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"What do you believe is true..."


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#21 JMR

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Posted 09 March 2005 - 05:22 PM

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/.../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!

#22 Free Capitalist

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Posted 09 March 2005 - 05:45 PM

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.
"I will tell you of the most native and greatest adornment of Athens, that which comprises and contains all the rest. Some lands are adorned as the birthplace of elephant and lion species, others as the birthplace of horses and dogs, and yet others of creatures the tales of which frighten children. But its land is adorned by the fairest thing on earth, not to be mentioned like some winged ants of India. For it was the first to bear Man."
-Aelius Aristides, 2nd c. AD

#23 Stephen Speicher

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Posted 09 March 2005 - 06:52 PM

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).

<{POST_SNAPBACK}>

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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#24 Betsy Speicher

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Posted 09 March 2005 - 08:11 PM

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?

<{POST_SNAPBACK}>

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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#25 Betsy Speicher

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Posted 09 March 2005 - 08:18 PM

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

<{POST_SNAPBACK}>

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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#26 JMR

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Posted 09 March 2005 - 10:16 PM

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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Right, I am aware of these formulations and agree with them, but the thing I am having trouble with is integrating this with proof and the question of what is provable.

So take "this apple is sweet," which is self-evident. It is valid because self-evidencies are one type of way of validating an idea. But that self-evidency does not constitute a proof because it is not the result of a multi-step process of reasoning.

Is that much correct?

#27 kenstauffer

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Posted 09 March 2005 - 11:01 PM

Axioms are unprovable?


They are implicit in any proof. Proof rests on the idea that the law of identity has been established. Prove the law of identity, without the law of identity.

#28 Stephen Speicher

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Posted 09 March 2005 - 11:03 PM

So take "this apple is sweet," which is self-evident.  It is valid because self-evidencies are one type of way of validating an idea.  But that self-evidency does not constitute a proof because it is not the result of a multi-step process of reasoning. 

Is that much correct?

<{POST_SNAPBACK}>

Yes, exactly.

But we can loosely say to someone else: "You can prove to yourself that the apple is sweet by biting it." Such a "proof," however, is really nothing more than their direct reliance on the perceptually given, not an actual proof. Strictly speaking, proof is a chain of reasoning tracing back to perceptual reality, but "this apple is sweet" is a direct introspection which starts and stops at the perceptually given.
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#29 ADS

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Posted 10 March 2005 - 12:42 AM

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.

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Then the next question to raise would be whether the layman possesses certainty that the explanation given to him of orbital motion is true. So, perhaps I can better zero in on what I'm getting at by changing my example. Does a layman possess certainty that the Earth orbits the sun, rather than the other way around? If so, can he prove it? Here again, I want to say that the layman is justified in being certain of the heliocentric view, and at the same time it's not clear that he can prove it.

(Again, I know this sounds like a odd conclusion, but saying that the layman cannot be certain of -- or that he can prove -- the heliocentric view also strikes me as somewhat odd as well. So, I'm still stuck.)

#30 ADS

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Posted 10 March 2005 - 12:54 AM

What do you mean by "prove" -- why can't he prove it?

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Well, maybe a layman can prove the kinds of ideas I'm talking about; I'm not sure. As for what proof is, I'm using it in the same way that OPAR uses it: "'Proof' is the process of establishing truth by reducing a proposition to axioms, i.e., to sensory evidence" (OPAR, p. 120). Again, it sounds a little odd to me to say that a layman can perform such a reduction with the idea that the Earth revolves around the sun -- and, at the same time, it sounds equally odd to me to say that a layman isn't justified, here in the 21st century, in being certain of the heliocentric view.

#31 Burgess Laughlin

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Posted 10 March 2005 - 12:57 AM

If so, can he prove it?  Here again, I want to say that the layman is justified in being certain of the heliocentric view, and at the same time it's not clear that he can prove it.

<{POST_SNAPBACK}>

Are you assuming that one particular proof must fit all contexts of knowledge in order to produce certainty?

