The Logical Leap: Induction in Physics

[Philip Coates]

> Phenomenal knowledge is limited to what we can perceive via our sense organs, but it is real knowledge. [GHS]

But it's not of the noumenal world and that is real reality according to Kant. So knowledge of a world we create which we may or may not have created correctly is not real knowledge.

> Moreover, Kant did not claim that we "cannot really 'know' reality." He said that we cannot know the world as it is in itself

My point is not about what K -claims-. My point - and that of other philosophers or of anyone with common sense - is that if you can't know the world as it really is, then you don't know reality with certainty.

> Where Kant speaks of our forms of perception, Rand speaks of our means of perception

But they mean very different things. For Rand our form of perception does give us reality; for Kant we are forever separated from it and have to trust our 'filters', our created wordl to be accurate. But on K's philosophy, how do we know that for sure?

> Kant did not set out to prove that we have accurate knowledge of reality. He thought it is quite obvious that we do possess such knowledge

Once again, we are not talking about what Kant thought his philosophy showed, but about what his bifurcation into two different worlds actually does.

> Phil's contention that Kant was essentially a skeptic

Quit distorting my exact words. And stripping away the qualifications. Go back and reread post #111.

Point #4 in post #111.

[Philip Coates]

Subject: Kant and Skepticism

You want someone else who says it and explains it besides me?

Maybe it will be clearer coming from a professional philosopher. From an essay on Immanuel Kant's skeptical conclusions:

http://www.stephenhicks.org/2010/01/12/kants-skeptical-conclusion/

"Immanuel Kant is the most significant thinker of the Counter-Enlightenment. His philosophy, more than any other thinker’s, buttressed the pre-modern worldview of faith and duty against the inroads of the Enlightenment; and his attack on Enlightenment reason more than anyone else’s opened the door to the nineteenth-century irrationalists and idealist metaphysicians.

...Kant is sometimes considered to be an advocate of reason. Kant was in favor of science, it is argued. He emphasized the importance of rational consistency in ethics. He posited regulative principles of reason to guide our thinking, even our thinking about religion. And he resisted the ravings of Johann Hamann and the relativism of Johann Herder. Thus, the argument runs, Kant should be placed in the pantheon of Enlightenment greats.[2] That is a mistake.

The fundamental question of reason is its relationship to reality. Is reason capable of knowing reality—or is it not? Is our rational faculty a cognitive function, taking its material from reality, understanding the significance of that material, and using that understanding to guide our actions in reality—or is it not? This is the question that divides philosophers into pro- and anti-reason camps, this is the question that divides the rational gnostics and the skeptics, and this was Kant’s question in his Critique of Pure Reason.

Kant was crystal clear about his answer. Reality—real, noumenal reality—is forever closed off to reason, and reason is limited to awareness and understanding of its own subjective products. Reason has “no other purpose than to prescribe its own formal rule for the extension of its empirical employment, and not any extension beyond all limits of empirical employment.”[3] Limited to knowledge of phenomena that it has itself constructed according to its own design, reason cannot know anything outside itself. Contrary to the “dogmatists” who had for centuries held out hope for knowledge of reality itself, Kant concluded that “[t]he dogmatic solution is therefore not only uncertain, but impossible.”[4]

Thus Kant, that great champion of reason, asserted that the most important fact about reason is that it is clueless about reality.

Part of Kant’s motivation was religious. He saw the beating that religion had taken at the hands of the Enlightenment thinkers, and he agreed strongly with them that religion cannot be justified by reason. So he realized that we need to decide which has priority—reason or religion. Kant firmly chose religion. This meant that reason had to be put in its proper, subordinate, place. And so, as he stated famously in the Second Preface to the first Critique, “I here therefore found it necessary to deny knowledge in order to make room for faith.”[5] One purpose of the Critique, accordingly, was to limit severely the scope of reason. By closing noumenal reality off to reason, all rational arguments against the existence of God could be dismissed."

