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John Molineux

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  1. Eiuol, if we take empiricism to mean the belief that all knowledge comes from sense experience, and rationalism to be the belief that not all of it does, it is impossible to be "neither empiricist nor rationalist" as per the law of the excluded middle. Either all knowledge comes from sense experience, or it doesn't.
  2. Easy guys! =) Plastmatic, I'm not aware of ways that my usage of a priori is different than the typical use. I just mean proceeding from something other than sense experience--which, as I understand it, is the standard meaning. When you type "a priori" on google, the following definition comes up: The terms a priori ("from the earlier") and a posteriori ("from the later") are used in philosophy (epistemology) to distinguish two types of knowledge, justification, or argument: A priori knowledge or justification is independent of experience (for example "All bachelors are unmarried"). That is exactly how I'm defining it--basically as what does not come from sense experience. In addition to the science-based arguments I have given, I could add the following arguments that seem to me to literally prove with certainty that empiricism is false and self-defeating: the only knowledge that comes from sense experience is the knowledge of that sense experience itself. some of our knowledge is of things besides the objects of our sense experience (for instance, math, but also pretty much everything except for knowledge in the form "I am having the experience of seeing yellow," etc.) therefore, not all knowledge comes from sense experience (which, with the definition above, is exactly tantamount to saying that "we have a priori knowledge") Or this one: the statement "all knowledge comes from sense experience" does not (and cannot possibly) come from sense experience, and it is therefore self-defeating (this does mean that it cannot be TRUE, but that it cannot be KNOWN) Given the clarity and prevalence of arguments like this, it has been amazing to me how common empiricism is. So much harm has been done in philosophy (and by extension, science), by the fear of the "metaphysical" nature of the a priori. I understand that the enlightenment was largely about getting superstitious drivel out of philosophy, which is admirable and important. But (it seems to me) the over-extension of this idea resulted in "empiricism," for fear of "vague metaphysical superstitionism." And I think the idea is that a priori means something mystical is unfounded. I think it could very easily simply be a feature of our brains (which contain enough mystery to easily swallow up all the mystery contained in the question, "what is it?") and the way that we must conceptualize things based on the way our brains evolved. But the aprioriphobia of the enlightenment ran so deep that empiricism reached something like a consensus among the scientific and much of the philosophical community--not by argument (I am not aware of any argument FOR empiricism, and it wouldn't matter since from the two arguments above constitute a logically-tight proof that empiricism is self-defeating)--but simply (it has seemed to me) by riding a wave of popular anti-superstitious sentiment. And this empiricism has literally (in my view) destroyed philosophy. It has lead to the triumph of skepticism in philosophy, and has created in science its own form of the very mysticism that it set out to eliminate (I mean the current situation in Quantum Mechanics, which is a direct descendant of the dogma of the elightenment, empiricism). Now one of the few remaining schools (as I see it) where neither the new mysticism of quantum mechanics, nor the irrationalism of postmodern philosophy prevails, is Ojbectivism. But Oists seem to me to be largely isolated (and unfortunately, not taken too seriously) by mainstream philosophy (partly because that philosophy has itself become insane after embracing the consequences of the irrationalism that proceeded from the skepticism that resulted when near-consensus was reached about the impossibility of solving the problem of induction from an empiricist framework). Oism is one of the few schools (maybe the only) that is still actually trying to solve the problem of induction. Thanks God for that, but it seems plain to me that it will never be solved by sense experience (which can't even solve a schoolboy's math problem, much less the philosophical problem that brought down the Western intellectual tradition). In Godel you have a rigorous mathematical proof (close to the highest-possible certainty) with a half century of philosophical debate about its meaning, and something like consensus. In the above two arguments, you have two of the simplest, tightest arguments possible. Simple, old fashion syllogisms, with none of the meanings really in dispute. And what stands against that? Is there an argument of equal strength and clarity somewhere? I have read dozens of books by empiricists and I can't recall a single argument for it--all the authors took it for granted, and then proceeded to fail to solve the great problems of modern philosophy (and by extension, destroyed the western intellectual tradition). There is certainly nothing like the simple syllogisms above, which seem to me to be unassailable. Nevermind....I'm just ranting, which may or may not be helpful. But I genuinely don't understand why people cling to empiricism or refuse to allow in the a priori. Anyone who would be willing: what is at the core of the reason that you believe that all knowledge must come from sense experience? And how do you escape the above two arguments? By the way, does Ms. Rand's "implicit knowledge" come from sense experience? If so, how? If not, it's a priori under the definition above (which is the standard definition).
