JMR

"What do you believe is true..."

103 posts in this topic

(I just posed this question to my OAC classmates--I thought it might be a good topic for the forums here as well.)

Every year, a New York book publisher/editor named John Brockman asks

a question to semi-famous people in various fields. This year's

question was "What do you believe is true even though you can't prove it?"

As you would expect, some of the responses are outrageous but others are

not.

See: http://www.edge.org/q2005/q05_print.html

Taking the topics of reason and objectivity, I was wondering

what the philosophical status of that question is. Is there any

circumstance in which it is valid to believe in something that one

can't prove?

My initial reaction is that no, one should not believe anything one

cannot prove, for the standard reasons of what constitutes knowledge

and what constitutes the arbitrary, etc.. But on the

other hand, the question doesn't ask about things that are

*unprovable*, it just asks about things that cannot be proven

presently. So take the case of a scientist working on the cutting

edge of some field who forms a theory which he cannot yet prove but

which does not contradict prior knowledge, the laws of reality,

identity, etc. How should he properly hold it in his mind? i.e. Is

there anything special about the epistemological status of a theory?

What about a hypothesis?

Or, if anyone has anything that they believe is true but cannot prove, perhaps that would make more interesting discussion.

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I would believe what a credible expert had to say of his field of expertise without understanding exactly how it worked and being able to prove it myself.

That’s all I can think of.

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(I just posed this question to my OAC classmates--I thought it might be a good topic for the forums here as well.)

Every year, a New York book publisher/editor named John Brockman asks

a question to semi-famous people in various fields.  This year's

question was "What do you believe is true even though you can't prove it?"

It is perfectly appropriate to rely on the expertise of others for complex things about which we do not have true firsthand knowledge. But then we would say (with some degree of quantification) that we think such and such is probably true. To reach certainty we must grasp the issue and make firsthand identifications ourselves.

As to your question "if anyone has anything that they believe is true but cannot prove," I hold a multitude of things in that regard. For instance, I think that Lewis Little's Theory of Elementary Waves is true, but I cannot prove it with certainty. The theory explains such a broad number of scientific facts, and integrates so much of what is known, that I think the theory is true with a high degree of probability. But I cannot say so with certainty, if for no other reason than that a deeper form of the current theory may even better explain and integrate the facts.

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Actually I think that, for many of those who just start with Oism, the philosophy itself is one of such things too. They desperately want to believe that it's true, but they don't have yet a firm and confident grasp of it to really know. It's a very vulnerable state.

I think we first acquire all important and valuable ideas because we need them, and later find justification for them if they're true. Just look at AR who in her early years was beset from everyone about the evils of selfishness, but couldn't defend herself against them. Then she came to America, a land of selfishness, and here everyone continued telling her basically the same thing! It must have been incredibly vulnerable to cling onto the belief that this wasn't the end, that there was more, something everyone gave up and which she had to rediscover. For those early years - when she didn't have her philosophy formulated, was continually beset by whole culture out to convince her to give it up, and still clung on - that must have been a very vulnerable time.

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I believe that the Vietnamese word for "heart" is tim (pronunciation, not necessarily spelling), because I was told it is by a trusted scholar of the language who is a first-language speaker of Vietnamese (these are facts I know first-hand aout the person, though I've never learned any Vietnamese).

How do you interpret the question "What do you believe is true even though you can't prove it?" -- as applying only to things that I personally cannot prove at the moment, or as something that in principle I could never prove? As a matter of principle, I never believe anything that I know can never be proven. So I assume you don't mean "can't" in the sense "utterly impossible".

There are a number of things that I believe but cannot prove for the next 16 hours (I plan to do the test tomorrow morning at which point I will be able to prove the conclusions, assuming they are indeed correct). One of them is that the way you say "he's killing me" in Llogoori (my current research language) is yaanzítaa. I have very many reasons for believing this which I won't bore you with, but since I do not have that datum in my corpus, I can't say that I can "prove" that this is so (in fact, I have a datum which says otherwise, where I wrote yaazítaa -- I believe I wrote it down wrong, but cannot prove that until I verify the datum, as I will do tomorrow morning).

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[...] "What do you believe is true even though you can't prove it?"

Axioms of philosophy. They are true and unprovable.

"'Proof', in the full sense, is the process of deriving a conclusion step by step from the evidence of the senses, each step being taken in accordance with the laws of logic." (Leonard Peikoff, "Introduction to Logic" lecture series (1974), Lecture 1 -- as cited in "Proof," The Ayn Rand Lexicon, p. 387, but also see the last excerpt, on p. 388, for axioms.)

