Argument for the existence of God

[icosahedron]

Concepts and knowledge are both hierarchial and contextual - grasping them requires establishing both the hierarchy and the context, without which can demonstrably lead to the confusion we have just experienced, and subsequently establishing the hierarchy and context, clarify.

Well said. Agreed.

Using 'experience' in this context suggests that it could be an axiomatic concept.

I think maybe it is, an implicit one. Having two partners, Existence and Consciousness, even if the latter is defined as "the faculty of observing Existence", does not necessarily imply that the two actually get together and dance. Of course, why else would they exist? But, I think the explicit assertion that experience is a discrete, indivisible, and complementary conjunction of Existence with an individual Consciousness is worth making. The product is greater than the contributors, that's synergy -- like a tetrahedron formed by interconnecting two poles.

Circumscribe a sphere inside your tetrahedron. Is it's volume less than or greater than the tetrahedron? Circumscribe a tetrahedron inside the aforementioned sphere. It's volume is less than the sphere. Mathematically, this can be carried out repeatedly, beyond the resolution imposed by our physical abilities to discern the volume of the inscribed from the circumscribed.

Yes, it is fractal ... and with a particular "expansion factor" that is constant along the sequence up and down in scale. So can deal with variant frequencies of association, i.e., size is no obstacle to the description or its application.

Think about sight, and imagine the ideal of a single photon receptor per eye, to simplify things. Photons originate in the original position of the external entity that ejects/reflects them, take some time to travel to a receptor photon. The photon originator (the entity I see the image of after some time lag) must have material extent, and therefore the photons travel different paths from the parts of the entity to the eyes.

At any given moment, there are three cases:

1. Neither eye receives a photon

2. Both eyes receive a photon

3. Only one of the eyes receives a photon (two alternate ways)

Let's assume that it's a fairly bright place, so the number of photons is more or less a constant stream to each eye. Then both eyes can be assumed to receive photons at some fixed frequency without loss of generality.

By tracing each pair of received photons, at least imaginatively, back to its source, and then flicking the focus from one point to another on an extended body, one obtains a tetrahedron: the pole connecting the eyes interconnected to the two poles of focus creates a tetrahedron.

Now do this for all pairs of points that can be identified, and you get a geometric picture of the object of (scanning) focus. This can be programmed into a computer, too.

- ico

[Jacob86]

Jacob said:

Here's your other mistake. ALL evidence reduces to perception.This is bedrock to an Objectivist epistemology.It is again not an assumption but a requirement of objectivity. It also shows the impossibility of evidence being forthcoming.

Perhaps then, we have some deeper epistemological differences to work through as well..

But "Im still waiting"!

And I appreciate the patience..and honesty.

But you choose a worldview that pits the prefix of its name against the latter part of the word! There cannot be more than the universe by definition, just as there cannot be two levels of existence. Both concepts and concretes exist. IF there were non physical existents and matter independent minds they all would be simply existents.

No, you are assuming your definition of those words. If by "natural" I mean "all that exists", then the idea of "Supernature" is illogical and self-contradictory (there cannot be anything above and beyond "all that exists").

But that is not what I mean by nature. By nature I mean "the physical universe". Therefore the idea that something exists above and beyond the physical universe is not self-contradictory.

In fact, when I first read Rand's and Peikoff's objections to the Supernatural, I was thoroughly un-impressed. They assumed that other philosophers meant what they meant by the terms "universe" and "nature".

They assumed that by "nature", philosophers meant "all that exists" and by "supernature", philosophers meant "all that exists beyond all existence".

It's almost offensive that Rand thinks those philosophers are so stupid. And it's likewise offensive when that objection is made to me as if I have no grasp on the Law on Non-Contradiction whatsoever.

No offense taken though.

[icosahedron]

And I am saying that if nothing but physical matter exists, then that process is impossible.

You are saying "but it must be possible".

I am saying, "exactly. Therefore, more than physical matter must exist".