  3. Eiuol, as to what categories are, they are fundamental concepts which are not defined by other concepts, and are not understood by their definitions, but somehow by thought or reason itself. They are also the things according to which abstraction occurs. By abstraction I mean the consideration of the part. I believe that it is something like the essence of thought. But if abstraction is the consideration of the part, then the questions arises, "which part?"--or "which kind of part?" I believe the answer consists of a category (or a concept itself built upon a category). But abstraction is only possible if you have something according to which you are abstracting (like extension in space, time, kind, etc.). I believe they are similar to Ms. Rand's "foundational concepts." "How is it foundational?" It is foundational by means of the fact that it cannot be defined with other concepts, but only with synonyms (and obviously when you get down to the tight circle of 3-4 synonyms that all define each other, your ability to understand those concepts cannot lie in having heard the definition--it is presupposed that you already understand it in some other way). All concepts would be unintelligible if they were not attached to something that was understood directly. "What makes it valid?" I guess what makes it valid as a category is the fact that it meets the definition above (with a hat off to the good Prof McCaskey). "Is it an idea?" Yes. As to the "ontological" questions (where does it exist? What is it made of? Is it a platonic form?), I am agnostic. I would be lying if I claimed to know the answer to those questions, just as I would be lying if I said I was not certain that there must be categories at the foundation of understanding.
  4. I just read McCaskey's work on the problem of induction (http://www.johnmccaskey.com/joomla/images/for-download/PittVolume.pdf). I stand by what I said earlier--both about his ideas being deeply insightful and important, and about it failing to contain a complete solution to the problem, and I believe subject to the two objections I voiced above.
  5. I take that back. I'm not able to sort out the precise relationship between the following terms: property, type, kind, concept, idea. They are all pretty closely related. Sorry for the short and useless response, but my wife would not be too happy if I spend Christmas eve working out the relationship between those terms! =) Any help would be appreciated. I do think some of it may have to do with the accidents of the English language, although I am convinced that there is a genuine category in here.
  6. Eiuol, What I mean by a concept: I almost want to say that by concept I mean what everyone means by concept! It is itself a category, so it can't be defined without synonyms (which include "kind," type," maybe even "property," etc.). I think if I were forced to define it I may say something like "something that different things have in common." Why a category doesn't also require a category: The thing I think we know is that SOME concepts have to be foundational. I don't believe that they are reasoned to with a cosmological argument-type way where the first premise is, "all concepts can be understood by other concepts." If that were the case, a category would (as you say) also need a category. We simply observe that most words are understood by other concepts. We then ask ourselves, "are all words this way?" And if all words were understood by other concepts, there would only be two possibilities: Infinite concepts (clearly not the case) A circular structure "unattached to understanding" (clearly not the case, and also if it were, understanding would be impossible) I take your point about a child knowing a tree before the concept of existence. But as Ms. Rand says, the knowledge of existence may be "implicit."
  7. Plasmatic, your claim that we are justified to draw the universal conclusion that 1+1 will ALWAYS = 2 is "answered by knowing what in experience the symbols you are referring to mean," is, in my view, a significant source of our remaining disagreement. I actually thought the same thing at one time (again, the 1st time I read Kant I write something almost exactly like that in the margin). But for the following reasons, I now believe this cannot be the case. It has been shown to be impossible to derive all of mathematics from logic. The 20th-century attempt to do so by deriving all theorems from set theory ended up proving that there are theorems that cannot be proven (and moreover, it is subject to paradox such as Russell's paradox). Most famously, Godel's theorem proved that in any consistent mathematical system rich enough to contain arithmetic, there exist propositions that cannot be proven (or disproven) from the system's axioms--that is to say, there are propositions that are NOT simply a matter of (as you say) "knowing what the terms mean." I believe GrandMinnow (who is apparently seen as the resident Godel-interpretation expert) will attest to both these points, probably adding that "a philosophical argument is needed to draw the latter part of my conclusion on point #2." =) But I believe the burden of proof is rather light here, and the needed-philosophical arguments have been supplied and reached something like consensus among most experts. Rather, a philosophical argument is needed to say that our knowledge of mathematics is based on "knowing what the symbols mean," and such an argument has to contend with the whole 20th century, in which many of the world's most brilliant minds tried, and failed, to provide JUST such an argument, and were eventually silenced by Godel's proof. Yes, the Oist I am referring to is David Harriman. Thanks for the links on Prof McCaskey's discussions on the problem of induction. I plan to follow up with that stuff for sure! Minnow, when I mention the defeat of the "empiricist program," I am talking about such writers as Wittgenstein, Carnap, and the logical positivist camp, for whom the attempts to ground mathematics in logic / set theory was part of an attempt to settle one important part of the larger empiricist-rationalist debate. In order to maintain that all knowledge comes from sense experience, you have to explain mathematics in a way that is consistent with that. Since obviously sense experience itself can't give you the universal statements of mathematics directly, the ideas that it was simply a matter of the extrapolation of axioms is the only suggerstion I've ever heard argued. (Granted, I am not an expert in mathematical logic, and I'm confident that, as you say, "there are some informed holdouts.") For my part, there seems to me to be a direct path as follows: in any consistent mathematical system rich enough to contain arithmetic, there exist propositions that cannot be proven (or disproven) from the system's axioms. ...to… Some mathematical propositions of which we have knowledge do not consist of the mere extrapolation of concepts ...and since… Mathematical knowledge cannot come directly from sense experience (which only consists of itself) ...and… We have mathematical knowledge ...we can conclude… Some of our knowledge does not come from sense experience I believe I could put that all in syllogisms that would be very difficult to assail (I'll do so if requested). Merry Christmas everyone!
