JMR

"What do you believe is true..."

103 posts in this topic

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!

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?

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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.

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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?

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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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.

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.)

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

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.

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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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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?

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?

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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.)

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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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?

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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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.

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.

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

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.

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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?

You got it! :)

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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.

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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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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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.

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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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.

<{POST_SNAPBACK}>

At my college, I have spent three years in a math tutorial studying the history of math and astronomy through the original sources. I spent freshman year on Euclid and Ptolemy; sophomore year on more Ptolemy, Apollonius, Copernicus, and some others; and junior year on Galileo and Newton. Only with Newton am I arriving at what could be considered a modern proof of the heliocentric theory, and yet I distinctly remember, as I was going through Ptolemy freshman year, asking myself whether I was certain that the heliocentric view was correct. I concluded that I was indeed certain. Did I have anything the layman did not have? I think so. I had concepts of gravity and of inertia, so it made sense, for instance, to have the largest object in the solar system at the center, since I knew on some level that gravity is a function of mass. I also had knowledge of Ptolemy, so I was able to see how a real effort at geocentrism faired, and I was able to explain, for instance, how a failure to understand inertia led people into adopting the geocentric view. Maybe some observations from the Hubble that I was familiar with helped too. Oh, and I watched Star Trek!

My surprise reached a climax, however, when I found incidentally that he was ignorant of the Copernican Theory and of the composition of the Solar System. That any civilized human being in this nineteenth century should not be aware that the earth travelled round the sun appeared to me to be such an extraordinary fact that I could hardly realize it.

"You appear to be astonished," he said, smiling at my expression ofsurprise. "Now that I do know it I shall do my best to forget it."

--Sherlock Holmes

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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:

But all the things that you mentioned amount to "authorities say so" rather than proof. There is nothing wrong, per se, with respecting and accepting the word of authorities for things that you do not know, but the issue as raised by Alex was:

Does a layman possess certainty that the Earth orbits the sun, rather than the other way around? If so, can he prove it?

So, the question remains: are you certain that the Earth orbits the Sun, rather than the Sun orbiting the Earth, and, can you prove it? And, from a different perspective, can you be certain of things that you cannot prove?

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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.

Was your judgment of "ridiculous" meant to apply to your first comment about general relativity as well as to your second comment regarding the Ptolemaic system?

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At my college, I have spent three years in a math tutorial studying the history of math and astronomy through the original sources. I spent freshman year on Euclid and Ptolemy; sophomore year on more Ptolemy, Apollonius, Copernicus, and some others; and junior year on Galileo and Newton. Only with Newton am I arriving at what could be considered a modern proof of the heliocentric theory, and yet I distinctly remember, as I was going through Ptolemy freshman year, asking myself whether I was certain that the heliocentric view was correct.  I concluded that I was indeed certain. Did I have anything the layman did not have? I think so. I had concepts of gravity and of inertia, so it made sense, for instance, to have the largest object in the solar system at the center, since I knew on some level that gravity is a function of mass.

There is much I would like to ask you about your statements and your reasoning, but first I would like to focus on a single point. If I follow the flow of ideas correctly, your certainty of the Earth revolving around the Sun, rather than the Sun revolving around the Earth, is ultimately dependent on your grasp of "gravity is a function of mass." That being the case, why are you certain that "gravity is a function of mass?"

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But all the things that you mentioned amount to "authorities say so" rather than proof. There is nothing wrong, per se, with respecting and accepting the word of authorities for things that you do not know, but the issue as raised by Alex was:
Does a layman possess certainty that the Earth orbits the sun, rather than the other way around? If so, can he prove it?

So, the question remains: are you certain that the Earth orbits the Sun, rather than the Sun orbiting the Earth, and, can you prove it? And, from a different perspective, can you be certain of things that you cannot prove?

<{POST_SNAPBACK}>

I wasn't sure if this question was directed at me, or Alex, or both. If what I offered is not proof, even in the context of a layman, then I don't have proof. I was thinking that the second-hand kind of stuff for a layman on a science question constitutes proof.

But perhaps it just constitutes the only kind of information that a layman has. And as for whether I can be certain. Hmm. I can only be certain about whether or not scientists say they are certain. As for the theory itself, I suppose then that it would be probable -- in my mind.

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So, the question remains: are you certain that the Earth orbits the Sun, rather than the Sun orbiting the Earth, and, can you prove it? And, from a different perspective, can you be certain of things that you cannot prove?

I wasn't sure if this question was directed at me, or Alex, or both. If what I offered is not proof, even in the context of a layman, then I don't have proof. I was thinking that the second-hand kind of stuff for a layman on a science question constitutes proof.

Previously, I think we generally agreed (or, at least, there were no dissenters) that the specific content of proof would be different for the layman and the professional. However, I would say that "proof" for either one would still require some chain of reasoning reduced to perceptual reality.

But perhaps it just constitutes the only kind of information that a layman has. And as for whether I can be certain. Hmm. I can only be certain about whether or not scientists say they are certain. As for the theory itself, I suppose then that it would be probable -- in my mind.

Fair enough. Thanks.

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Was your judgment of "ridiculous" meant to apply to your first comment about general relativity as well as to your second comment regarding the Ptolemaic system?

I was referring primarily to the equation of geocentrism and heliocentrism via general relativity. It is true that a false theory, such as the Ptolemaic system, can provide accurate predictions, but it would be ridiculous, in my context of knowledge, to use that fact to undercut the heliocentric theory.

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That being the case, why are you certain that "gravity is a function of mass?"

I suppose I knew I would get this question, but I can't give an easy answer to it. Here are some things I knew back in freshman year, though:

- I am familiar with what happens when I jump up and down.

- Astronauts on the moon, I have seen, can jump higher and fall slower.

- The earth is larger than the moon.

- I was told in high school physics that experiments have been performed in which some tiny gravitational force was found in objects of one ton or some such weight. I relied on authority here, somewhat, but the fact did integrate well with other knowledge, so it bolstered my certainty.

- I knew about the phenomenon of tides, the only explanation of which (that I knew) involved the distant moon exerting force on the oceans.

- I was told about the Newtonian integration of falling bodies with orbits, which integrated well with all of these things and with other knowledge.

- One very interesting fact is that my certainty that gravity is a function of mass was bolstered by my placing the sun at the center. All I can say is that knowledge is a whole. This is an example of circular reasoning which is permissible, I think.

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I was referring primarily to the equation of geocentrism and heliocentrism via general relativity.

Could you be more specific as to what you mean by "the equation of geocentrism and heliocentrism via general relativity," and then explain why it would be "ridiculous?"

It is true that a false theory, such as the Ptolemaic system, can provide accurate predictions, but it would be ridiculous, in my context of knowledge, to use that fact to undercut the heliocentric theory.

I would agree. That would be ridiculous. So, could you point to the "group of scientists" you mentioned who make that exact claim?

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I suppose I knew I would get this question, but I can't give an easy answer to it. Here are some things I knew back in freshman year, though:

[...]

To me, the glaring thing absent from your several supporting examples is a causal explanation. Your examples ranged from secondhand information ("I was told") to the identification of supposed facts, but no causal explantion relating the two. How can you be certain of a physical principle governing deterministic behavior, absent of certainty of the causal explanation that makes the physical principle possible?

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