Material objects have a finite lifetime. Concepts are eternal, in the sense that two rational individuals will come to the same concept (operationally, i.e., names aside) given the same evidence and logics. So if the law of Identity (and hence causality) is valid, then concepts are reproducible by disjoint minds, even if those minds are not communicating. In this sense, the concept represented by the word "triangle" is eternal; whereas every experience that corresponds to "triangle" is terminal, begins and ends.

This is the essential difference between concepts and experiences: concepts are eternal, reproducible, generic (once discovered); experiences are timely, unique, and specific.

But, concepts do not exist in and of themselves. They reside in minds, which reside in bodies. If you want to get technical, all that is required is an unique focal point to which all experiences, however ingested, come to. One can see that such focal points (centers of consciousness) are predicated on the living body, can't exist without it, are irrelevant without it. So you can't separate the focal point and call it a separately existent entity. You are looking at a part that cannot exist except as part of its whole, and attempting to ignore the whole that it belongs to. That is like trying to isolate a quark -- it can't be done.

Physical matter, and my ability to process my experience of it, both exist. Matter can exist independent of me, but not vice versa. The implementation is irrelevant (which is why the brain as ultimate driver and seat of volition is a conceptual dead-end -- it is a functioning body, including brain, that is the basis, provides the focus; and a rational mind that coordinates the focus. That this coordination burns calories is known, so it too has a physical aspect; but the process is generic, i.e., eternally regenerative (of itself) in every special case.

- ico

Edited November 7, 2010 by icosahedron

[Eiuol]

This was an argument to show the irrationality of a worldview. The reference to a particular concrete which you demand is the fact that we can indeed reason and that therefore any premise which logically implies the inability to reason is false.

If you mean that deductive argument was supposed to show the irrationality of a worldview, of course it would appear irrational, since it was an entirely rationalist argument. Anyone who argues like that will end up with big philosophical problems that apparently you recognized (the problem is lack of concretes). Anyway, without a brain, there is no mind; mind is basically an abstraction that describes the experience of thinking made possible by your brain.

Edited November 7, 2010 by Eiuol

[ctrl y]

Yes, indeed we CAN. But that is because we live in the world where Naturalism is false. What I have stated in my argument is that the ability to reason demands that more than the physical universe exists.

What you are saying is akin to someone saying that they don't believe in the Laws of Logic, but that they still have the ability to reason and therefore Logic is not necessary for reason.

What mistake have they made? They have mistaken "belief in Logic" in the first premise with "the actuality of Logic" in the second. Or, in other words, they have mistaken the Subjective use of Logic for the Objective use of Logic. Subjectively, one must not "believe in Logic" in order to reason accurately (though it would obviously be helpful). However, Objectively, accurate reasoning is dependent upon Logic whether anyone ever realizes it or not.

So it is with my argument. The ability to reason is Objectively dependent on the fact that more than the physical universe exists- whether or not any individual ever Subjectively realizes that it is so.

This misrepresents my argument. I wasn't saying that we, in this world, can evaluate the argument. I was saying that the people in non-dualistic-minds world, whether that world is identical to this world or not, can evaluate the argument.

Hahaha. But the Determinist is right. "IF everything is deterministic cause and effect at the smallest level, then everything is deterministic cause and effect at all levels". "All levels" are dependent upon the smallest level and therefore cannot be thought to gain any magical powers simply because they are at a different level.

This isn't a problem for MY worldview, it's a problem for the Naturalist worldview. (Remember, I do not hold that premise).

You say the Objectivist overcomes this problem by being "more empirical than that". I'd say he overcomes this problem by being less logically consistent than that- and subsequently evading the fact that part of his worldview (Naturalism) does not cohere with his "empirical" observation that he is indeed reasoning.

This insistence that "somehow, free will emerges at the human level" smack awfully of mysticism.

The Determinist reasons (rightly) that: if Naturalism, No reason. But then ignores or evades the empirical experience of reasoning.

The Objectivist reasons (rightly) that: If experience of reason, ability to reason. But then ignores or evades the fact that their worldview (Naturalism) contradicts this experience.