  8. Phew! A lot to take in! Thanks everyone for staying in this discussion! It's very helpful to me and I'm glad to have a chance to discuss this stuff! GrandMinnow, I'm not sure I explicitly disagree with anything you're saying. I sense that you're just trying to stop wild speculation about the meaning of Godel's proof, which is admirable. Your response to my initial statement did not appear to address it directly. Do you believe that my initial statement (that Godel's proof defeated mathematical formalism) is true? I agree with your later statement that it was not (as I had said ) "PRECISELY" what Godel proved, but requires a philosophical argument from the mathematical result. But I believe that the dust has settled from several decades of debate, and there is something in the area of consensus about the above statement. About the clock where 2+2=0--yes, fine, but that's just a trick of words. 2 (with its usual meaning) plus 2 (with its usually meaning) equals four (with its usual meaning) though obviously if you change the rules governing the symbols, you can get any result you want. Plasmatic, I don't believe I have changed the way I'm defining a priori at all. Interestingly, the 1st time I read Kant I actually thought he was doing the same thing you're accusing me of, and I wrote as much in the margin (because at one time he defined a priori as independent of experience, but than later said that experience causes it to arise). I just didn't understand what he meant. When I did, I saw that what he meant was consistent with both statements. And all my statements that you quoted are consistent with each other, and what I mean. A priori knowledge is that which... Can't be proved or justified by sense experience Allows us to conclude things beyond what is justified by sense experience ...though sense experience can and does cause such knowledge to arise I can see how you can think the 3rd statement contradicts the 1st two--partly because I once thought the same thing about Kant! Maybe an example will help you see why I don't believe they're contradictory at all. When I learn mathematics, I do so by means of a teacher drawing shapes on a board. This allows me to see (in my "mind's eye" or with intuition) not only that the particular triangles she is drawing have certain properties, but that ALL TRIANGLES MUST HAVE THOSE PROPERTIES. That is something that I didn't conclude by reasoning that, "all the triangles my teacher drew had those properties, therefore ALL triangles have those properties." That would be a fallacy (like concluding "all swans are white" from the fact that all the ones you've seen are so). Rather, I see the necessity in my mind. Thus, the sense experience (of watching my teacher draw it on the board) caused my knowledge to arise, but that experience does not justify my drawing a universal conclusion (like "all triangles have such and such properties")--the justification consists in something I saw with my minds' eye (or by intuition). And all attempts to draw universal conclusions from limited sense experience is subject to the problem of induction. Thus the universal conclusions we draw (in math for instance) must be based on something else. About Ms. Rand's quote on intuition--I think there are two sense in which the word "intuition" is used: (1) a vague feeling that something is true without being able to say why (i.e. "I had an intuition when I woke up this morning that such-and-such would happen"), and the other (2) is more technical, in the sense of the necessary connections we see between triangles in the examples above. I don't believe Ms. Rand's definition of reason can be squared with Godel's proof. Trying to explain how mathematical knowledge did not violate empiricism was exactly the goal of the formalist program that it defeated. Specifically basing it on logic was the idea (and the topic of Russel and Whitehead's Principia Mathematica, and in the end that program failed because of the paradoxes, and was forever closed with Godel's proof). That, anyway, is my understanding of it. I agree with what Ms. Rand says about intuition in the interview. People often use "intuition" to describe very fast unconscious reasoning that we are not aware of--but in fact, it is often just plain old reason that's just not aware of itself. But that's different than the a priori intuition I'm talking about. Yes, what I mean by categories is very similar to what Ms. Rand means by "irreducible primaries." But the way she defines existence (by sweeping one's arm around and saying, "I mean this") is not sufficient to define it for someone who does not implicitly recognize it. Sweeping ones arms around is not sufficient to impart understanding of the meaning of the term "existence," and all of the "irreducible primaries" on which language rests are such that they cannot be defined by pointing as many "concretes" can. Think the Helen Keller moment when she suddenly understands the idea that there is a connection between experiences of different kinds, and that such concepts ("kinds" if you will, and "kind" is itself an irreducible primary par excellence) have names. You can't get that from the sense experience itself (since the only information given by sense experience is itself). You can go on pointing to different things and naming them, but unless someone understands the concept of a "kind," they'll just be like poor Helen was prior to her awakening moment. I think the best Oist reply to this would be to say that you CAN get them by abstraction. You abstract from sense experience to get to such irreducible categories (the Oist might say). But abstraction itself requires a category. To consider only