Edited July 16, 2010 by Philip Coates

[George H. Smith]

Subject: Kant and Skepticism

You want someone else who says it and explains it besides me?

Maybe it will be clearer coming from a professional philosopher. From an essay on Immanuel Kant's skeptical conclusions:

http://www.stephenhicks.org/2010/01/12/kants-skeptical-conclusion/

"Immanuel Kant is the most significant thinker of the Counter-Enlightenment. His philosophy, more than any other thinker’s, buttressed the pre-modern worldview of faith and duty against the inroads of the Enlightenment; and his attack on Enlightenment reason more than anyone else’s opened the door to the nineteenth-century irrationalists and idealist metaphysicians.

...Kant is sometimes considered to be an advocate of reason. Kant was in favor of science, it is argued. He emphasized the importance of rational consistency in ethics. He posited regulative principles of reason to guide our thinking, even our thinking about religion. And he resisted the ravings of Johann Hamann and the relativism of Johann Herder. Thus, the argument runs, Kant should be placed in the pantheon of Enlightenment greats.[2] That is a mistake.

The fundamental question of reason is its relationship to reality. Is reason capable of knowing reality—or is it not? Is our rational faculty a cognitive function, taking its material from reality, understanding the significance of that material, and using that understanding to guide our actions in reality—or is it not? This is the question that divides philosophers into pro- and anti-reason camps, this is the question that divides the rational gnostics and the skeptics, and this was Kant’s question in his Critique of Pure Reason.

Kant was crystal clear about his answer. Reality—real, noumenal reality—is forever closed off to reason, and reason is limited to awareness and understanding of its own subjective products. Reason has “no other purpose than to prescribe its own formal rule for the extension of its empirical employment, and not any extension beyond all limits of empirical employment.”[3] Limited to knowledge of phenomena that it has itself constructed according to its own design, reason cannot know anything outside itself. Contrary to the “dogmatists” who had for centuries held out hope for knowledge of reality itself, Kant concluded that “[t]he dogmatic solution is therefore not only uncertain, but impossible.”[4]

Thus Kant, that great champion of reason, asserted that the most important fact about reason is that it is clueless about reality.

Part of Kant’s motivation was religious. He saw the beating that religion had taken at the hands of the Enlightenment thinkers, and he agreed strongly with them that religion cannot be justified by reason. So he realized that we need to decide which has priority—reason or religion. Kant firmly chose religion. This meant that reason had to be put in its proper, subordinate, place. And so, as he stated famously in the Second Preface to the first Critique, “I here therefore found it necessary to deny knowledge in order to make room for faith.”[5] One purpose of the Critique, accordingly, was to limit severely the scope of reason. By closing noumenal reality off to reason, all rational arguments against the existence of God could be dismissed."

Hicks presents the standard Randian line on Kant. I never imagined that you were clever enough to concoct the "Kant qua skeptic" argument all by your lonesome; I knew you were merely parroting what you had read elsewhere. So what? You are still wrong.

Hicks cherry-picks isolated, out-of-context snippets from Kant (such as his objections to "dogmatists") to make it appear that Kant said things he never meant. To assert that reason, according to Kant, is "clueless about reality," is absurd. So is the claim that Kant launched an attack on "Enlightenment reason." So is the claim that Kant sought to dismiss "all rational arguments against the existence of God." (Kant's withering criticisms of "rational arguments" for the existence of God are among the best ever written; they remain classics to this day.) What a crock all this is.

As for the question, "Is reason capable of knowing reality—or is it not?" Kant answered this with a resounding Yes. The fact that he may have failed in his vindication of reason does not transform him into a skeptic.

Ghs

[George H. Smith]

> Phenomenal knowledge is limited to what we can perceive via our sense organs, but it is real knowledge. [GHS]

But it's not of the noumenal world and that is real reality according to Kant. So knowledge of a world we create which we may or may not have created correctly is not real knowledge.