My worldview holds "Supernaturalism" (the idea that more than the physical universe exists) and therefore has no such need to pit reason against experience on this issue.

In other words, we don't know how free will could emerge from determined matter, so let's posit a supernatural explanation for it. The Objectivist is content to be empirical and say that he doesn't know how free will emerges. You are, for some reason, wanting to go beyond experience and posit an explanation that's not really an explanation.

[Plasmatic]

But that is not what I mean by nature. By nature I mean "the physical universe". Therefore the idea that something exists above and beyond the physical universe is not self-contradictory.

So what we have here again is actually another arbitrary concept from you then.

In fact, when I first read Rand's and Peikoff's objections to the Supernatural, I was thoroughly un-impressed. They assumed that other philosophers meant what they meant by the terms "universe" and "nature".

They assumed that by "nature", philosophers meant "all that exists" and by "supernature", philosophers meant "all that exists beyond all existence".

It's almost offensive that Rand thinks those philosophers are so stupid. And it's likewise offensive when that objection is made to me as if I have no grasp on the Law on Non-Contradiction whatsoever.

What Rand was doing was refusing to acceptt an arbitrary usage of a concept and evaluating what it would actually mean, that is, from an Oist epistemology. Would you rather her exegesis focus on the arbitrary facet of these invalid concepts? So you are not contradicting yourself only reality and objectivity, fine.

Edited November 7, 2010 by Plasmatic

[Jacob86]

If you mean that deductive argument was supposed to show the irrationality of a worldview, of course it would appear irrational, since it was an entirely rationalist argument. Anyone who argues like that will end up with big philosophical problems that apparently you recognized (the problem is lack of concretes). Anyway, without a brain, there is no mind; mind is basically an abstraction that describes the experience of thinking made possible by your brain.

I'm not sure what you mean by "entirely rationalist argument" or why you think that my argument is lacking in some way.

Let me put a smaller version of a similar argument forth and see if you would reject or accept it..

This is an argument against someone who believes that "there is no absolute truth"

If there is no absolute truth, than no proposition about reality is true.

The proposition that there is no absolute truth is a proposition about reality.

Therefore, the proposition that there is no absolute truth is not true. LNC

Therefore there is absolute truth. LEM

(LI throughout)

This does not necessarily tell us any details about what is absolutely true. But it does tell us that there is absolute truth and that any worldview which denies absolute truth is irrational and must be rejected.

Do you disregard such an argument? If so why? If not, what is the difference between this argument and the one pertaining to Naturalism?

[Jacob86]

This misrepresents my argument. I wasn't saying that we, in this world, can evaluate the argument. I was saying that the people in non-dualistic-minds world, whether that world is identical to this world or not, can evaluate the argument.

I'm sorry. I do not at all wish to misrepresent your argument.

To be clear- you are saying that "even in a reality in which only physical matter exists, people would still be able to evaluate arguments"? Is this correct?

What is your reasoning for this? I have given fairly strong reason(imo) to believe that it is impossible. Do you see a hole in my argument??

In other words, we don't know how free will could emerge from determined matter, so let's posit a supernatural explanation for it. The Objectivist is content to be empirical and say that he doesn't know how free will emerges. You are, for some reason, wanting to go beyond experience and posit an explanation that's not really an explanation.

Not quite. I haven't yet posited a thorough supernatural explanation for it (to be honest, I still see it as much of a mystery in some ways). I.e. I am not saying "THIS is how reasoning works supernaturally:......".

I'm simply saying that in order for reason to "work" or be valid, there must be a "Supernature" or more than the physical universe- regardless of any attributes about it and how it works and interacts with physical nature, this much must be true: that it exists.

Even if we know nothing else about it, by virtue of Logic, it must exist.

Edited November 7, 2010 by Jacob86

[Jacob86]

So what we have here again is actually another arbitrary concept from you then.

What Rand was doing was refusing to acceptt an arbitrary usage of a concept and evaluating what it would actually mean, that is, from an Oist epistemology. Would you rather her exegesis focus on the arbitrary facet of these invalid concepts? So you are not contradicting yourself only reality and objectivity, fine.

