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What about the method of Proof By Contradiction?  Assuming the opposite of a proposition is true and then demonstrating that such an assumption leads to a contradiction is a way to prove a negative. 

@StrictlyLogical I agree with you that any claim is made has to be based on SOME evidence.  And that is exactly why whenever anyone makes any meaningful claim they are at the very least implicitly making an assertion that is NOT ARBITRARY on some level.  And in those cases, if an any assertion made either implicitly or explicitly implies a contradiction, the claim can be dismissed as FALSE.  Take for example your statement about the fact that a nonexistent thing CANNOT leave behind any evidence.  How did you know that?  What evidence do you have to support that claim that it CANNOT leave behind any evidence?  You know because the opposite proposition implies a contradiction. 

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9 hours ago, [email protected] said:

What about the method of Proof By Contradiction?  Assuming the opposite of a proposition is true and then demonstrating that such an assumption leads to a contradiction is a way to prove a negative. 

@StrictlyLogical I agree with you that any claim is made has to be based on SOME evidence.  And that is exactly why whenever anyone makes any meaningful claim they are at the very least implicitly making an assertion that is NOT ARBITRARY on some level.  And in those cases, if an any assertion made either implicitly or explicitly implies a contradiction, the claim can be dismissed as FALSE.  Take for example your statement about the fact that a nonexistent thing CANNOT leave behind any evidence.  How did you know that?  What evidence do you have to support that claim that it CANNOT leave behind any evidence?  You know because the opposite proposition implies a contradiction. 

Are you proposing that the sheer absence of evidence (not the presence of contradictory evidence) can constitute proof of ... well, anything?  If so could you identify exactly how that would work?

Note, the claim “nothing can leave behind evidence” is by definition an arbitrary claim... there is no evidence to support it.

Edited by StrictlyLogical

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On 5/30/2019 at 4:14 PM, EC said:

You posted this one HBL too? I saw this there yesterday and had clicked on it because it's exactly what I've been thinking on the subject lately, also. I've been thinking about it because of the non-stop irrational questions I've been seeing on god and religion on Quora lately.

One would have to explain by what means and laws of physics and reality a god would exploit to violate all the other laws of physics for it to exist. As a "god" that couldn't violate any of the known laws of physics and reality could not be really defined as an actual god. "God magic" would have to be fully explainable and defined for an actual "god" to exist.

The above is more of a thought experiment on the subject which can be rationally dismissed prior to even getting that far because of such a concept being both arbitrary and counter to the Primacy of Existence to begin with.

Right, one would have to prove that the Law of Identity is false and then establish a new system of reality in order to prove an existence that can exist with no identity, which is quite arbitrary. 

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19 hours ago, [email protected] said:

What about the method of Proof By Contradiction?  Assuming the opposite of a proposition is true and then demonstrating that such an assumption leads to a contradiction is a way to prove a negative. 

@StrictlyLogical I agree with you that any claim is made has to be based on SOME evidence.  And that is exactly why whenever anyone makes any meaningful claim they are at the very least implicitly making an assertion that is NOT ARBITRARY on some level.  And in those cases, if an any assertion made either implicitly or explicitly implies a contradiction, the claim can be dismissed as FALSE.  Take for example your statement about the fact that a nonexistent thing CANNOT leave behind any evidence.  How did you know that?  What evidence do you have to support that claim that it CANNOT leave behind any evidence?  You know because the opposite proposition implies a contradiction. 

I think that one can prove a negative in certain circumstances, but it has to be something that pertains to reality. One cannot prove a negative statement about something that is arbitrary and I think that is what they were getting at. For example I can prove that Karl is not in the room by simply opening up the room and seeing that Karl is not there. But Karl is at least a possible person and not arbitrary. The idea of God (strictly the miracle working god) is incoherent (rationally speaking) and arbitrary in regards to reality. 

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On ‎6‎/‎1‎/‎2019 at 11:08 AM, StrictlyLogical said:

Are you proposing that the sheer absence of evidence (not the presence of contradictory evidence) can constitute proof of ... well, anything?  If so could you identify exactly how that would work?

Note, the claim “nothing can leave behind evidence” is by definition an arbitrary claim... there is no evidence to support it.

@ StrictlyLogical No that is not at all what I am proposing.  I am simply saying that if somebody makes a claim that contradicts an axiom (which we have validated by evidence plenty of times) that claim is not merely arbitrary but more importantly, it is a metaphysical impossibility.  That's what I'm saying.  I think it's important that we answer a few questions before we go any further if it wouldn't be too much trouble.

1.  What does it mean to "prove" something?

2.  What does it mean to "validate" something?  I ask this because I'm not sure if "validate" means the same as "prove" and Objectivists use the word "validate" a lot.

3.  Do you know something ONLY IF you prove it?  The reason I ask this is because when we observe something we gain knowledge.  We learn.  We know stuff from observing stuff.  But do we "prove" anything when we observe and gain knowledge from observation?  I say no but I think the answer to this will depend on what it means to "prove" something?