Please explain to me how we can know the world without perceiving it in some form, as determined by the nature of our sense organs. This was Kant's point about the thing-in-itself, or the noumenal world. As G.J. Warnock explains in his excellent article on Kant in A Critical History of Western Philosophy (ed., D.J. O'Connor, Free Press, 1964, 300):

It is...certain that what exists appears to human beings in a particular way, and is by them classified interpreted, categorized, and described in a particular manner. If our sense organs had been radically different from what they are, certainly the world would have appeared to us as being radically different....Thus though our faculties and capacities make no difference at all to the nature of what exists in itself, they do partly determine the character of the world as it appears; they determine the general form that it has....

Nothing in this approach leads to skeptical conclusions.

> Moreover, Kant did not claim that we "cannot really 'know' reality." He said that we cannot know the world as it is in itself

My point is not about what K -claims-. My point - and that of other philosophers or of anyone with common sense - is that if you can't know the world as it really is, then you don't know reality with certainty.

Again, Kant didn't say that we can't know the world as it really is. The noumenal world is not the world as it "really is." It is the world as known independently of our perception of it. As Warnock explains in his article on Kant:

[T]he desire to know, or even to talk, about the world as it is in itself is a desire without sense. It amounts to the desire to perceive without the employment of any particular mode of perception, to describe without the use of any particular descriptive vocabulary. In perception and thought we necessarily employ those faculties and propensities that we have; our subject matter is, unavoidably, the world as it appears to one possessed of those faculties.

In this respect, as I pointed out earlier, Kant's approach bears certain similarities to Rand's. Both agree that a knowledge of reality unvarnished by perception is impossible. They agree, moreover, that the fact that all knowledge is processed, with the nature of the process being determined, in part, by the specific characteristics of our sensory organs, does not invalidate our knowledge or render it unreliable.

Thus, contrary to Descartes and other "dogmatic" metaphysicians (i.e., rationalists) who maintained that our senses act as distorting mediums, and that ideal knowledge consists of knowledge uncontaminated by sensory data, Kant defends the authenticity and reliability of empirical knowledge. He does so by distinguishing the form of knowledge from its content. The fact that we perceive reality in a specific form and organize perceptual data in a certain manner, as determined by our sensory and cognitive attributes, does not render our knowledge unreliable.

If this fundamental approach qualifies as skepticism, or if it leads to skeptical conclusions, then I say, "Three cheers for skepticism!"

Ghs

[George H. Smith]

Once again, we are not talking about what Kant thought his philosophy showed, but about what his bifurcation into two different worlds actually does.

Noumena and phenomena, for Kant, are not two different worlds. They are the same world viewed from two different perspectives.

> Phil's contention that Kant was essentially a skeptic

Quit distorting my exact words. And stripping away the qualifications. Go back and reread post #111.

Point #4 in post #111.

I'm very well aware of what your horseshit argument is. I feel silly even discussing it.

Ghs

[merjet]

Excellent post #124, GHS. I have a hunch that when Rand learned that Kant tried to drain all self-interest from morality, it upset her so much she was thereafter incapable of giving him any kind of a fair hearing. Lest anyone jump to such an unreasonable conclusion, I am no fan of Kant.

[merjet]

duplicate deleted

Edited July 16, 2010 by Merlin Jetton

[bmacwilliam]

Thus, contrary to Descartes and other "dogmatic" metaphysicians (i.e., rationalists) who maintained that our senses act as distorting mediums, and that ideal knowledge consists of knowledge uncontaminated by sensory data, Kant defends the authenticity and reliability of empirical knowledge. He does so by distinguishing the form of knowledge from its content. The fact that we perceive reality in a specific form and organize perceptual data in a certain manner, as determined by our sensory and cognitive attributes, does not render our knowledge unreliable.

This I have never understood properly.