Imagine a highly intellectually advanced village which lived in the shadow of Mt. Everest. The inhabitants, though very wise philosophically, had never seen any other part of the world.

They reason that "Existence exists" and that Mt. Everest and the surrounding area which they experience is the sum total of all existence and the necessary existent.

Now imagine a young boy comes into the picture and suggests that there might be more to existence than they thought. At first they accuse him of denying the axiom. Eventually he helps them distinguish between existence as such and that which they hold to be existence as such (Mt. Everest). Then he posits that other parts of reality may exist, to which they swiftly reply "absurd!" based on the fact that they have no empirical evidence to suggest such a thing (they are not able to cross the mountains and have never met anyone from across the mountains).

Is it really absurd? Or is it a knee-jerk reaction to protect the most precious piece of their worldview (the center) regardless of caring whether or not it is accurate.

I am not necessarily accusing YOU of such a knee-jerk reaction, but I am asking you to consider that refusal to have the discussion because of seeming absurdities seems to suggest such insecurities.

If it really is that obvious of an absurdity, then it should show itself to be irrational fairly quickly...so you don't have much to worry about..right?

Edited November 7, 2010 by Jacob86

[Plasmatic]

I am not necessarily accusing YOU of such a knee-jerk reaction, but I am asking you to consider that refusal to have the discussion because of seeming absurdities seems to suggest such insecurities.

If you are not accusing me of the above [which doesn't apply to me in any way] , then why ask me such a question and make such suggestions?

If it really is that obvious of an absurdity, then it should show itself to be irrational fairly quickly...so you don't have much to worry about..right?

Well it IS already obvious to me that your comments heretofore have been arbitrary and it only took reading one paragraph to do so. Its your failure to address this problem that should be worrisome. In other words all further discussion should be about epistemology and why the arbitrary should be dismissed.[with a dab of why perception is the only basis for evidence]. Until then condescension, in the form of allegories ascribing limited knowledge of the philosophical landscape to your opponents only amounts to ad hominem/evasion.....

Pay attention:

Objectivist dont start evaluatiing a set of propositions deductively in mid stream. They begin by evaluating the content of said deductive propositions, i.e. the concepts they consist of. If you ask me "Will you consider an argument for the existence of a non- physical purple zig zag as a fundamental constituent of entities" We are gonna start by discussing the validity of such a concept and what in perception it is based on.

Edited November 7, 2010 by Plasmatic

[dream_weaver]

Imagine a highly intellectually advanced village which lived in the shadow of Mt. Everest. The inhabitants, though very wise philosophically, had never seen any other part of the world.

They reason that "Existence exists" and that Mt. Everest and the surrounding area which they experience is the sum total of all existence and the necessary existent.

Now imagine a young boy comes into the picture and suggests that there might be more to existence than they thought. At first they accuse him of denying the axiom. Eventually he helps them distinguish between existence as such and that which they hold to be existence as such (Mt. Everest). Then he posits that other parts of reality may exist, to which they swiftly reply "absurd!" based on the fact that they have no empirical evidence to suggest such a thing (they are not able to cross the mountains and have never met anyone from across the mountains).

Is it really absurd? Or is it a knee-jerk reaction to protect the most precious piece of their worldview (the center) regardless of caring whether or not it is accurate.

I am not necessarily accusing YOU of such a knee-jerk reaction, but I am asking you to consider that refusal to have the discussion because of seeming absurdities seems to suggest such insecurities.

If it really is that obvious of an absurdity, then it should show itself to be irrational fairly quickly...so you don't have much to worry about..right?

A similar argument would be to point out to a two-dimensional creature living on a two-dimensional plane that there is a three-dimensional world that the two-dimensional creature is unaware of, references different aspects of reality which are quite demonstatable to us as three-dimensional creatures.

To use that to suggest that there is a fourth-dimension that we as three-dimensional creatures are not aware of, could be referred to as 'digging Plato's cave'.

The third-dimesional world can be demonstrated: relative to a demonstratable two-dimensional world: is not the demonstration of a four-dimensional world: relative to a demonstratable three-dimensional world.