4.  Can claims be BOTH ARBITRARY AND self-contradictory (incoherent or self-refuting)?  Arbitrary because they have no evidence to support them (definition of arbitrary) AND self-contradictory because they contradict themselves.

There are statements that are arbitrary and your statement "nothing can leave behind evidence" is an arbitrary claim.  I agree with you.  But it also implies a metaphysical contradiction.  "Nothing" by definition is a non-existent.  There is no such thing as "nothing."  To exist is to be and to be is to be something.  "Nothing" is that which is not anything at all, which means it cannot DO ANYTHING AT ALL.  It has no capabilities whatsoever including the capability to "leave behind" ANYTHING AT ALL, let alone evidence.  This is why I say it also implies a contradiction.  The act of making a claim requires you to mean something by the words that you state to make the claim.  When you analyze the meaning behind the word "nothing" in your claim, you can show that that claim is ALSO self-contradictory.  That's all I'm saying.

@Veritas I agree with you about proofs having to pertain to reality.  At this point, I am reluctant to take a position on your "Karl-in-the-room" example because I am not sure at this moment if any axioms get contradicted if we see an empty room but Karl is still inside the room.  In order to apply the "proof of contradiction" that I mentioned to the Karl-In-The-Room example, the negative of Karl not being in the room would have to be assumed and, from that assumption, a metaphysical contradiction would have to be deduced. "Proof by contradiction" is mostly a mathematical technique and it applies mostly because math is a very delimited subject with pretty much every claim being reduced to an axiom.  But this is not the case in everyday life, although it is the case for claims such as the one that StrictlyLogical proposed.

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7 hours ago, [email protected] said:

@ StrictlyLogical No that is not at all what I am proposing.  I am simply saying that if somebody makes a claim that contradicts an axiom (which we have validated by evidence plenty of times) that claim is not merely arbitrary but more importantly, it is a metaphysical impossibility.  That's what I'm saying.  I think it's important that we answer a few questions before we go any further if it wouldn't be too much trouble.

1.  What does it mean to "prove" something?

2.  What does it mean to "validate" something?  I ask this because I'm not sure if "validate" means the same as "prove" and Objectivists use the word "validate" a lot.

3.  Do you know something ONLY IF you prove it?  The reason I ask this is because when we observe something we gain knowledge.  We learn.  We know stuff from observing stuff.  But do we "prove" anything when we observe and gain knowledge from observation?  I say no but I think the answer to this will depend on what it means to "prove" something?

4.  Can claims be BOTH ARBITRARY AND self-contradictory (incoherent or self-refuting)?  Arbitrary because they have no evidence to support them (definition of arbitrary) AND self-contradictory because they contradict themselves.

There are statements that are arbitrary and your statement "nothing can leave behind evidence" is an arbitrary claim.  I agree with you.  But it also implies a metaphysical contradiction.  "Nothing" by definition is a non-existent.  There is no such thing as "nothing."  To exist is to be and to be is to be something.  "Nothing" is that which is not anything at all, which means it cannot DO ANYTHING AT ALL.  It has no capabilities whatsoever including the capability to "leave behind" ANYTHING AT ALL, let alone evidence.  This is why I say it also implies a contradiction.  The act of making a claim requires you to mean something by the words that you state to make the claim.  When you analyze the meaning behind the word "nothing" in your claim, you can show that that claim is ALSO self-contradictory.  That's all I'm saying.

@Veritas I agree with you about proofs having to pertain to reality.  At this point, I am reluctant to take a position on your "Karl-in-the-room" example because I am not sure at this moment if any axioms get contradicted if we see an empty room but Karl is still inside the room.  In order to apply the "proof of contradiction" that I mentioned to the Karl-In-The-Room example, the negative of Karl not being in the room would have to be assumed and, from that assumption, a metaphysical contradiction would have to be deduced. "Proof by contradiction" is mostly a mathematical technique and it applies mostly because math is a very delimited subject with pretty much every claim being reduced to an axiom.  But this is not the case in everyday life, although it is the case for claims such as the one that StrictlyLogical proposed.

 

1,2 I wont define proof or validation, but the nature of proof is such that, and I take it as something well accepted, one cannot and should not try to "prove" the axioms. 

The axioms are valid because and any denial is self-refuting.  Note that self-refutation of a denial is insufficient for a proof of the positive claim, which would have to rely on something else.

I take it equally that any assertion which reduces to the axioms as such is also not subject to "proof".  Arguments which jettison the axioms, are thus self-refuting, but one cannot prove the opposite of those arguments is true only with proof of this self-refutation any more than one can prove the axioms are true via "a proof of self-refutation" applied to a denial of the axioms.  Such claims are properly (validly) dismissed but their opposites are not positively proved.  Now, claims which implicitly rely on or are consistent with the axioms can be demonstrated as false by means of contradictory evidence, but if the claim which is consistent with the axioms is also arbitrary, it is to be dismissed because of the lack of any evidence, even in the absence of any contradiction. 