the shape, or only the kind, or only the feel, or only the number, only this-or-that aspect of something, you have to have the concept of the aspect to-be-considered. Wow, I was actually shocked when I read this (quoting you quoting Ms. Rand): "Axiomatic concepts identify explicitly what is merely implicit in the consciousness of an infant or of an animal. (Implicit knowledge is passively held material which, to be grasped, requires a special focus and process of conscious-ness—a process which an infant learns to perform eventually, but which an animal's consciousness is unable to perform.)" I'm not (from that, anyway) seeing any clear difference between what I am calling categories and what Ms. Rand is calling axiomatic concepts, or between what I am calling "a priori" and she is calling "implicit knowledge." (Except perhaps that I wouldn't claim to know anything about what goes on in the minds of animals….) If we have implicit knowledge, then all knowledge does not come from sense experience (some of it is implicit). That's what I've been saying! Ms. Rand's definition of an axiom that you gave works very well with the law of identity and non-contradiction in logic, but not so well in (for instance) mathematics, where there are also axioms which are not "propositions that defeat their opponents by the fact that they have to use it in the process of attempting to deny it." Furthermore, the empiricist program to show that mathematics was based on logic (or set theory) (a) failed to accomplish that, and ( it was shown by Godel's proof that it is impossible to accomplish that. The interview at the end of your post gives a very brief window into Ms. Rand's view on how arithmetic is based on sensation, but I don't see enough details to comment. Personally I am skeptical (I may even go so far as to say I think its impossible). I believe that it is more-like the "implicit knowledge" that she described. Your comment following that section about "getting to induction soon" was timely. When I read Rand I felt that she didn't understand the problem of induction or its significance. I also read a book by an Objectivist alleging to contain a solution to the problem of induction, and my sense was that the "solution" consisted of failing to understand the problem. I saw your comment about Professort McCaskey "making inroads on the problem of induction." I've tried to search out his idea, and I found that he makes the distinction of Socratic (as opposed to Scholastic) induction, and defines it as "a compare-and-contrast process for discovering properties that characterize all members of a kind." He makes the point that it goes from things (rather than individual statements) to universal terms (rather than universal statements). From what I was able to follow, his idea is something like this: we start out not knowing what a thing is or its cause, but by constant experience we are able to narrow our definition of the concept. Thus early experiences with cholera involved knowledge of certain conditions under which it was known to arise. Eventually, human experiment was able to isolate the cause as certain type of bacteria, etc., in seeing more-and-more cases where the presence of the bacteria seems to lead to cholera. Eventually it is isolated in a laboratory and scientists are able to directly observe the connection between the bacteria, and cholera. This seems like a straightforward and clearly reasonable description of something like the scientific method. But the genius of Professor McCaskey (it seems to me) was in this. To the Humean tradition which voices the objection, "yes, perhaps in the case observed by scientists on such-and-such an occasion, in the laboratory, and in the cases documents, in THOSE cases the bacteria led to the disease, but how do you know that it will always be so? --that tomorrow you won't wake up and find that eating apples causes cholera (etc.)…?" His reply is, "THAT (the disease caused by the bacteria in question) is what I mean by cholera." I think this is eminently reasonable, an excellent point, and one of the very few far-reaching attempts to solve the problem of induction that I've ever seen. Moreover, I think something exactly like what he's describing is actually true of how scientific conclusions can may come to constitute real knowledge despite the problem of induction. Something like this is certainly a significant part of any solution to the problem of induction. However, I see at least two reasons why (at least as far as my limited understanding goes) it doesn't solve the problem of induction: There are such a things as "natural kinds," and the scientific method in general, and the particular method proposed above presupposes as much. There really is something called "cholera" and something called "vibrio cholerae" and those two things (a) are different, and ( involve certain characteristics which everything that is that thing have in common (all true cases of cholera have certain things in common, etc.). But the Humean question (how do you know that tomorrow apples won't cause cholera) has real significance here, and Professor McCaskey's reply constitutes something like a retreat. It may actually be the case that the real thing called cholera is not actually caused by the bacteria in question, and simply saying "that's how I define cholera" may actually end up obscuring this fact. Note: the situation is different in the case of simple mechanics, contrary to Hume, and in line with both Professor McCaskey and the Oist whose book I had read on the problem of induction, I believe we actually DO SEE the cause and its necessity (by what I've been calling "a priori intuition," even if that's not what the Prof and Ms. Rand prefer to call it--I will accept it under any name!). There are many scientific conclusions where the concepts themselves are not the things in question. For instance, some such conclusions describe relationships where the concepts are well-understood and agreed to, but the mathematical relationships among them are the topic of the conclusions. So for example, an equation about the force of gravity purports to describe the actual movement of planets in measurable terms. The terms are not in question; the measurements are. So when the Humean asks, "how do you know tomorrow that gravity will continue to exert a force inverse to the square of distance?"