Nobel physicist calls ID "dead-end" idea for science

[ceo_esq]

Sure they are - they're based on the behavior of physical systems.

Are you suggesting that statements about, say prime numbers, or logical relationships, are really empirical statements about brains and computers? You might equally say that statements about anything from art to chemistry are not about the phenomena they appear to refer to, but are really empirical statements about brains.

Good luck persuading people, particularly mathematicians and scientists, that all mathematics is empirical. The standard sense of the term empirical is not used in that way.

[ETA: Does your stance imply that we need to reject, as well, the customary understanding of a priori knowledge/truths?]

Oh, really? Take away all physical tools, and let him produce mathematical results. Let him perform a single calculation without the physical world.

The more relevant questions are whether the results are physical, and whether their truth can only be derived by reference to the physicality of the object of study (not the tool). Mathematicians say "no"; you apparently think "yes".

Switching contexts, an artist couldn't produce artistic results without a physical universe in which to work - yet few would suggest that art is a purely empirical enterprise, and that statements about, say, artistic merit are scientific statements.

If you make a statement about God that is a prediction, or that permits a prediction to be made, you're within the bounds of science and reason. If you don't, your statement has no implications.

A statement that does not constitute or imply a prediction to which the empirical, experimental method can be applied does not have scientific implications (although it could have rational ones; one can't equate reason with science), and science could not tell you what sort of implications it might have. But neither does science tell us whether all implications are empirical ones, or whether there is no meaning outside the empirical context. I think that was part of Dr. Cornell's point, and it seems to be a generally acknowledged truth (present company excepted).

 

[Melendwyr]

Are you suggesting that statements about, say prime numbers, or logical relationships, are really empirical statements about brains and computers? You might equally say that statements about anything from art to chemistry are not about the phenomena they appear to refer to, but are really empirical statements about brains.

There is certainly a distinction between chemistry (to use one example) and mathematics. In chemistry, we use concepts to model the behavior of chemicals. In mathematics, we use computational systems to study the associations between concepts. Our brains are used in both, of course.

Good luck persuading people, particularly mathematicians and scientists, that all mathematics is empirical. The standard sense of the term empirical is not used in that way.

Most mathematicians and scientists do not commonly think about the systems on which their minds are being run. Ultimately, the only way to determine whether a mathematical assertion is correct is to reference some empirical data. (Watching young children trying to learn a new mathematical technique is a particularly good demonstration of this principle. Oftentimes they will be convinced that they followed the correct procedure, even though they got the wrong answer. By what means could they determine that their answer is incorrect?)

[ETA: Does your stance imply that we need to reject, as well, the customary understanding of a priori knowledge/truths?]

Yes. The truths that are of the world that creates us are eternal and immutable. We can also never know for certain what they are.

The more relevant questions are whether the results are physical, and whether their truth can only be derived by reference to the physicality of the object of study (not the tool). Mathematicians say "no"; you apparently think "yes".

The results aren't physical? How do the mathematicians speak, write, or otherwise communicate them?

Switching contexts, an artist couldn't produce artistic results without a physical universe in which to work - yet few would suggest that art is a purely empirical enterprise, and that statements about, say, artistic merit are scientific statements.

If the concept of 'artistic merit' is anything other than a wholly arbitrary one, then it's subject to scientific examination. If it is arbitrary, it has no reality for science to grasp it by. (Whether given individuals held specific artistic standards, the nature of those standards, and similar points, are still within the domain of science as historical truths.)

But neither does science tell us whether all implications are empirical ones, or whether there is no meaning outside the empirical context. I think that was part of Dr. Cornell's point, and it seems to be a generally acknowledged truth (present company excepted).

Implications that have no empirical content at all are empty. A difference that makes no difference is no difference.

 

[ceo_esq]

I'll be delighted to. Just explain how you plan to permit "him" to still be there to produce the results -- and how you plan to have him communicate them to you without use of the physical.

Good point.

There is certainly a distinction between chemistry (to use one example) and mathematics. In chemistry, we use concepts to model the behavior of chemicals. In mathematics, we use computational systems to study the associations between concepts. Our brains are used in both, of course.