How is it that with limited, imperfect, and easily fooled senses that our knowledge can be anything but unreliable?

I can see that through logic, modelling and confirmation that reliability can increase and perhaps approach total reliability. It seems that "raw" knowledge is inherently unreliable, but deeper, more complete and reliable knowledge is certainly possible in spite of this. But this doesn't remove the basic unreliability of knowledge. In fact, isn't it skepticism itself, in a rather direct way, responsible for our knowledge growth?

Is this what he means?

Bob

[dan2100]

Thus, contrary to Descartes and other "dogmatic" metaphysicians (i.e., rationalists) who maintained that our senses act as distorting mediums, and that ideal knowledge consists of knowledge uncontaminated by sensory data, Kant defends the authenticity and reliability of empirical knowledge. He does so by distinguishing the form of knowledge from its content. The fact that we perceive reality in a specific form and organize perceptual data in a certain manner, as determined by our sensory and cognitive attributes, does not render our knowledge unreliable.

This I have never understood properly.

How is it that with limited, imperfect, and easily fooled senses that our knowledge can be anything but unreliable?

How do you know that the senses are unreliable or less reliable than, say, the intellect -- presuming the two to be different?

[BaalChatzaf]

Let me recommend a book that will unsnarl the difficulties of the Kantian distinction between the noumenal and the phenomenal world. Please read -Invariances:The Structure of the Objective World- by Robert Nozick. Nozick, who is no longer with us, was one of the smartest 20th century philosophers. None of his books are "easy reads" but they are well constructed and presented.

The "real" reality is not lost or destroyed by the transformations performed by out sense organs and the temporal orderings produced by our memory. If one is clever one can construct the inverse transformations (some of them, at least) and recover the "real" reality from the phenomena. This is what physics has been used for since Newton.

One can reconstruct the "real" circle from a finite set of its projections on a plane, for example. Computer Tomography Scanning does a similar thing with x-ray and MRI projections through tissue. This is how an MRI machine, for example, reconstructs the real body (or its geometry) from a finite set of projection made by the scanning machine.

Ba'al Chatzaf

[Michael Stuart Kelly]

Your analysis of space and time is too skeptical (to use Phil's word) for Kant's taste. He would not agree that space and time are simply "artifact of our limited mind." Rather, he maintains that these forms of perception are necessary presuppositions of all experience and therefore of all knowledge.

Moreover, Kant did not claim that we "cannot really 'know' reality." He said that we cannot know the world as it is in itself, i.e., reality as it exists apart from our perception of it. We know the world only as it appears to our senses, and how it appears is influenced by the nature of our sensory organs. This is the world of phenomena, i.e., things as they appear to us.

It is a huge mistake -- one that Phil commits again and again -- to assume that Kant's phenomenal world is somehow not real, or that it is a distortion of reality. This is not Kant's point at all. Phenomenal knowledge is limited to what we can perceive via our sense organs, but it is real knowledge.

Although I don't wish to push the point too far, there are interesting parallels between Kant's approach and Rand's. Where Kant speaks of our forms of perception, Rand speaks of our means of perception; and, like Kant, Rand insists that our sensory organs have specific natures which determine how we perceive reality. And, like Kant, Rand insists that to speak of knowing reality as it exists apart from our perception of it makes little if any sense, for this would require knowledge without a means of attaining that knowledge. Lastly, Rand, like Kant, argues that although our knowledge is limited to our specific means of perception, this limitation does not somehow invalidate the knowledge that we acquire thereby.

Major differences between Kant and Rand emerge when we move from forms of perception to Kant's categories of the understanding. They differed as well in how they approached the fundamental problems of epistemology. Kant did not set out to prove that we have accurate knowledge of reality. He thought it is quite obvious that we do possess such knowledge, including absolutely certain knowledge , based solely on reason, of a fundamental kind. (The latter are Kant's so-called synthetic a priori truths.)