3 Asserting knowledge, is a positive act.  You can assert that a first conclusion is consistent with all observed fact (and logic applied thereto) and that a second is not.  As you know, certainty is on a spectrum (possible... probable... certain) of evidence in accordance with the amount of evidence and its consistency and it is contextual since humans are finite and fallible rather than omniscient.  One should be careful to remember that in a metaphysical sense, precisely because one is fallible and finite, that one's certain knowledge (contextual) that something "is true" could metaphysically be wrong.  This would NOT mean that the process of thought or the certainty was invalid, nor that one should not claim "I am certain" or "I know it" in context , only that Man is not omniscient.  He can be metaphysically wrong when he is certain, but he is still justifiably "certain" while actually being "wrong".  So one difference between "proof" and "validation" is that one has an implicit standard of correspondence with metaphysical reality while the other standard is more of an epistemological standard of man's knowledge in context.

I think there is a nuance even with knowledge in the context of the arbitrary. Now, one can know that an arbitrary claim IS arbitrary and should be dismissed as a matter of epistemological fastidiousness... as Peikoff says in OPAR, treat it AS IF nothing were said.  One absolutely knows "There is no basis whatever to accept the claim as true".  Note, "certainty" by definition is on a spectrum of amount of evidence not a spectrum of absence of evidence. 

This I think is why we never, ever, hear in any of Rand's works that one KNOWS that the arbitrary IS false.

 

I think Rand's counsel surrounding the arbitrary, validity, the onus of proof, knowledge-certainty, and the validity of the axioms is spot on.

 

As for claims which are BOTH arbitrary and self-contradictory... such is possible, but I think arbitrary claims tend to be so arbitrary that self-contradiction is neither the exception nor the rule.  Moreover, those who fabricate and protect arbitrary claims can often move whatever "contradiction" exists into the realm of the arbitrary, by expanding the arbitrary claims, removing the self-contradiction.  (Consider also explication of evidence, reason, and the "groundless maybe" in Leonard Piekoff's speech about the OJ Verdict : "A Philosopher Looks at the O J Verdict" starting at about 24 minutes)

https://www.youtube.com/watch?v=MfYP8dr4Eos

(Note the arbitrary claims were not at issue ... it was not something which was to be proved or disproved... but they were improperly used to claim something was "possible")

 

A few scenarios/claims for consideration:

I)

1. God Exists and all of observable existence exists within God. God + Observable existence exist.

2. God is conscious, although not all of existence is (nor all of God is) conscious.  Some living organisms are also conscious.  God and those organisms can identify that which exists using their consciousness.

3. God and Observable existence have identity, and act according to their nature.  God's nature is wholly superior and omnipotent in regard to Observable existence, and wholly superior and omniscient in regard to Observable existence.  God is finite, but sufficiently larger than Observable existence, such that God has utter and complete domination over all of Observable existence.  It is in the identity of all Observable existence that it cannot access God of its own accord, and it is in the nature of God that God can access Observable existence at will.  God has free will.  It is in God's nature that God "could have chosen otherwise"...(to focus or not??... but alas we, as part of the Observable existence cannot know God)

 

II)

God has created existence in himself, in which it appears to us

1. Existence exists

2. Consciousness exists

3. Things have identity

God is beyond existence as it appears to us.  The "existence" of God is not the same in any way to the things existing in Existence as they appear to us, he "is" not in this sense but "IZ" in a completely different sense.  He IS infinite and omniscient in ways we cannot know.  Our belief that ONLY existence exists is right (in the sense of "is" and existence as it appears to us) AND wrong (in the sense that God's being and "IZ" is outside of our knowledge)....

Axioms 1, 2, and 3 ARE, in the Being of the God and things in themselves, illusions, which appear to us... they are our reality but not real reality.  Outside of things as they appear to us, are things as they really are in the "IZ"ness which is beyond our perception and our logic, and even our imagination (only revelation works).  Identity is real in the existence as it appears to us, but things in themselves are more flexible, as in the mind of God, each thing "IZ" AND "IZ not" according to with the will of God...  which makes no sense to us etc. etc.

 

I am not a theologian, but given the intellects of Aquinas, and Kant, I am sure that even though they did not know enough of philosophy to make their arguments "properly arbitrary" and not "self-refuting", their ideas were likely more than enough to arm modern theologians with ample ammunition to create arbitrary theological accounts which are not self-refuting, and are beyond "disproof".

I do not think it is tenable to believe any contest with modern theologians (with such an arsenal of the arbitrary) can be won by proof.

 

We KNOW we can and should dismiss what they say, and all the reasons why... and that has to be enough.

Edited by StrictlyLogical

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