In particular, working with your example, do you expect a layman to be able to prove the heliocentric theory in the same way that an astronomer would prove it in order to reach certainty?
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#32 ADS

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Posted 10 March 2005 - 01:23 AM

Are you assuming that one particular proof must fit all contexts of knowledge in order to produce certainty?

In particular, working with your example, do you expect a layman to be able to prove the heliocentric theory in the same way that an astronomer would prove it in order to reach certainty?

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To both questions: no, not necessarily. I understand that some proofs contain more confirming evidence than other proofs, even though they are all proofs and all lead to certainty. But if one tries to spell out what a layman could say in the way of evidence for how he knows that the heliocentric view is true, it's not clear that it would amount to a proof. But maybe it would?

#33 Stephen Speicher

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Posted 10 March 2005 - 02:02 AM

Then the next question to raise would be whether the layman possesses certainty that the explanation given to him of orbital motion is true.  So, perhaps I can better zero in on what I'm getting at by changing my example.  Does a layman possess certainty that the Earth orbits the sun, rather than the other way around?  If so, can he prove it?  Here again, I want to say that the layman is justified in being certain of the heliocentric view, and at the same time it's not clear that he can prove it.

(Again, I know this sounds like a odd conclusion, but saying that the layman cannot be certain of -- or that he can prove -- the heliocentric view also strikes me as somewhat odd as well.  So, I'm still stuck.)

<{POST_SNAPBACK}>

The layman must possess certainty about the relevant facts that account for his direct observations. But the specific evidence for reaching that certainty is not the same for him as it would be for the specialist in celestial mechanics. As you well-know, certainty is contextual, and within the context of the layman's knowledge he must, just like the specialist, make sure that his understanding accounts for all his observations, and make sure that some other explanation does not do the same. So both the layman and the specialist can reach certainty, but the detailed level of the specific knowledge each requires will be different.

But then, the more an issue is removed from direct observation, and the more complex the explanation is, the more difficult it is for a layman to ever reach certainty about the issue.
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#34 Stephen Speicher

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Posted 10 March 2005 - 03:20 AM

But if one tries to spell out what a layman could say in the way of evidence for how he knows that the heliocentric view is true, it's not clear that it would amount to a proof.  But maybe it would?

<{POST_SNAPBACK}>

Out of curiosity, why do you think the heliocentric view is essential for the issue you raised, certainty that the Sun will rise tomorrow?
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#35 ADS

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Posted 10 March 2005 - 05:04 AM

The layman must possess certainty about the relevant facts that account for his direct observations. But the specific evidence for reaching that certainty is not the same for him as it would be for the specialist in celestial mechanics. As you well-know, certainty is contextual, and within the context of the layman's knowledge he must, just like the specialist, make sure that his understanding accounts for all his observations, and make sure that some other explanation does not do the same. So both the layman and the specialist can reach certainty, but the detailed level of the specific knowledge each requires will be different.

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Yes, I agree entirely that the layman can be certain of the heliocentric view, even though he is a layman. The question I'm primarily raising, though, is whether the layman is able to prove that the heliocentric view is true. And if he is able to prove it, how? It's fairly clear to me how and why he can be certain, but it's much less clear to me how he could prove the heliocentric theory himself.

#36 ADS

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Posted 10 March 2005 - 05:19 AM

Out of curiosity, why do you think the heliocentric view is essential for the issue you raised, certainty that the Sun will rise tomorrow?

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Oh, I don't. I just brought up the heliocentric idea, because I thought it a better example than the "will the sun rise tomorrow?" example. This is because I think the former example is a claim not as easily decided by direct perception, and I'm trying to find examples of ideas that a layman is completely justified in being certain about, and yet at the same time don't seem like he could prove himself.

This may be a hopeless quest; and if it is, I'm very interested to see how a layman can go about proving things like the heliocentric theory. Either way, I'm focusing on proof, not certainty.