True, but this distinction is part of the reason why mathematics is generally held not to be a branch of empirical science. It is a question both of subject-matter and of epistemic basis. Dr. Stewart Shapiro observes in Thinking About Mathematics (Oxford UP, 2000) that mathematics appears to be different from other "epistemic endeavors" (science, in particular):

Basic mathematical propositions do not seem to have the contingency of scientific propositions. Intuitively, there do not have to be nine planets of the sun. There could have been seven, or none. Gravity does not have to obey an inverse-square law, even approximately. In contrast, mathematical propositions, like 7 + 5 = 12, are sometimes held up as paradigms of necessary truths. Things just cannot be otherwise.

The scientist readily admits that her more fundamental theses might be false. This modesty is supported by a history of scientific revolutions, in which long-standing, deeply held beliefs were rejected. Can one seriously maintain the same modesty for mathematics? Can one doubt that the induction principle holds for the natural numbers? Can one doubt that 7 + 5 = 12? Have there been mathematical revolutions that resulted in the rejection of long-standing mathematical beliefs? On the contrary, mathematical methodology does not seem to be probabilistic in the way that science is. Is there even a coherent notion of the probability of a mathematical statement? At least prima facie, the epistemic basis of the induction principle, or '7 + 5 = 12', or the infinity of the prime numbers, is firmer, and different in kind, than that of the principle of gravitation. Unlike science, mathematics proceeds via proof. ...

There is no contingency in the mentally grasped mathematical ideas. We may, of course, err in our grasp of mathematical ideas or in attempting a demonstration, but, if properly carried out, the methodology of mathematics delivers only necessary truths. Of course, this perspective is not available to the empiricists, and they do not have such a straightforward explanation of the seeming necessity of mathematics.

A. J. Ayer, in his famous Language, Truth and Logic (1936), offered the following observation on empiricists (in this context, those folks who, like you, have suggested from time to time that mathematics is truly a science):

[W]hereas a scientific generalisation is readily admitted to be fallible, the truths of mathematics and logic appear to everyone to be necessary and certain. But if empiricism is correct, no proposition which has a factual content can be necessary or certain. Accordingly the empiricist must deal with the truths of mathematics or logic in one of the two following ways: he must say either that they are not necessary truths ... or he must say that they have no factual content, and then he must explain how a proposition which is empty of all factual content can be true and useful and surprising.

Faced with the dilemma Ayer outlined, you seem to be responding exactly as he would have predicted (specifically, you've effectively taken the first route).

The results aren't physical? How do the mathematicians speak, write, or otherwise communicate them?

Speaking, writing, and otherwise communicating about abstractions is something human beings do often and, arguably, rather well.

If the concept of 'artistic merit' is anything other than a wholly arbitrary one, then it's subject to scientific examination. If it is arbitrary, it has no reality for science to grasp it by.

Particularly in light of your previous dubious assertions about the nature of mathematics, it would be reassuring to see proofs for such propositions as All non-arbitrary concepts are subject to scientific examination, or Arbitrary concepts are not real concepts.

Implications that have no empirical content at all are empty.

Yet as the eminent mathematical logician Willard Quine, in discussing the undeniable usefulness of mathematics to the empirical sciences, acknowledged bluntly, "logical and mathematical truths ... are [themselves] clearly devoid of empirical content."

I think your last statement illustrates in a nutshell what strikes me as a probable underlying error in your reasoning on this topic: you are proceeding from the unshakeable premise that anything meaningful must have empirical content. Accordingly, when you confront the reality that pure mathematics and logic do not appear to be meaningless, you are led to conclude erroneously that pure mathematics and logic must have empirical content. The fact that rationalizing this result has required you to resort to some fairly unorthodox characterizations of mathematical epistemology suggests (to me, at least) that the real trouble lies in your initial - and still unestablished - premise regarding meaning.

 

[Melendwyr]

True, but this distinction is part of the reason why mathematics is generally held not to be a branch of empirical science.

Math isn't considered to be empirical because people don't like to think about the fact that thinking is a physical process.

Speaking, writing, and otherwise communicating about abstractions is something human beings do often and, arguably, rather well.

You've missed the point, or perhaps you're deliberately avoiding it. Abstractions are physical things, in the same way that computations are physical things.