[Jacob86]

If you are not accusing me of the above [which doesn't apply to me in any way] , then why ask me such a question and make such suggestions?

Well it IS already obvious to me that your comments heretofore have been arbitrary and it only took reading one paragraph to do so. Its your failure to address this problem that should be worrisome. In other words all further discussion should be about epistemology and why the arbitrary should be dismissed.[with a dab of why perception is the only basis for evidence]. Until then condescension, in the form of allegories ascribing limited knowledge of the philosophical landscape to your opponents only amounts to ad hominem/evasion.....

I mentioned it as an allegory for what seemed to be the case in this discussion so far- not as a means of condescension. (And I apologize if it came across that way). In the allegory, it is POSSIBLE that the boy is wrong. The emphasis was not on the right or wrong position of each side, but rather on whether or not the boy was being absurd in asking the questions. Another way to put it is: "Does the boy have an intellectual right to ask such questions?" OR still another observation would be that "the village philosophers were defining absurdity in such a way that prevented the ability to question their definition of absurdity..which is circular reasoning".

Regardless, we can leave that behind for now because I think you hit the nail on the head when you suggested that a discussion on Epistemology is in order.

Pay attention:

Objectivist dont start evaluatiing a set of propositions deductively in mid stream. They begin by evaluating the content of said deductive propositions, i.e. the concepts they consist of. If you ask me "Will you consider an argument for the existence of a non- physical purple zig zag as a fundamental constituent of entities" We are gonna start by discussing the validity of such a concept and what in perception it is based on.

Based on what you have said here, I agree that there must indeed be some extreme clarifications on epistemology and what is meant by "absurd".

[As a side note, I want to express my appreciation of your willingness to evaluate the issue and attempt to identify the necessary point of disagreement (epistemology here) in order to establish common ground... rather than declaring the discussion irrational and not worth your time].

When I first began this thread, I had what I THOUGHT to be a good amount of understanding about what Objectivism teaches. As discussion has continued, it has become obvious that what I thought was meant by certain terms or concepts and what I thought was being used as fundamental assumptions in Objectivism are not the case.

Let me start by asking you WHY the Objectivist (or you in particular) starts with perception? Also, in order to clarify terms, by "perception" do you mean what is commonly referred to as "empirical evidence" / "induction"? If you mean something different could you briefly elaborate on the difference? I think I have an idea as to your answer, but I do not want to assume anything so I'd like to hear your explanation.

Thanks again for your civility in the discussion.

[Jacob86]

A similar argument would be to point out to a two-dimensional creature living on a two-dimensional plane that there is a three-dimensional world that the two-dimensional creature is unaware of, references different aspects of reality which are quite demonstatable to us as three-dimensional creatures.

To use that to suggest that there is a fourth-dimension that we as three-dimensional creatures are not aware of, could be referred to as 'digging Plato's cave'.

The third-dimesional world can be demonstrated: relative to a demonstratable two-dimensional world: is not the demonstration of a four-dimensional world: relative to a demonstratable three-dimensional world.

Please see my elaboration on the allegory in the above reply to Plasmatic. The allegory is not being used to PROVE the existence of Supernature (let alone a "fourth dimension")...as the allegory does not assume either party to be necessarily right or wrong (as I intended it). The point of the allegory was to demonstrate:

1)The intellectual right of the boy to question the assumptions of the village (even if he ended up being wrong).

And

2) the circular reasoning of the village philosophers in their definition of "absurd"-- even if they ended up being right.

[Plasmatic]

Jacob said:

Now imagine a young boy comes into the picture and suggests that there might be more to existence than they thought. At first they accuse him of denying the axiom. Eventually he helps them distinguish between existence as such and that which they hold to be existence as such (Mt. Everest). Then he posits that other parts of reality may exist, to which they swiftly reply "absurd!" based on the fact that they have no empirical evidence to suggest such a thing (they are not able to cross the mountains and have never met anyone from across the mountains).