#37 Betsy Speicher

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Posted 10 March 2005 - 05:40 AM

So take "this apple is sweet," which is self-evident.  It is valid because self-evidencies are one type of way of validating an idea.  But that self-evidency does not constitute a proof because it is not the result of a multi-step process of reasoning. 

Is that much correct?

<{POST_SNAPBACK}>

You got it! :)
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#38 Stephen Speicher

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Posted 10 March 2005 - 05:48 AM

Oh, I don't.  I just brought up the heliocentric idea, because I thought it a better example than the "will the sun rise tomorrow?" example. This is because I think the former example is a claim not as easily decided by direct perception, and I'm trying to find examples of ideas that a layman is completely justified in being certain about, and yet at the same time don't seem like he could prove himself.

My apologies. I see now I missed your earlier statement where you changed the example:

So, perhaps I can better zero in on what I'm getting at by changing my example. Does a layman possess certainty that the Earth orbits the sun, rather than the other way around? If so, can he prove it?

So then, let me volunteer you as a layman. Are you certain that "the Earth orbits the sun, rather than the other way around," and, can you prove it?
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#39 Rose Lake

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Posted 11 March 2005 - 11:43 PM

I think a layman can prove that the earth orbits the sun in his own context. For me this proof is all the following things taken together:

I have been taught the heliocentric theory all my life, which I realize, in itself is almost as good as nothing, and would make a reasonable person wonder, if there was nothing else.

But there are other things too. I have seen drawings of our own solar system in what I thought were reputable science books with illustrations, though not at school. I have seen explanations of it in encyclopedias and science books over and over.

The heliocentric theory, as far as I tell, has been accepted by virtually every reputable scientist on earth for the last several hundred years. If it has not, then there must be a huge conspiracy to keep me from finding out about this reputable group of protesting scientists who have evidence against what I have always understood to be a theory that has not been in serious dispute since Galileo's time and some period of time after that, which time-span I don't know for certain.

I have known of not one reputable person in my lifetime to offer arguments against it. And if today's scientists do not know as much as what Copernicus theorized and Galileo offered evidence for, according to history books, hundreds of years ago; then I don't see how they could do advanced things, like sending men to the moon, sending satellites into outer space that take photographs of distant galaxies, etc. And what would 'distant galaxy' even mean, if there were no such thing as our own solar system, not to mention a few others?

Granted this is not technical at all. But I think I would be a fool if I were not certain given this evidence, which I say constitutes overwhelming proof on the level of a layman.

Now if I'd been going to the Van Damme Academy I would probably be able to prove the heliocentric theory in a much more educated way, but I went to public schools. I do not think they even pretended to teach us science that I remember, until high school. Actually, now that I think of it, maybe they did pretend to. But that was all they did, pretend.

It is actually very interesting to me that the most lame support for the theory I ever experienced was in school, when I observed other children, during the presentation of "science" projects, presenting Styrofoam models of the solar system, alongside the papier-mache 'volcanoes' with vinegar, baking-soda, and food-coloring 'lava' flows.
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Posted 12 March 2005 - 12:14 AM

I have been taught the heliocentric theory all my life, which I realize, in itself is almost as good as nothing, and would make a reasonable person wonder, if there was nothing else.

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Actually, there is a group of scientists today that says that the geocentric theory is just as good as the heliocentric theory, as shown by the theory of general relativity. Then more scientists would chime in that Ptolemy provides us with reliable predictions of astronomical phenomena, so isn't it possible that the heliocentric view's contributions to astronomy are similar? Granted this line of reasoning is ridiculous in my context of knowledge, but it would be a problem for your layman.

Now if I'd been going to the Van Damme Academy I would probably be able to prove the heliocentric theory in a much more educated way, but I went to public schools.


Dana Densmore's Newton's Principia: The Central Argument is worth studying for that "more educated way." But frankly, I'm not sure I could have made it through the book outside of the context of my college tutorials over the course of three years (which began with Euclid and Ptolemy). It is a shame that such studies had to wait until college.




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