Particularly in light of your previous dubious assertions about the nature of mathematics, it would be reassuring to see proofs for such propositions as All non-arbitrary concepts are subject to scientific examination, or Arbitrary concepts are not real concepts.

If an assertion makes any predictions that aren't tautological, it can be tested. If it can be tested, it's subject to scienific examination. If it can't, it implies nothing and means nothing.

I think your last statement illustrates in a nutshell what strikes me as a probable underlying error in your reasoning on this topic: you are proceeding from the unshakeable premise that anything meaningful must have empirical content.

If it has no empirical content, it cannot affect our minds. It cannot inform our statements and discussions. We cannot know it, use it, detect it, or interact with it. It isn't real.

 

[drkitten]

Math isn't considered to be empirical because people don't like to think about the fact that thinking is a physical process.

This, oddly enough, is true.

Of course, the reason that it's true is because people don't believe that thinking is a physical process, and there's a multi-thousand year philosophical tradition supporting them, and shedloads of philosophical argument and evidence in favor of their position.

Similarly, people don't like to think about the fact that 2+2=7.

You've missed the point, or perhaps you're deliberately avoiding it. Abstractions are physical things, in the same way that computations are physical things.

So what's your definition of "physical"? At this point, your definition of "physical" has become so all-encompassing as to be meaningless. Which is part of why your usage of the terms doesn't fit any standard philosophical or lexicographic tradition.

Basically, "calling a tail a leg doesn't make it one."

 

[Melendwyr]

Of course, the reason that it's true is because people don't believe that thinking is a physical process, and there's a multi-thousand year philosophical tradition supporting them, and shedloads of philosophical argument and evidence in favor of their position.

I'm not aware of any evidence, philosophical or otherwise, that indicates thinking is not a physical process.

Similarly, people don't like to think about the fact that 2+2=7.

"2+2=7" is a false statement. "Thinking is a physical process" is not known to be a false statement - in fact, it's rather obviously true.

So what's your definition of "physical"? At this point, your definition of "physical" has become so all-encompassing as to be meaningless.

Which is precisely how science uses it - every time a new thing which doesn't fit into the old definition is found, the definition is expanded. It's rather like "natural" in that way.

It makes no difference whether a calculator is clockwork, electrical, or pure software. The calculator's behavior is always describable in "physical", mechanical terms.

 

[ceo_esq]

Math isn't considered to be empirical because people don't like to think about the fact that thinking is a physical process.

That's undoubtedly part of it, although drkitten has already addressed this point. However, look at the particular reasons given in my prior post by the cited mathematical thinkers for why math isn't considered empirical or scientific. They have more to do with necessity versus contingency than with whether thinking is a physical process.

You've missed the point, or perhaps you're deliberately avoiding it. Abstractions are physical things, in the same way that computations are physical things.

For an abstraction to be a physical thing is logically untenable and semantically nonsensical; the Oxford English Dictionary indicates that something that is abstract is "Withdrawn or separated from matter, from material embodiment, from practice, or from particular examples. Opposed to concrete."

If an assertion makes any predictions that aren't tautological, it can be tested. If it can be tested, it's subject to scienific examination. If it can't, it implies nothing and means nothing.

You call that a proof? At any rate, a (correct) mathematical statement is tautological, in the sense that it is unconditionally and necessarily true.

If it has no empirical content, it cannot affect our minds. It cannot inform our statements and discussions. We cannot know it, use it, detect it, or interact with it. It isn't real.

You are merely restating your assertion. How do you know it to be true?

 

[Melendwyr]

They have more to do with necessity versus contingency than with whether thinking is a physical process.

Yes. So? All of our conclusions are contingent. There is a considerable difference between a thing being necessarily true and our needing to consider it necessarily true.

For an abstraction to be a physical thing is logically untenable and semantically nonsensical; the Oxford English Dictionary indicates that something that is abstract is "Withdrawn or separated from matter, from material embodiment, from practice, or from particular examples. Opposed to concrete."

Are computer programs abstract? What about stories?

I consider a lump of silicon dioxide with some impurities to be a glass, not because of the substance it's made of, but because of its arrangement. Melt or break it, and it's glass, but not a glass. If the glass was an arrangement, was it an abstraction? If so, what was I holding?