--it doesn't really work to just say, "well that's how I define gravity" (or worse, since gravity predicts certain positions, to say, "that's how I define distance," etc.). That would be like (ahem) claiming that 2+2=0 on the basis of a clock made that way. It is still possible to ask, "how do you know tomorrow that gravity will have such a force?"--and unless (like in simple mechanics) we actually see the necessity in it (as we do in simple mechanics), we have to admit that we're assuming something that is not justified. Incidentally, I believe we DO see the necessity in the inverse square law that defines gravity (or something very close to it). But in my view, the problem of induction is much-worse than this, and any enquiry serious enough to be called science depends on a number of ideas that cannot be justified in this way, or in any other way but by a type of knowledge that cannot come from sense experience.
  9. Aleph, I think we have an example of geometry being discovered from the perspective of someone confined to live in a lesser-dimensional reality (whatever that means)--namely, this world, where the development of non-Euclidian geometry and the discovery that the universe consisted of curved space occurred was accomplished despite the limitations of our intuitions (and our inability to intuit anything beyond 3 dimensions). Even if it were not possible to see that those lines are curved, the essential fact is that they ARE curved, regardless of how they appear. Limited perspective does not nullify truth! Objects look bigger when they are closer to us. Are we ready to say therefore that they ARE bigger?--knowing, as we do, that it is possible to walk up and measure them? I've always felt that it was just bad philosophy that wanted to draw big important conclusions from the riddles created by the limitations of various perspectives (if a tree falls and no one hears its sound….). I think we can only know whether space is curved by experiment and observation working within a framework of a priori intuitions (as we have). But its important to note that mathematics remains the same. You can talk meaningfully of 2-dimensional math in a 10 dimensional universe, or visa versa, and in all universes the same laws apply for the given geometrical system. The object of math is math (not the physical universe). It's not clear to me how the Continuum Hypothesis is the premier application of Godel's theorem. Also, I'm not aware of math where 2+2=0. I would be quite surprised if it were anything more than a matter of changing the rules for the symbols or something, since I believe myself to know with as much certainty as anything that 2+2=4! Plastmatic, New Buddha told me that "objectivism holds that essence is not ontological, but epistemological and contextual," and that "there is no characteristic which is more essential than others," and no "at bottom definition." That seems to contradict the "objective definition," mentioned by Ms. Rand. Moreover, I think Ms. Rand's definition does not seem to me to even go far enough to reach even plain everyday truth--in which a truth is a truth regardless of the particular stage of mankind's development at the moment. As you said, "there is such a thing as 'the way things are'." If so, the truth is that (the way things are), again, regardless of mankind's developmental progress. Eiuol, I'm not arguing that all knowledge is a priori--just that we have some a priori knowledge which combines with experience to form the conclusions of science. Thus I fully agree that experience is required for scientific knowledge. I find it hard to believe that anyone could deny that! In the debate between empiricism and rationalism, empiricists say that "all knowledge comes from sense experience," but rationalists do not say correspondingly "all knowledge is a priori." Rather, rationalists acknowledge that much knowledge clearly comes from sense experience, but just not ALL knowledge--some of it is a priori. I take your point about the connection between justification and formation. You're right in pointing out that they are essentially the same. Insofar as something really is knowledge, the only way we can come to have it is by experiencing / thinking through the justification. About categories, by "fundamental" I mean that understanding itself rests on them, and they cannot be understood by definitions using other words. It seems self-evident to me that there are such categories, or else understanding could never take hold. It is impossible to have a free-floating circular structure of concepts where A is defined by B, B by C...and so on, until Z is again defined by A---this is not only manifestly impossible, but not the case. When you actually extrapolate out concepts by their definitions you find at the bottom certain fundamental concepts which are defined only with synonyms, and thus which are NOT (like other concepts) understood by their definition, but in some other way--namely, directly. These are categories.