Dr. Peikoff's words, "in the full sense," reminds me that the method and standard of proof vary from field of study to field of study. Philosophical proof relies on universally available observations and reaches certainy. Rationality isn't probably a virtue, it is a virtue. Philosophers can reach certainty because "all" they need to do is look around and think. They require no special tools and no specialized knowledge from experts.

In the field of history, however, proving a claim (1) requires specialized methods (as distinct from the universal methods of philosophy), and (2) must often accept assurance less than certainty (at least initially). An example claim in history would be: "The Vikings were more raiders than traders." An historian will have more or less confidence in his proof as he continues to gather evidence from newly discovered manuscripts, newly uncovered archaeological sites, and new technologies (such as aerial mapping of settlements).

In much of everyday knowledge (such as the belief that cigarette smoking destroys health), the appropriate proof (for most of us) may be simply a combination of our own anecdotal observations (smokers cough alot and look sickly over time) and the testimony of individuals we judge to be experts. Our "proof," in such cases rests on our confidence in our casual observations and in our assessment of the individuals providing the testimony.

So, not counting axioms, I would say that I believe no claim is true without proof of some kind and degree.

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Axioms of philosophy. They are true and unprovable.

"'Proof', in the full sense, is the process of deriving a conclusion step by step from the evidence of the senses, each step being taken in accordance with the laws of logic." (Leonard Peikoff, "Introduction to Logic" lecture series (1974), Lecture 1 -- as cited in "Proof," The Ayn Rand Lexicon, p. 387, but also see the last excerpt, on p. 388, for axioms.)

Axioms are unprovable? I disagree. You are correct in that proof is the process that you reference. But in the case of axioms, nothing is closer to the senses than the axiom itself. Take "existence exists." It is self-evident, which is the easiest type of proof to construct.

To be precise, the axioms don't require proof because they constitute the standard of proof. But that doesn't mean they are less than proven--they can be considered proved.

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Axioms of philosophy. They are true and unprovable.

"'Proof', in the full sense, is the process of deriving a conclusion step by step from the evidence of the senses, each step being taken in accordance with the laws of logic." (Leonard Peikoff, "Introduction to Logic" lecture series (1974), Lecture 1 -- as cited in "Proof," The Ayn Rand Lexicon, p. 387, but also see the last excerpt, on p. 388, for axioms.)

Axioms are unprovable? I disagree. You are correct in that proof is the process that you reference. But in the case of axioms, nothing is closer to the senses than the axiom itself. Take "existence exists." It is self-evident, which is the easiest type of proof to construct.

To be precise, the axioms don't require proof because they constitute the standard of proof. But that doesn't mean they are less than proven--they can be considered proved.

I think strictly speaking Burgess is correct, but his choice of the word "unprovable" is somewhat unfortunate because of the connotation of undecidability. You can take an axiom as being "true," but not as being "proved," because there is no means of applying the process of proof. Note these comments by Ayn Rand, in reference to the axioms of existence and consciousness.

These three facts need not and cannot be proved. Any proof rests on them and implies them as axioms. Proof by physical demonstration implies a physical fact (in the external world) demonstrated to an observer (man) who grasps it through a faculty of consciousness which permits him to grasp it (the rational faculty). Proof by rational demonstration implies an entity (man) who possesses a faculty of consciousness (the rational faculty) which permits him to acquire knowledge about facts (in the external world). Proof cannot begin in a vacuum. Existence begins by existing. Proof begins with something that exists proving something about something that exists.

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How do you interpret the question "What do you believe is true even though you can't prove it?" -- as applying only to things that I personally cannot prove at the moment, or as something that in principle I could never prove? As a matter of principle, I never believe anything that I know can never be proven. So I assume you don't mean "can't" in the sense "utterly impossible".

The Brockman fellow left the question pretty wide open, so anything is fair game in that regard. He did give a brief elaboration:

"Great minds can sometimes guess the truth before they have either the evidence or arguments for it (Diderot called it having the 'esprit de divination'). What do you believe is true even though you cannot prove it?"

I don't think there is much value in discussing what one cannot personally prove, because none of us is a universal expert. For example, I believe in continental drift, but not being a geologist, I don't have all of the data and specialized knowledge about plate tectonics at my fingertips. I do know that there exist people who do have all of that data and the requisite training to make sense out of it. But if you asked me to replicate all of the experiments and observations that would be necessary, I would hardly know where to start.