You call that a proof? At any rate, a (correct) mathematical statement is tautological, in the sense that it is unconditionally and necessarily true.

Given its premises, and given that we've applied the rules properly.

You are merely restating your assertion. How do you know it to be true?

It's a tautological statement. Assuming otherwise leads to self-contradiction.

 

[ceo_esq]

Yes. So? All of our conclusions are contingent. There is a considerable difference between a thing being necessarily true and our needing to consider it necessarily true.

As Professor Shapiro pointed out, what does it even mean for a pure mathematical or logical statement to be contingently true? Is that conceivable?

Are computer programs abstract? What about stories?

You might want to ask a computer programmer or a storyteller. Whether they are abstractions, however (or perhaps have both abstract and concrete components), does not establish that abstractions are empty, meaningless or unintelligible, which is what you appear to be suggesting despite widespread agreement to the contrary.

It's a tautological statement. Assuming otherwise leads to self-contradiction.

In that case, please lay out your formal reductio ad absurdum proof for us, numbering each step.

 

[bignickel]

"To continue reading the complete article, login or subscribe below and get free instant access. Get 6 issues of TIME for only $1.99"

Any other way to read it?

 

[Melendwyr]

As Professor Shapiro pointed out, what does it even mean for a pure mathematical or logical statement to be contingently true? Is that conceivable?

It means precisely the same thing it does when we talk about other types of contingent truth. Yes, it's conceivable.

You might want to ask a computer programmer or a storyteller. Whether they are abstractions, however (or perhaps have both abstract and concrete components), does not establish that abstractions are empty, meaningless or unintelligible, which is what you appear to be suggesting despite widespread agreement to the contrary.

No, my point is that the things we call abstractions are really nothing of the sort, in the same way that an "empty" glass isn't actually empty at all. This is not a particularly difficult concept.

 

[drkitten]

It means precisely the same thing it does when we talk about other types of contingent truth. Yes, it's conceivable.

Really? Could you give us an example of a contingently-true theorem in mathematics?

 

[Melendwyr]

Really? Could you give us an example of a contingently-true theorem in mathematics?

Since all of the theorems we've generated depend upon our ability to accurately represent conceptual rules in our minds, there are no examples which wouldn't serve.

If you can prove that human minds accurately model the fundamental rules that underlie mathematics, I will personally give you a million dollars.

 

[drkitten]

Since all of the theorems we've generated depend upon our ability to accurately represent conceptual rules in our minds, there are no examples which wouldn't serve.

"Assumes facts not in evidence." Since this is the fundamental point under discussion, you might want to find an example that doesn't explicitly involve begging the question.

Of course, I also believe that you cannot, because you can't actually find any non-circular evidence for anything you've stated in this thread. But you're welcome to prove me wrong.

If you can prove that...

I don't need to prove a thing -- I'm not the one who's suggesting a wholesale revision of three thousand years of epistemology, ontology, linguistics, and lexicography.

 

[Melendwyr]

"Assumes facts not in evidence." Since this is the fundamental point under discussion, you might want to find an example that doesn't explicitly involve begging the question.

Oh, brother.

You suggest that we could demonstrate that our minds don't have built-in logical flaws that cause us to draw incorrect conclusions from correct premises? How, exactly, could we accomplish this? Demonstrating anything requires that we use our minds to draw conclusions from premises.

I don't need to prove a thing -- I'm not the one who's suggesting a wholesale revision of three thousand years of epistemology, ontology, linguistics, and lexicography.

Who is, then? It's certainly not me. (Epistemology and ontology can be junked, not revised, and the issue is a semantic, not a linguistic one.)

 

[drkitten]

You suggest that we could demonstrate that our minds don't have built-in logical flaws that cause us to draw incorrect conclusions from correct premises?

No, but I don't see how this has anything to do with the question of whether mathematical truths are necessary or contingent.

If a mathematical result is obtained by flawed reasoning, that doesn't actually have any effect on the truth of the statement -- it still might be (spuriously) true, or it might be false.

But in particular, a mathematical truth is still true -- and under the standard definitions of "necessary truth," necessarily so. A mathematical truth that is not known to be true is still true (which is why mathematicians do research) -- and a mathematical statement that is false is, by definition, not true, which means it's neither contingently true nor necessarily true.