..............................

but rather on whether or not the boy was being absurd in asking the questions. Another way to put it is: [1.]"Does the boy have an intellectual right to ask such questions?" OR still another observation would be that [2.] "the village philosophers were defining absurdity in such a way that prevented the ability to question their definition of absurdity..which is circular reasoning".

There is a difference in the absurdity of a notion to one who knows better and the innocence of one who is ignorant of implicit errors in the notion.

The answer is to [1.] is: Of course! Objectivism holds independence as a virtue. Consider these words in Atlas Shrugged

" Consider the reasons which make us certain that we are right," said Hugh Akston, "but not the fact that we are certain. If you are not convinced, ignore our certainty. Don't be tempted to substitute our judgment for your own."

The answer to [2.] is: This is just a preposterous strawman. There could be no such "prevention" precisely because ones mind is their own. All one has to do is start discussing what a valid definition must entail and why![instead of the straw man about absurdity and nefarious intentions built into Oist definitions]

Edited November 7, 2010 by Plasmatic

[Jethro Bodine]

Jacob 85 Wrote:

The point of the allegory was to demonstrate:

1)The intellectual right of the boy to question the assumptions of the village (even if he ended up being wrong).

And

2) the circular reasoning of the village philosophers in their definition of "absurd"-- even if they ended up being right.

As a member of the village, I would say, "Let's go on a journey to find out!" The villagers are capable of validating or invalidating the claims of the boy by their own experience. Until that trip is made, there is no reason to believe the boy's story. If the trip cannot be made and the boy could not possibly have made the trip, having claimed to have received special knowledge in a dream, then the claim must be held to be arbitrary and invalid.

I perceive another error you make in that you claim to be able to deduce the existence of something not observable. Let me give you a similar example. Cantor's Theorem in Set Theory says that the cardinality of a set is strictly less than the cardinality of its power set (set of all subsets). The proof is very simple and is by Reduction Ad Absurdum. An immediate consequence of Cantor's Theorem is that there are in infinity of infinite cardinalities, each of different size.

One can either accept the proof that there are different sizes of infinite cardinality, or one can suspect that a premise upon which the proof lies is false. Most mathematicians make the former choice because the alternative is that the Law of the Excluded Middle (LEM) is false and this would fly in the face of two millennia of mathematics. Of course, no experiment can be performed to make a distinction between the cardinality of two infinite collections of objects.

Philosophically, occam's razor indicates that the latter choice is the proper one. However, without empirical evidence one way or the other, does it really matter? Ah, but with the advent of quantum physics came quantum logic, which specifically violates LEM. One could say that LEM is empirically false and with it all Reductio Ad Absurdum proofs.

Now, you have used just such a proof in your argument for the existence of absolute truth. I reject this argument, not only because I reject the Law of the Excluded Middle but because every theory, no matter how logically arrived at, requires validation by reference to perceivable reality. A claim that cannot be reduced to observation is rejected on its face, regardless of how reasonable. In fact, if a claim can be deduced that cannot be verified, it is better to start looking for weaknesses in the underlying hypotheses.

Jethro Bodine

[Eiuol]

Do you disregard such an argument? If so why? If not, what is the difference between this argument and the one pertaining to Naturalism?

"4)If only physical cause and effect can explain the activity in our brains, then only cause and effect can explain the act which we call “reasoning” or “thinking” or “being objective”.

But “to reason objectively” means for the activity of one’s brain to correspond accurately to outside reality.

5)If only physical cause and effect can explain all activity in the brain, then one’s brain cannot be said to accurately correspond to reality except by extremely low probabilities of mere chance."

5 doesn't even follow from 4. Where did "except by extremely low probabilities" even come from?

Also, what I mean by rationalistic is that there are NO concrete examples given in those numbered steps.

[Jacob86]

Jacob said:

There is a difference in the absurdity of a notion to one who knows better and the innocence of one who is ignorant of implicit errors in the notion.