On the other extreme, I don't think there would be much value in discussing things that are purposely concocted so as to be unprovable, like God. Those are downright arbitrary and in my opinion are not worthy of the effort.

I was shooting for things on the boundary of knowledge, such as new theories (of anything) that lack full evidence but a) may have some speck of evidence, and B) are not logically impossible.

For instance, one scientist who responded to Brockman's question, Terrence Sejnowski, said he believes that the location of memory in the brain is outside of the synapses in the cellular matrix, as opposed to between them, as is currently postulated.

I suppose an implicit assumption in my recasting of the question is that man has the potential to understand and prove anything that is true.

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Axioms are unprovable? I disagree. You are correct in that proof is the process that you reference.  But in the case of axioms, nothing is closer to the senses than the axiom itself.  Take "existence exists."  It is self-evident, which is the easiest type of proof to construct. 

To be precise, the axioms don't require proof because they constitute the standard of proof.  But that doesn't mean they are less than proven--they can be considered proved.

<{POST_SNAPBACK}>

Do you see self-evidence as a type of proof? If so, I can see your point.

However, I see self-evidence as one type of validation. Proof is another type of validation.

What is a validation? It is, as Leonard Peikoff notes, "in the broad sense ... any process of relating mental contents to the facts of reality. Direct perception, the method of validating axioms, is one such process. 'Proof' designates another type of validation. Proof is the process of deriving a conclusion logically from antecendent knowledge." (See: "Validation," The Ayn Rand Lexicon, p. 520, excerpted from Leonard Peikoff, "The Philosophy of Objectivism" lecture series (1976), question period, Lecture 3.)

No knowledge is antecedent to an axiom. No proof is possible.

(Thank you for your critical comments. They have helped me clarify these ideas.)

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Do you see self-evidence as a type of proof? If so, I can see your point.

I do (or did, at least). But perhaps I need to revisit that idea.

On page 8 of OPAR, Dr. Peikoff says:

"'Validation' I take to be a broader term than 'proof,' one that subsumes any process of establishing an idea's relationship to reality, whether deductive reasoning, inductive reasoning, or perceptual self-evidence. In this sense, one can and must validate every item of knowledge, including axioms. The validation of axioms, however, is the simplest of all: sense perception."

So from that we know how validation relates to proof, and that self-evidency is acceptable as a means to validate. But I'm still not sure what further test, if any, it would have to pass to also be considered proved. Can something be validated but not proven? If not, then "validation" is just an umbrella term for three different acceptable methods of arriving at a proof.

The quotation that Stephen provided ("These three facts need not and cannot be proved...") seems to lay out a verdict pretty clearly; my only cause for hesitation is that it comes from the Journals, where she is writing for herself for her own development, so her precision can vary. Then again, Ayn Rand on even a bad day could be orders of magnitude clearer than me on my best!

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Oh, woops, your quote of "Proof' designates another type of validation..." just registered. I need to go take a look at that Lexicon entry. I'm in a cafe and all I have with me is the first chapter of OPAR in text format! I definitely want to get proof and validation squared away.

In the meantime, to offer something that I believe but don't think has been proven one way or another is that migratory birds can sense, and thus navigate by, the North/South magnetic orientation of the earth. (At least, I'm pretty sure it hasn't been proven yet.)

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So from that we know how validation relates to proof, and that self-evidency is acceptable as a means to validate.  But I'm still not sure what further test, if any, it would have to pass to also be considered proved.

It would have to be capable of proof.

Can something be validated but not proven?

Yes. Fundamental axioms.

If not, then "validation" is just an umbrella term for three different acceptable methods of arriving at a proof.

I do not think so. Look at the precision of Dr. Peikoff's words: "Validation' I take to be a broader term than 'proof,' one that subsumes any process of establishing an idea's relationship to reality, whether deductive reasoning, inductive reasoning, or perceptual self-evidence." This latter forms the basis of our validation of the axioms, and it is a different method than proof in "establishing an idea's relationship to reality."

The quotation that Stephen provided ("These three facts need not and cannot be proved...") seems to lay out a verdict pretty clearly; my only cause for hesitation is that it comes from the Journals, where she is writing for herself for her own development, so her precision can vary.  Then again, Ayn Rand on even a bad day could be orders of magnitude clearer than me on my best!