Kant then proceeds to ask his celebrated "transcendental" question, viz: What presuppositions must be true in order to explain the fact that we possess the knowledge that we do? What must be true of our senses and of our mind in order to make sense of our experiences and account for our knowledge of reality?

Kant's transcendental methodology is why we frequently find "stolen concept" arguments in his writings. For example, to those philosophers who, like Hume, denied necessary causal relationships, Kant replies (in effect) that such relationships are presupposed in any attempt to make sense of the world, and that even philosophers who deny causation must assume its truth in science and other fields. Another example is found in Kant's defense of free will. One of his arguments is essentially identical to the stolen concept argument presented by NB in "The Contradiction of Determinism." to the effect that knowledge presupposes volition.

There is much more that could be said, obviously, but I will stop here.

George,

This is one of the best layman-term-like explanations of Kant I have ever read.

btw - I believe Kan't transcendental nut gets cracked when we include our senses and mind as part of reality. They are not separate, I don't care if there is an "in here" and "out there." Perspective merely implies that someone is perceiving, not a separate metaphysical condition for reality per se (an "out there" that we can never "know"). Our senses and mind are made out of the same stuff as reality, thus they are fit to register and process correct knowledge of it--i.e., such registration and processing belong to the same reality that is being registered and processed.

In metaphysical terms, priority-wise we are a part of all of reality. We fall under it. All of reality is not part of us. Instead, it governs what we are.

If one presumes that the mind and knowledge somehow exist as a system outside of reality, that the mind and knowledge are on equal metaphysical footing as all of reality, this transcendental stuff--and even categorical imperatives--make a hell of a lot more sense. But that presumption is obviously false.

Another point is that, from what little I have read of Kant, he dismissed the origin of concepts in his "a priori"stuff. Once you have a concept and it is defined, "a priori" can kick in. However, as experience is needed to get to that point, i.e., needed to formulate the concept and definition in the first place, it seems like a cop-out or shooting yourself in the foot to dismiss experience as not needed for "a priori" reasoning.

I want to mention that this is my own thinking, not stuff I have read in Rand.

Michael

[merjet]

Another point is that, from what little I have read of Kant, he dismissed the origin of concepts in his "a priori"stuff. Once you have a concept and it is defined, "a priori" can kick in. However, as experience is needed to get to that point, i.e., needed to formulate the concept and definition in the first place, it seems like a cop-out or shooting yourself in the foot to dismiss experience as not needed for "a priori" reasoning.

This reminded me of something I wrote in 1995. Go here and then page 72.

[bmacwilliam]

Thus, contrary to Descartes and other "dogmatic" metaphysicians (i.e., rationalists) who maintained that our senses act as distorting mediums, and that ideal knowledge consists of knowledge uncontaminated by sensory data, Kant defends the authenticity and reliability of empirical knowledge. He does so by distinguishing the form of knowledge from its content. The fact that we perceive reality in a specific form and organize perceptual data in a certain manner, as determined by our sensory and cognitive attributes, does not render our knowledge unreliable.

This I have never understood properly.

How is it that with limited, imperfect, and easily fooled senses that our knowledge can be anything but unreliable?

How do you know that the senses are unreliable or less reliable than, say, the intellect -- presuming the two to be different?

I honestly do not understand the question. I don't think it matters how unreliable they are. The point is simply that if they (senses and/or intellect) are wrong sometimes, they are unreliable. Since this obviously is indeed the case, I don't understand the argument to the contrary (if there is one).

Bob

[bmacwilliam]

Another point is that, from what little I have read of Kant, he dismissed the origin of concepts in his "a priori"stuff. Once you have a concept and it is defined, "a priori" can kick in. However, as experience is needed to get to that point, i.e., needed to formulate the concept and definition in the first place, it seems like a cop-out or shooting yourself in the foot to dismiss experience as not needed for "a priori" reasoning.

