Reason" and "The Understanding" he's being critical of the Scholastic a priori reasoning that was still being taught in the Universities. He writes of the peripatetic philosophy (Aristotle) that St. Thomas had incorporated into Christian Theology/Natural Science/Metaphysics. The empiricists (Newton, Locke, Hume, etc.) rejected Aristotle's metaphysics which made ZERO appeal to sensory based evidence - but were still very much in vogue in the seminaries and Universities.
Hume was only a sceptic wrt the scholastics.
great I am taking class about hume-Kant, do you want to make a video about the critic of pure reason? it's so hard to read.
I have the same reaction to that text, which is one reason why I'm not planning on doing a video on it. Sorry about that!
@@KaneB Hey Kane you ever gonna do a video on the philosophy of death? (Just kidding, keep up the good work.)
@@Trynottoblink My thoughts on death: th-cam.com/video/QjF4U-3Qz0U/w-d-xo.html
@@JulioCSilvaPhilosophy Just to clarify, I have pretty serious death anxiety (about my own death, not about the death of others). The only thing that really works for me is to just not think about it. So it's unlikely that I'll ever do a video on philosophy of death, or even study it. I've mentioned this before, which is what Trynottoblink's joke was about.
@@KaneB : People tend to fear that which they do not understand. I don't know if studying the philosophy of death could really help with anxiety, but it wouldn't be greatly surprising if it did. As an analogy, some people find that doubt gives them anxiety, but one wouldn't expect that in a skeptic. Maybe skeptics are skeptical due to their lack of anxiety over doubt, but maybe studying skepticism could be a cure for anxiety over doubt. Spend enough time with a thing and it becomes like an old friend. Or maybe it makes anxiety a hundred times worse; do not take this as medical advice.
4:37
Moore
Isnt this the one Daniel Dennett has covered?
Not as far as I'm aware. There's nowhere near as much literature on this particular argument as there is on the classics like induction, causality, selves, etc.
Hume was the GOAT
couldn't there be another objection, that each increase in uncertainty in a chain is so small, and all chains of reasoning are in the practice of course finite, so the extra uncertainty from chains of reasoning does not lead to never believing anything, but simply acting on beliefs probabilistically?
I think I'm with Hume here on 1+1=2. It may seem inconceivable, but the mind is plenty capable of experiencing even the most patent and direct of incoherencies as undeniably coherent, and vise-versa. This is probably easier to accept if you've witnessed it, and especially if you've experienced it yourself. One of the ways of potentially experiencing this is through the use of certain substances, like psilocybin mushrooms. It's not impossible for that sort of experience you have of just directly "seeing" the necessary truth of something like 1+1=2, to be experienced in regard to something like 1+1=1. That sense of rational coherency/incoherency isn't derived directly from the concepts in question; it's produced in your mind, in response to the coherent/incoherent content, but it doesn't necessarily need to do so accurately. One can *experience* a direct contradiction as inarguably coherent
Skeptics still believe in the standard of absolute truth. They judge everything by it when they make their arguments. You can go further and reject the notion of absolute truth. I even suspect that absolute truth is a religious artefact in culture. It's supposed to be eternal, immutable and transcendent. Of course it's an impossible standard then.