Ha! That point is hardly restricted to just you. :)

But anyway, I put the quote out for consideration, but I do not think it is necessary for reaching the conclusion. For that I think the preceding arguments suffice.

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I've managed to pinpoint my hangup. Not surprisingly, it has to do with my understanding of the definition of "self-evident" and the role it plays in proofs.

First, let me revisit the definition of proof. LP: "Proof is the process of deriving a conclusion logically from antecendent knowledge."

So anything that is considered proven must be the result of a multi-step process (the proof) leading back down to the perceptual level. Got it.

Okay, so consider the perceptual-level proposition "there is a tree in front of me." Either this is a) unprovable because it is perceptually self-evident, which means that it only involves one step and a proof must consist of multiple steps, or B) provable because it is not perceptually self-evident (it still requires another step, which is the reduction to the axioms of existence and identity).

If "b" is correct, as I think it is, then I'm with you on everything. But it also means that I (and a lot of people) have been using the term "self-evident" way too loosely. It seems to suggest that "self-evident," strictly speaking, only applies to the axioms. Is that correct?

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It is perfectly appropriate to rely on the expertise of others for complex things about which we do not have true firsthand knowledge. But then we would say (with some degree of quantification) that we think such and such is probably true. To reach certainty we must grasp the issue and make firsthand identifications ourselves.

I agree that it is entirely proper to believe things that one is not able to prove conclusively. I think the more interesting issue here, which Stephen raised in the quote above, is one of certainty. Leaving aside self-evdient truths, can one be certain of an idea that one cannot prove?

The very notion sounds bizarre, but I'm not ready to dismiss it yet. For, take the idea that the sun will rise tomorrow. I want to say that a layman is able to claim certainty here -- i.e., the evidence, even in his context, is conclusive -- and at the same time it's not clear that he could prove it. Could it be that having conclusive evidence for a conclusion doesn't require that one be able to prove it? Or can a layman prove that the sun will rise tomorrow?

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For, take the idea that the sun will rise tomorrow.  I want to say that a layman is able to claim certainty here -- i.e., the evidence, even in his context, is conclusive -- and at the same time it's not clear that he could prove it.  Could it be that having conclusive evidence for a conclusion doesn't require that one be able to prove it?  Or can a layman prove that the sun will rise tomorrow?
What do you mean by "prove" -- why can't he prove it?

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But it also means that I (and a lot of people) have been using the term "self-evident" way too loosely.  It seems to suggest that "self-evident," strictly speaking, only applies to the axioms.  Is that correct?

As I see it, strictly speaking, as used in Objectivism, the self-evident literally means perceptually self-evident, with perception applying equally well to introspection as to extrospection. The self-evident is that which is provided to us by direct perception.

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It is perfectly appropriate to rely on the expertise of others for complex things about which we do not have true firsthand knowledge. But then we would say (with some degree of quantification) that we think such and such is probably true. To reach certainty we must grasp the issue and make firsthand identifications ourselves.

I agree that it is entirely proper to believe things that one is not able to prove conclusively. I think the more interesting issue here, which Stephen raised in the quote above, is one of certainty. Leaving aside self-evdient truths, can one be certain of an idea that one cannot prove?

The very notion sounds bizarre, but I'm not ready to dismiss it yet. For, take the idea that the sun will rise tomorrow. I want to say that a layman is able to claim certainty here -- i.e., the evidence, even in his context, is conclusive -- and at the same time it's not clear that he could prove it. Could it be that having conclusive evidence for a conclusion doesn't require that one be able to prove it? Or can a layman prove that the sun will rise tomorrow?

Note that the wording I used was for "complex things," meaning abstractions far removed from the perceptual level, requiring a long chain of reasoning and integration in order to properly validate. Although the details of celestial mechanics -- the mathematical and physical principles that fully explain the motions of the Earth-Sun system with great care and precision -- are not readily accessible to the layman, the fact of the rising Sun is itself perceptually given. The layman only need be given a simple explanation regarding the orbital motion which he can combine with his own direct perception in order to reach epistemological certainty. The level of "proof" involved does not rely on an understanding and integration of complex abstractions. So, yes, I would say that there are a multitude of things that can be accepted with certainty by a layman without the stringent proof that would be required for the professional. However, the more abstract the nominal proof becomes, the further removed from certainty the layman will be.