Michael

Well doesn't that dismiss an entire realm of mathematical knowledge and principles that are not connected to experience in any real way? Even with simple arithmetic one could argue that the knowledge exists and could be discovered outside of experience. But the much more abstract necessary truths are most certainly far outside the realm of experience, but is knowledge of these truths nonetheless based on experience? I don't think so.

Perhaps with arithmetic you can argue that arithmetic is essentially empirical regularities. But I don't think that position makes much sense. The rules of arithmetic are necessary truths quite separate from everything - time, space, experience - whatever.

Paul Benacerraf (Math Philosopher) had a thought experiment that went something like this (roughly - from foggy memory):

Suppose that you know that 2+2=4 and you invite a particular couple over every Thursday for dinner with your wife and yourself and of course there's 4 people around the table as expected every time. All of a sudden you send out the same invitation for two but now there's somehow 5 people around the table. Then you walk up 4 flights of stairs and end up on the fifth floor. Your sister has two sets of twins but somehow has 5 kids. Obviously something has changed, if you're not insane (counting wrong) then you must conclude:

1) The physical laws of the Universe have changed

OR...

2) The rules of Arithmetic/Math have changed

Think about this, because if you pick (1) this means that you conclude that Arithmetic and Mathematical truths are OUTSIDE of experience. I think this is indeed the case.

Bob

Edited July 16, 2010 by Bob_Mac

[George H. Smith]

I previously quoted G.J. Warnock on Kant. Below are parts 2 and 3 of a 5 part interview with Warnock about Kant. These parts have the most relevance to the current discussion, but I recommend listening to the other 3 parts as well. The interviewer is Brian Magee.

Wanock, a remarkably lucid speaker, begins part 2 by explaining Kant's objection to the analytic-synthetic dichotomy. Sir Geoffrey James Warnock (1923–1995) was a philosopher and Vice-Chancellor of Oxford University.

The HTML settings have disappeared from my Options menu, so I am unable to embed the videos. Here are the links.

Geoffrey Warnock on Kant: Section 2

Geoffrey Warnock on Kant: Section 3

Ghs

[merjet]

Obviously something has changed, if you're not insane (counting wrong) then you must conclude:

1) The physical laws of the Universe have changed

OR...

2) The rules of Arithmetic/Math have changed

Think about this, because if you pick (1) this means that you conclude that Arithmetic and Mathematical truths are OUTSIDE of experience. I think this is indeed the case.

I wouldn't pick either one.

[bmacwilliam]

Obviously something has changed, if you're not insane (counting wrong) then you must conclude:

1) The physical laws of the Universe have changed

OR...

2) The rules of Arithmetic/Math have changed

Think about this, because if you pick (1) this means that you conclude that Arithmetic and Mathematical truths are OUTSIDE of experience. I think this is indeed the case.

I wouldn't pick either one.

Well then, what would you conclude if your experience began telling you that 2 plus 2 now equals 5?

Bob

[merjet]

Well then, what would you conclude if your experience began telling you that 2 plus 2 now equals 5?

My experience isn't telling me that. You posed different situations and I see no anomaly at all.

[bmacwilliam]

Well then, what would you conclude if your experience began telling you that 2 plus 2 now equals 5?

My experience isn't telling me that. You posed different situations and I see no anomaly at all.

Well I hope your experience is not telling you that. It's just a thought experiment to shine some light on where you feel the Mathematical truths lie. There's not an "anomoly" as I see it. Either the laws of the universe changed, or Math did. Which one is more plausible? If you think it's neither then I guess you're somewhere in the middle of Math being anchored in experience and not being anchored in experience and I don't think that position makes sense.

Bob

[merjet]

Well I hope your experience is not telling you that. It's just a thought experiment to shine some light on where you feel the Mathematical truths lie. There's not an "anomoly" as I see it. Either the laws of the universe changed, or Math did. Which one is more plausible? If you think it's neither then I guess you're somewhere in the middle of Math being anchored in experience and not being anchored in experience and I don't think that position makes sense.