  10. Aleph, I'm not an expert in advanced mathematics, but my understanding of the situation has been as follows. You can tell me where / if I am misunderstanding and guide me as to how I can come to understand. First, my understanding of non-Euclidian geometry is that it is essentially geometry in which the parallel postulate does not hold (and those about triangles adding up to 180 degree, etc.). Secondly, that it is impossible to decide from the axioms of mathematics, what type of geometry (Euclidian or not) describes the universe. Thirdly, that in the theory of General Relativity, space is curved and so non-Euclidian geometry is used to describe it. And this has been tested empirically and is not doubted by scientists. But I have never seen the ideas discussed without reference to the way that objects which appear 2 dimensional from one point-of-view are actually 3-dimensional, such as this: http://en.wikipedia.org/wiki/File:Triangles_(spherical_geometry).jpg In this example, it is clear to me that the object in question is not a triangle, so the normal "laws of triangles" do not apply to it. It LOOKS like a triangle if you are directly overhead, but in fact, since the sides are not linear, it is plainly not a triangle. Thus to say that this shows that Euclid's axioms do not hold seems to me to be cheating. They do hold--just not when you are describing something in 3 dimensions at one time (when you are showing how and why the axioms do not hold), and in 2 dimensions at another time (when you are applying that conclusion as some sort of sweeping undermining of all of mathematics). That is equivocation, and I don't accept it. You might say, "but the universe is non-Euclidian, and therefore Euclid's axioms really don't hold!" But I think they do still hold, just not in either hypothetical or real "curved space." Or perhaps I am misunderstanding something, and if so, what? I'm not sure what to say about the continuum hypothesis. I'm afraid I don't have anything mind-blowing to say about it. It seems to me to be self-evidently false. Obviously that can't be proven. I fail to see the relevance to this discussion though, except that if it were in fact self-evidently false and unprovable, that would lend further support to the idea that mathematics is not merely axiomatic. But I'm sure I'm over my head in even commenting on it, which is why I've tried to avoid doing so. New Buddha, how does objectivism square itself with Godel's proof? According to objectivism, is there such a thing as "the way things are?"
  11. Eiuol, I think what you said pretty close sums up my position. I would make a few minor modifications. Rather than saying "the justification does not always require experience," I would say that "sense experience alone cannot justify many of the conclusions of math and science." About Godel, I would put it something like this: "Godel proved that mathematics is not merely axiomatic--and thus for us to really know mathematics, we must have knowledge of some mathematical objects that is more than merely human-made definitions." To your statement about observations, I would put it this way: "observations can falsify, but can never verify the universal statements at the core of every scientific theory." About thought experiments: I think they do often use logic, and they also may use our temporal-spatial intuitions. I think the "a priori categories" that you mentioned are real. I can define them and say what I think they are. I would define them as that according to which abstraction must take place, and I think they include concepts like place, time, kind, and cause. By "categories," I mean fundamental concepts at the back of all other concepts, which cannot be defined using other concepts, but only with synonyms. When I say "I don't know what they are," I mean that I don't know ontologically what they really actually are. (Are they like Plato's forms?--ideas in the mind of God?--features of all possible worlds?--clusters of neurons in our brains?) I don't think we need to solve that problem in order to believe in the existence of a priori categories. (In the same way, we don't really know what numbers--for example--are, and they are I think subject to the same possibilities mentioned here….)