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As I see it, strictly speaking, as used in Objectivism, the self-evident literally means perceptually self-evident, with perception applying equally well to introspection as to extrospection. The self-evident is that which is provided to us by direct perception.

So are there two types of self-evident things that we (or perhaps just I) have been lumping together as one: the conceptually self-evident and the propositionally self-evident? (I don't know what to call the latter one, so I just picked that word.)

Take these examples of self-evident things:

"I control my mind."

"This apple is sweet."

"I am bored."

"The sun is bright."

Those four are straight from exercise #1 from Harry Binswanger's course on logical thinking from last summer's conference. He did say in the instructions "consider only whether or not the fact stated is self-evident, not whether its conceptual formation is." Unfortunately, I don't have any more about that distinction in my notes.

So then my understanding is that the above are propositionally self-evident but not conceptually self-evident. And a propositionally self-evident fact is provable because although it may seem like a single-step process to the person making the formulation, it really does involve antecedent knowledge (the knowledge of the concepts).

I think that would solve my prior entanglement.

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Every year, a New York book publisher/editor named John Brockman asks

a question to semi-famous people in various fields.  This year's

question was "What do you believe is true even though you can't prove it?"

See: http://www.edge.org/q2005/q05_print.html

I just finished reading through them all. There are some pretty interesting ones.

One funny thing is that two of the contributors are at odds with each other. The "I believe, but cannot prove" that Daniel Dennett offers is the opposite of the one that Alison Gopnik offers!

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I think this is a fascinating topic.

can one be certain of an idea that one cannot prove?
Alex, can't the example I used with AR, or Stephen's personal example with TEW, be taken as evidence of this?

Some proof may take a long time to accumulate (in AR's case it took decades before she could go toe-to-toe with those who would try to convince her out of her hero-worshiping; but she believed in her ideas for all those decades when she couldn't go toe-to-toe with them). Until the final proof is arrived at, the "preliminary evidence", kind of a subconscious and not fully definable belief, can be taken as appropriate. How does this differ from a Christian, all of whose fundamental ideas are not fully provable beliefs? The latter does not seek for final proof, he does not really seek to found his ideas in definite statements; he's content to stay in the indefinite land. The former person, though he doesn't have definite statements either, seeks to make them definite, to put his belief system on a solid and objective footing.

There have been visionaries in history (Galileo, for example) who were from birth confronted with a society set out against them, and required an entire lifetime to put into definite words what they never doubted internally. Some allowance definitely should be made for them, and for their approach.

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So then my understanding is that the above are propositionally self-evident but not conceptually self-evident.  And a propositionally self-evident fact is provable because although it may seem like a single-step process to the person making the formulation, it really does involve antecedent knowledge (the knowledge of the concepts).

Jared, I am having difficulty following your point. The examples you gave are self-evident because they are the perceptually given, whether from extrospection or introspection. By contrast, if a chain of reasoning is required to reach a conclusion, then the conclusion is not self-evident. It may seem self-evident, and, indeed, we sometimes loosely use that term to apply to a reasoned conclusion that should be obvious to all, but, strictly speaking, the self-evident is the perceptually given.

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Okay, so consider the perceptual-level proposition "there is a tree in front of me."  Either this is a) unprovable because it is perceptually self-evident, which means that it only involves one step and a proof must consist of multiple steps, or :) provable because it is not perceptually self-evident (it still requires another step, which is the reduction to the axioms of existence and identity).

If "b" is correct, as I think it is, then I'm with you on everything.  But it also means that I (and a lot of people) have been using the term "self-evident" way too loosely.  It seems to suggest that "self-evident," strictly speaking, only applies to the axioms.  Is that correct?

No. Self-evident also applies to the perceptual level.

What does "self-evident" mean? It means that the thing, itself, is all the evidence you need to establish its existence. You establish the existence of the tree (you make it real to yourself) in the act of seeing it. You make someone else aware of the existence of the tree by pointing to it. "See?"

Actually, the axioms are contained, implicitly, in all perceptions and the only way we become explicitly aware of the axioms is by generalizing from sense perception. This tree is what it is. That house is what it is. I am what I am. Everything that is, is what it is!

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Leaving aside self-evident truths, can one be certain of an idea that one cannot prove?

One shouldn't be.

It is important to be aware of how much and what kind of evidence one has when accepting ideas and acting on them. Certainty should be reserved only for first-hand knowledge that one can reduce to sense perception and axiomatic relationships. Anything else is only probable to various degrees and should be regarded as such.

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