I'm still waiting for you to explain in a non-circular fashion how a mathematical truth could be contingent. You can't prove that mathematical truths are contingent by assuming that because they're produced by mathematicians, they must be contingent. That's circular reasoning. You can show that mathematical truths are contingent by showing a possible world where mathematical truths are false. Not "are believed" false, but are actually false.

 

[Melendwyr]

No, but I don't see how this has anything to do with the question of whether mathematical truths are necessary or contingent.

You don't? Then we've isolated the problem.

You can't prove that mathematical truths are contingent by assuming that because they're produced by mathematicians, they must be contingent. That's circular reasoning.

No, it isn't. Circular reasoning contains the conclusion in the premises, and that's not what's going on.

You can show that mathematical truths are contingent by showing a possible world where mathematical truths are false. Not "are believed" false, but are actually false.

Easy: we could be living in such a world and never know it. You're confusing our ideas of what's true with what's actually true. Just because we label something as a mathematical truth doesn't necessarily make it so. Our statements always have an element of uncertainty in them as regards their accurate representation of the world - thus, they are necessarily contingent. Conclusions derived from axiomatic systems are only as good as our ability to state and apply the rules, and we can never be certain that our minds' applications match the world's; thus, the conclusions hold if our minds accurately reflect the world. If they don't, they don't.

Looks like a contingency to me.

 

[69dodge]

I'm still waiting for you to explain in a non-circular fashion how a mathematical truth could be contingent. You can't prove that mathematical truths are contingent by assuming that because they're produced by mathematicians, they must be contingent. That's circular reasoning. You can show that mathematical truths are contingent by showing a possible world where mathematical truths are false. Not "are believed" false, but are actually false.

On the other hand, can you explain in a non-circular fashion what it means for a mathematical statement to be necessary? Talking about possible worlds doesn't help unless we know how to decide which worlds are possible and which are impossible. I guess the usual way to make such decisions is by using mathematical/logical reasoning, but that's circular, isn't it?

 

[drkitten]

On the other hand, can you explain in a non-circular fashion what it means for a mathematical statement to be necessary? Talking about possible worlds doesn't help unless we know how to decide which worlds are possible and which are impossible. I guess the usual way to make such decisions is by using mathematical/logical reasoning, but that's circular, isn't it?

Well, the usual way to prove anything impossible is using logic and math.

But in the case of proving something possible, you just have to show it. The best proof of the existence of a grapefruit doesn't involve logic and math, but a just a grapefruit.

If you can show a world where the truths of logic and math don't hold, then you've demonstrated that they're contingent.

But, of course, Melendwyr can't. Instead, she asserts, without proof or even evidence, that "we could be living in such a world and never know it." Even if her statement were true (which I doubt), that doesn't produce the necessary grapefruit.

 

[drkitten]

Just because we label something as a mathematical truth doesn't necessarily make it so. Our statements always have an element of uncertainty in them as regards their accurate representation of the world - thus, they are necessarily contingent. Conclusions derived from axiomatic systems are only as good as our ability to state and apply the rules, and we can never be certain that our minds' applications match the world's; thus, the conclusions hold if our minds accurately reflect the world. If they don't, they don't.

So you don't understand the defintion of "contingency," and I'm afraid that you're the one that is confusing the difference between our understanding of the world and the world itself.

"Contingent truth" is not a statement about how well "our minds' approximations match the world's." The biggest fool in the universe can say the sun is shining, but that doesn't make it dark out.

The statement "the sun is shining" is true if, and only if, the sun is in fact shining. Whether I believe (and whether I have a rational basis for belief) that the sun is shining is independent of this truth -- I may be mistaken. The walls of my bathroom are still painted blue even if you've never seen them.

It is possible for us to believe something is false -- and for that thing not only to be true, but to be necessarily true. (And, of course, vice versa.) Our beliefs have no causal effect on the epistemological and ontological status of the world. More bluntly, "our statements always have an element of uncertainty in them as regards their accurate representation of the world " is true -- you cannot, for example, tell me with 100% certainty what color my bathroom walls are. I just told you they were blue, but I might have lied -- or been mistaken -- or even repainted them in the past thirty seconds. But your uncertainty about their accuracy does not have any effect on the actual color of the walls.