Much, but not all, of math is anchored in experience. That makes no sense to you?

[dan2100]

Thus, contrary to Descartes and other "dogmatic" metaphysicians (i.e., rationalists) who maintained that our senses act as distorting mediums, and that ideal knowledge consists of knowledge uncontaminated by sensory data, Kant defends the authenticity and reliability of empirical knowledge. He does so by distinguishing the form of knowledge from its content. The fact that we perceive reality in a specific form and organize perceptual data in a certain manner, as determined by our sensory and cognitive attributes, does not render our knowledge unreliable.

This I have never understood properly.

How is it that with limited, imperfect, and easily fooled senses that our knowledge can be anything but unreliable?

How do you know that the senses are unreliable or less reliable than, say, the intellect -- presuming the two to be different?

I honestly do not understand the question. I don't think it matters how unreliable they are. The point is simply that if they (senses and/or intellect) are wrong sometimes, they are unreliable. Since this obviously is indeed the case, I don't understand the argument to the contrary (if there is one).

Bob

There's a difference between sense perception and perceptual judgment -- between, say, feeling something to be cold to the touch and judging it to be cold or, with the more classical example, between seeing a stick in water and judging it to be bent. In this sense (pun not intended), the senses merely give evidence; they don't, per se, contain judgments. It is the judgments, though, that might be right or wrong. Think about it this way, one would never say, I think, that a rock is wrong for, say, falling or staying in place on a ledge, but one might be wrong about judging whether the rock will fall or will stay in place. (For example, if you close your eyes, assuming you have roughly normal human eyes, and press on them, you'll see colors, maybe green. Your visual system is literally detecting this, but this is not because it's wrong. You would be wrong, however, to judge that the inside of your eyelids are green. Or so I've been led to believe.)

Moreover, doubt (of any sort) always presupposes a standard by which to doubt something. Typically, the presumed standard for the unreliability of the senses is other evidence of the senses. To stick with the stick in water example, you view the stick out of water and say, "A ha! It's not really bent!" But this means trusting sensorily reliability -- in this case, trusting your eyes when viewing the stick out of water. (I believe David Kelley brought up the example of why no one uses the argument that the same stick in tar looks like part of it no longer exists as a skeptical attack on sense perception: it's too easy to confute.) In this case, as Coppleston (IIRC, in his multivolume history whilst discussing Berkeley) and others have pointed out, it takes sense perception out of context: the stick is always supposed to appear the same regardless of context. (The same criticism can be used against the square tower, the different perceived heat of buckets (put one hand in ice water, another in hot water, then, after a few minutes, place both hands in another bucket of lukewarm water; to one hand it will feel hot, to the other cold), and how objects seem larger as one moves closer to them. All these skeptical arguments presume that some perceived features should remain constant despite varying conditions of perception.)

[bmacwilliam]

Well I hope your experience is not telling you that. It's just a thought experiment to shine some light on where you feel the Mathematical truths lie. There's not an "anomoly" as I see it. Either the laws of the universe changed, or Math did. Which one is more plausible? If you think it's neither then I guess you're somewhere in the middle of Math being anchored in experience and not being anchored in experience and I don't think that position makes sense.

Much, but not all, of math is anchored in experience. That makes no sense to you?

No, in fact it does not. Just because we CAN experience math in a physical way doesn't mean that experience is necessary for mathematical knowledge. To me Math is either based in experience or it's not. No halfsies....

But even if only some of math is outside of experience, the sense/knowledge connection is broken.

Bob

[bmacwilliam]

Moreover, doubt (of any sort) always presupposes a standard by which to doubt something. Typically, the presumed standard for the unreliability of the senses is other evidence of the senses. To stick with the stick in water example, you view the stick out of water and say, "A ha! It's not really bent!" But this means trusting sensorily reliability -- in this case, trusting your eyes when viewing the stick out of water.