  12. Euiol, at times I feel like we're close to agreeing, and then we keep getting stuck on the same points! It seems that we keep coming back to the argument that knowledge cannot be a priori if it arises through experience. But I feel that I've repeatedly accepted that experience causes a priori knowledge to arise, but that I define it as that which cannot be justified by sense experience alone. I'm not sure how to make myself more clear. I think in every post I've made thus far I've mentioned the fact that experience causes a priori knowledge to arise, but that the key distinction (in my meaning) is not what causes it to arise, but the basis of its justification--which, in the case of a priori knowledge, cannot be sense experience. I even quoted your initial email, in which you yourself said that a priori "isn't referring to inborn knowledge. It is referring to what you can figure out from logic or purely abstractions, without reference to the real world." Assuming that "figuring something out" is itself a type of experience (and one which certainly occurs only in adults whose minds are well-versed in a lifetime of sense experience), this is saying something very close to what I'm saying. I'm not clear where you're getting the idea of "passively arising knowledge," or how it relates to what I'm saying. The distinction I'm trying to make it between: Knowledge that can be justified by sense experience alone (a posteriori knowledge, which includes only the content of what we experience) Knowledge that can't be justified by sense experience alone (a priori knowledge) Here's what I mean about babies. If we define a priori in the way that people keep suggesting, as "that which we come to know without having any experience," then babies would have as much of it as anyone. Their lack of experience would not matter, since this suggested-definition explicitly defines it to be independent of (and perhaps prior to) experience. But I don't define it that way, nor (I think) does anyone. To my admission that I don't know exactly how to explain the existence of a priori knowledge, you said, "Then don't introduce an idea you can't explain!" But we can argue for the existence of something (and I think even have certain knowledge of the existence of that thing) without being able to say exactly what that thing is in its essence. I think we know that we exist, but the idea of the self and its essence is wrapped in mystery and even paradox. Matter is another familiar example. We know it exists by constant experience, but even scientists cannot say what--at bottom--it really is, and all their explanations (to date) end in more mystery and paradox.
  13. Eiuol, given the way that I define a priori, I don't believe the necessity of experience for forming knowledge in any way entails that that knowledge is not a priori. I believe that it is both true that we have a priori intuitions which underlie much of our knowledge, AND that those intuitions are awoken by experience. Again, the distinction (as I define it) has nothing to do with the conditions under which knowledge comes to arise--rather, it is about its justification. The comment I made about babies was meant to show this. If a priori was a matter of the conditions under which knowledge arises (and was inconsistent with any knowledge that arises from experience), then newborn babies would necessarily have as much a priori knowledge as adults (since the thing that separates adults from babies is experience, and if experience caused the knowledge-difference between the two and yet was inconsistent with a priori knowledge, it would follow that babies would have to have all the a priori knowledge which adults do). Your distinction between content and mechanism seems reasonable. Here's what I think I would say: a priori knowledge is something like a mechanism, but it can also produce content, just like looking at a photo from a digital camera tells you something about the photo's subject, but also something about the camera itself. In the same way, through experience the mechanism which is our mind can not only tell us about the content of sense experience (which, again, consists only of itself), but other things (for instance, logic). I think we have real knowledge (for instance) that a contradiction cannot be, and this is plainly not something given to us by sense experience--even if experience involves the conditions under which it arises. But it can never be justified by sense experience. You asked, "what exactly is an a priori category?" My answer is that I don't know. There are many things that we know by association without knowing what exactly they are--including matter, people, beauty, and just about everything in the world!
  14. Eiuol, you yourself in your first post here said a priori was referring to "what you can figure out from logic or pure abstraction without reference to the real world." I don't believe any philosopher define a priori as "that which babies know the instant they are born." =) I would say that at least in practice experience is necessary intuition to conclude anything--even if its just the experience of thinking. But, in the real world, clearly our conclusions arise out of a combination of sense experience and thought, both of which children progress in as they grow. But thought about sense experience itself can't produce the kind of knowledge that we have without something else. I'm not sure I would say "abstract thought is a priori reasoning." I think what I would say is that the essence of thought it abstraction, and abstraction has to be done according to a priori categories (concepts which cannot be given by experience). For example, shape or extension. To begin naming and recognizing objects out of the mess of sense perception, you have to abstract according to shape / extension. But that concept is not given by sense experience (all that's given by sense experience is its own content). As for how we explain where it comes from, I don't know if I could venture to say. Embodied cognition seems to be one viable theory. It could simply be a matter of the way our brains and bodies are. Almost certainly that has much to do with it. But I think there is real mystery here, and philosophy is always better off being honest about what it does and does not know, and I feel that much error has come about when philosophers have substituted dogmatic ignorance for wonder (in the sense of "I don't know what this is, therefore it cannot be real.") And the conversation to me seems to have been shrouded in very loose thinking--such as the metaphor that the mind is a blank slate. That's just a very loose, sloppy metaphor that has no place in philosophy, to my mind. The mind is not a slate--it is a mind (which is something both complex and mysterious, unlike a slate). You can begin to describe the difference between two very different things--a mind and a slate, by describing the a priori categories by which the mind abstracts (at least, so long as you don't believe that all knowledge comes from sense experience, which practically amounts to a nullification of all the properties that minds have which slates do not). Plasmatic, I do consider myself a Popper fan. He seems to me to be right about a lot, and one of the few people to have understood the problem of induction. I don't agree with everything I've read though.