The answer is to [1.] is: Of course! Objectivism holds independence as a virtue. Consider these words in Atlas Shrugged

" Consider the reasons which make us certain that we are right," said Hugh Akston, "but not the fact that we are certain. If you are not convinced, ignore our certainty. Don't be tempted to substitute our judgment for your own."

Agreed. ..And love the quote.

The answer to [2.] is: This is just a preposterous strawman. There could be no such "prevention" precisely because ones mind is their own. All one has to do is start discussing what a valid definition must entail and why![instead of the straw man about absurdity and nefarious intentions built into Oist definitions]

By prevention I mean "disallowing it to stand in a discussion". What I'm getting at here is that they defined "absurdity" in such a way as to make it "absured" to question the definition of "absurdity".

"Absurdity is the idea of anything outside of our experience- therefore to question whether or not there is anything outside of our experience is absurd and furthermore it is absurd to suggest that a different standard of absurdity be used because in order to do so, one must commit the absurd act of postulating something outside of our experience"

[Jacob86]

Jacob 85 Wrote:

As a member of the village, I would say, "Let's go on a journey to find out!" The villagers are capable of validating or invalidating the claims of the boy by their own experience. Until that trip is made, there is no reason to believe the boy's story. If the trip cannot be made and the boy could not possibly have made the trip, having claimed to have received special knowledge in a dream, then the claim must be held to be arbitrary and invalid.

The allegory assumed that such a trip was impossible. It did not assume that the boy was certain of his idea or that he had any special revelation- only that he was considering/questioning the possibility. However, as all allegories, it is incomplete and insufficient, so I'd rather move on. I believe I've made my intended point with it.

I perceive another error you make in that you claim to be able to deduce the existence of something not observable. Let me give you a similar example. Cantor's Theorem in Set Theory says that the cardinality of a set is strictly less than the cardinality of its power set (set of all subsets). The proof is very simple and is by Reduction Ad Absurdum. An immediate consequence of Cantor's Theorem is that there are in infinity of infinite cardinalities, each of different size.

One can either accept the proof that there are different sizes of infinite cardinality, or one can suspect that a premise upon which the proof lies is false. Most mathematicians make the former choice because the alternative is that the Law of the Excluded Middle (LEM) is false and this would fly in the face of two millennia of mathematics. Of course, no experiment can be performed to make a distinction between the cardinality of two infinite collections of objects.

Philosophically, occam's razor indicates that the latter choice is the proper one. However, without empirical evidence one way or the other, does it really matter? Ah, but with the advent of quantum physics came quantum logic, which specifically violates LEM. One could say that LEM is empirically false and with it all Reductio Ad Absurdum proofs.

Now, you have used just such a proof in your argument for the existence of absolute truth. I reject this argument, not only because I reject the Law of the Excluded Middle but because every theory, no matter how logically arrived at, requires validation by reference to perceivable reality. A claim that cannot be reduced to observation is rejected on its face, regardless of how reasonable. In fact, if a claim can be deduced that cannot be verified, it is better to start looking for weaknesses in the underlying hypotheses.

Jethro Bodine

Hm. I disagree, but I will suspend a full response until I see Plasmatic's (or others') responses to this (unless of course it takes too long for them to respond..) haha.

[Jacob86]

Real quickly; could you tell me whether or not you would accept the argument given concerning absolute truth? So I can know where you stand? Thanks.

"4)If only physical cause and effect can explain the activity in our brains, then only cause and effect can explain the act which we call “reasoning” or “thinking” or “being objective”.

But “to reason objectively” means for the activity of one’s brain to correspond accurately to outside reality.

5)If only physical cause and effect can explain all activity in the brain, then one’s brain cannot be said to accurately correspond to reality except by extremely low probabilities of mere chance."

5 doesn't even follow from 4. Where did "except by extremely low probabilities" even come from?

Also, what I mean by rationalistic is that there are NO concrete examples given in those numbered steps.

Well- whatever the probability is of random molecules bumping into each other in such a way as to cause a chemical reaction in our brains which would produce an idea which happened to correspond accurately to reality. I haven't attempted to run the figures, but I assume it's rather low.