No I don't see it this way at all. This logic seems rather silly to me.

I see this situation as consistent partial trusting of your senses and using logic to uncover the deeper truths and often the apparent or real "errors" (or causes of discepancy that is not in fact error) of the senses as more data is collected. To say that you "trust sensory reliability" in order to "confirm sensory unreliability" smells a bit like a typical Objectivist bait and switch tactic when the truth is that you consistently partially trust your senses in all cases and use logic to fill the gaps and build a knowledge model that fits the facts.

Bob

[Dragonfly]

The first thing one should ask oneself is "what is exactly meant by reality"? The notion of something called reality is the result of the fact that our experiences are not random but seem to reflect some invariant "core", where invariant doesn't mean that there are no changes in that core, but that those changes follow regularities, in contrast for example to our experiences in a dream. So we formed the abstraction "reality" as that reliable and dependable core that is behind our experiences. That core would be the noumenal world and our experiences the phenomenal world. By definition the noumenal world is unknowable, it is an abstraction that we form on the basis of our experiences, that show systematic regularities that we can formalize as physical laws. We can make models of which we assume that these are representative of reality, but these remain models that are based on empirical evidence, but that are not reality itself, just as we can draw a figure that is representative of the concept "circle", but that is not itself a circle, which is an abstract notion.

In modern physics this difference between "reality" and our models of reality is even much more pronounced than in the "Newtonian" world of the past. This is illustrated by the fact that there exist many different "interpretations" of quantum mechanics that are completely different, but that lead to exactly the same formalism that allows us to make experimental predictions of unparallelled precision. That can only mean that those interpretations are irrelevant, there is no way to conclude that a certain interpretation is the correct one as there is no way to test one interpretation against another one. Such interpretations are merely crutches to help us conceiving that model in images that we more or less intuitively can relate to. Nevertheless there remains always a certain "weirdness" that we cannot reason away. Different interpretations merely shift that weirdness to different images, so that the choice of interpretation becomes a personal preference. From our intuition formed by living in a macroscopic world we'd like to imagine the world as consisting of exactly localized masses, as that is the way we perceive the world in our daily life. Nevertheless that image is wrong. So we cannot merely not know "reality", but we cannot even assimilate our experiences via scientific experiments at atomic scales by integrating them to a clear intuitive picture, we can only use our instruments and logic to describe them (just as we cannot perceive spaces of higher dimensions, only reason about them). That is also why Feynman said that nobody understands quantum mechanics, that doesn't mean that nobody could understand the technical details, but that the world they reveal is not well conceivable to us.

[bmacwilliam]

Senses, like the toss of a coin give you partial information (if you can only see one side each toss). You see heads come up, so you can make a conclusion (the coin has a head on at least one side). You can't conclude for sure that the other side is tails. And of course there's even a small chance that you hallucinated the head, but that's so small we normally dismiss this possibility or it doesn't enter our mind. Certainly if we keep tossing the coin and keep seeing only heads, very quickly the possibility of hallucination becomes vanishingly small, and the possibility of the coin having heads on both sides becomes more and more plausible (never certain).

So we can play word games and pretend that we're assuming our senses are reliable in order to confirm or deny that they are unreliable.

Or we can get real, use math, and compute the statistical probability of every possibility taking into account our possibility for error and eventually conclude that the coin is heads on both sides when we reach some level of certainty we're comfortable with. That's what's really happening, not the former.

In more math-like lingo: IT IS CERTAINLY POSSIBLE TO REACH AN ARBITRARY LEVEL OF CERTAINTY WITH ERROR-PRONE EQUIPMENT - EVEN IF WE'RE ONLY ESTIMATING OUR RELIABILITY!

Even if this might not be clear linguistically, it is mathematically.

Bob

Edited July 16, 2010 by Bob_Mac