  15. Aleph, my understanding of the much-touted curved space in which parallel lines meet, is that a line in curved space curves with that space, and so is really not a line, and so the parallel postulate is in no way disproved by non-Euclidian geometry, as is often alleged. You can't choose which form of mathematics to adopt. There is only one--the real one. And the existence of certain riddles and controversies in a very few areas of mathematics does not prove we can simply "choose which math to adopt," and that on the basis of that freedom, conclude that it's man-made. There are right and wrong answers in mathematics (except, again, in the handful of areas where there remains mystery or controversy). Even in those, there is likely a right answer even if we don't know it yet (there was a time when much of math was not yet discovered). And I maintain what I said about what Godel proved meaning that mathematics was not man-made (which is to say, "merely axiomatic" or formal). That's how he himself interpreted it and that interpretation is widely accepted in those who have not invested too much publically in the opposite ideas to consider following the argument to change their minds. Bullialdus's hypothesis (of which I was not aware until your post) actually seems to me to be an excellent case in point. There's no way he had the tools to measure the intensity of light in 1650! It follows from the idea of something's intensity being spread out over a greater area that it would occur over the surface of a sphere. If you trace all the points a certain distance from something, you have a sphere--and if you "spread out" the force of that something over the surface of that sphere, you arrive at the inverse square law. Eiuol, I agree that we are made aware of our intuitions by experience. But they go beyond what sense experience alone can provide. The sense in which they are intuitive is that I can draw a simple machine on a piece of paper, show it to a child he will be able to tell just from looking at the paper and thinking about it, not only what will happen when I build that machine, but what MUST happen! Sense experience can never tell us what must always happen. It can just tell us what we've sensed. Spiral, I don't believe you understand the problem of induction. "If you see one apple, and then another (etc.)," you say, "I hope you can draw the conclusion pretty fast!" But if you meet one Dutch person who is tall, and then another, and then another, at what point are you justified in drawing the conclusion "Dutch people are always tall," in the same way you can draw the conclusion, "1+1=2"? Experience + induction can NEVER lead to a universal statement (such as those of mathematics and science). I think the ambiguity in your explanation in contained in the way you're using the phrase, "logical leap," and this will be clear if you try to define it precisely. Plasmatic, in reference to the article you cited about the analytic-synthetic distinction. The author says, "definitions that are formed with reference to things in the world are called a posteriori. (They are posterior to experience.) Those that could be formed without reference to the way the world is would be a priori. (They are prior to experience.) But concepts can’t be formed without reference to the way the world is." I don't accept that way of defining a priori. Rather than the distinction being about what is referenced by the concept, it is about what justifies them. While a posteriori statements are justified by sense experience alone, a priori statements are justified independent of experience. The author himself admits the following: "Such mature essentialized definitions are the building blocks of the exact sciences. They make it possible to have truly universal statements, statements that allow no exception. If what you measure doesn’t come out to be the ratio of voltage to current, then what you are measuring is not resistance. Simple. If the angles don’t add up to 180°, then the figure isn’t a planar triangle, because that sum can be derived from the very definition of a planar triangle." That is pretty much what I'm saying in this post. But such statements can never be justified by pure experience, per the problem of induction. And they are NOT analytic--that is precisley what Kurt Godel proved they are not (at least with mathematics)! I haven't had time to listen to the lecture yet, but I agree with what you're saying about the state of physics being deplorable. It is precisely empiricism that has lead to the current situation in physics. What is ITOE? (I'm assuming the last two words are "Objectivist Epistemology…"?) The description you give about "where understanding the linguistic nature of concepts come in," seems to be precisely what Godel proved was not the case (that mathematics was a matter of the extrapolation of man-made concepts). Logic is what you can use FROM 1+1=2. But I am talking about how you get there in the first place. Neither logic alone, nor experience alone, nor the two working together can get you there! You say "the meaning of a concept is its referents." What is the referent of the number 1? You lost me at the bottom of your post.
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