Regardless, even if it happened to be HIGH probability, it is only probability and chance; and therefore any degree of certainty would be impossible in such a world. Therefore all propositions would be suspect- including the proposition that nothing but physical matter exists.

I still don't know what you mean by "concrete examples". If you mean referents to reality they are

A ) The idea that only physical matter exists and

B ) The fact that we have the ability to reason.

The form of the argument is basically as follows:

"If A is true, B cannot be true. B is true. Therefore A cannot be true."

It's not rocket science.

Edited November 7, 2010 by Jacob86

[Jethro Bodine]

Jacob 86 wrote

The form of the argument is basically as follows:

"If A is true, B cannot be true. B is true. Therefore A cannot be true."

It's not rocket science.

You forgot to add Reductio ad absurdum at the end of your proof. At least, all such proofs require the Law of the Excluded Middle.

Edited November 7, 2010 by Jethro Bodine

[dream_weaver]

Regardless, we can leave that behind for now because I think you hit the nail on the head when you suggested that a discussion on Epistemology is in order.

<snip>

Let me start by asking you WHY the Objectivist (or you in particular) starts with perception? Also, in order to clarify terms, by "perception" do you mean what is commonly referred to as "empirical evidence" / "induction"? If you mean something different could you briefly elaborate on the difference? I think I have an idea as to your answer, but I do not want to assume anything so I'd like to hear your explanation.

Thanks again for your civility in the discussion.

And while Objectivism views Metaphyisics as the foundational, it is essentially relies on Objectivists Epistimology to integrate them together.

Keep in mind, this a broad overview and simplification which relies on contextual usage of many of the concepts used to explain it here.

Why start with perception? In short, we open our eyes, we listen with our ears, etc., sensations automatically integrated into percepts (entities) are what we first encounter and concretize. Conceptual consciousness differentiates and integrates the material provided by the senses. Primarily, consciousness is a difference detector if you will. When we observe specific entities to be similar, induction allows us to integrate those instances under the concept we are taught by our parents as 'dog', 'cat', 'table', 'chair'.

Later, as we expand our range of knowledge, we further integrate 'dog' & 'cat' under the concept 'animal'; 'table' & 'chair' under the concept of 'furniture'. Note that there are no existents 'animal' or 'furniture'. Animal subsumes 'cat', 'dog', 'horse', 'bird' - which we can point to ostensively and state 'by dog', I mean (pointing at Fido) Fido here. This permits us to 'validate' concepts like 'dog' & 'cat'. This permits us to 'prove' a concept as 'furniture' by identifying the existent/entities it refers to and wrap up the proof with the validation of 'table', 'chair', 'bed', etc.

Objectivist epistemology can be touched upon in a forum setting. To be fully grasped, it is best to grapple with it via it's source, "Introduction to Objectivist Epistemology" or in conjunction with "Objectivism: The Philosophy of Ayn Rand".

[Jacob86]

Jacob 86 wrote

You forgot to add Reductio ad absurdum at the end of your proof.

To be perfectly honest, I never was aware of the fact that "reductio ad absurdum" was a form of argument- let alone the form of the one I was applying. (That is until I just looked it up in response to this). Thanks.

[Jacob86]

So, does everyone else agree with Jethro that the LEM is not valid????

Just curious.

[Plasmatic]

So, does everyone else agree with Jethro that the LEM is not valid????

Just curious.

He'll no! He has no idea what he's talking about! He has to assume LI and all it's corollaries to even make the stupid mistake many physicist have made in not understnading the foundational nature of philosophy. Let's not waste

any more time on such nonsense in this thread.

Need more time to respond to your other posts....

Edited November 8, 2010 by Plasmatic

[Jethro Bodine]

Jacob86 wrote

So, does everyone else agree with Jethro that the LEM is not valid????

Just curious.

Your question is valid, and I would like to read any responses. However, to focus on this is to miss my point that even the rules of logic require validation by reduction to perception. Logic is not a primary or first order concept. You may deduce theorems to you heart's content, but those theorems still require additional validation.

Edited November 8, 2010 by Jethro Bodine