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Post 40

Sunday, January 27, 2008 - 7:41pmSanction this postReply
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Similarly, a person might simply enjoy living moment to moment...and the more moments, the better.

That is a psychological abberation - is like living as an animal, not human.....


Post 41

Sunday, January 27, 2008 - 9:06pmSanction this postReply
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That is a psychological abberation - is like living as an animal, not human.....

Humans are animals.

Seems to me a life is just as valuable whether a person wishes to live his life celebrating only the "rational" part of himself, or only the "animal" part of himself.

Personally, I find ostentatious displays of wealth to be more of a psychological aberration than mere hedonistic self-indulgence. The latter involves no one but the hedonist, and is not meant to affect anyone else (despite the fact that Objectivists seem to take offense at it); the former is almost always done as a put-down to others -- a not-so-subtle reminder of their lower status.

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Post 42

Tuesday, January 29, 2008 - 12:46pmSanction this postReply
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I wrote, "In Post #3, I disproved the possibility of an after life, by showing that the idea is self-contradictory."

Claude Shannon replied,
You asserted that it was self-contradictory. You never substantiated your assertion. You merely define consciousness in such a way that a contradiction follows if we assert its independent existence. Big deal.
I didn't simply define it (arbitrarily) in such a way that a contradiction follows. I pointed out its necessary preconditions, which are that it requires a particular form and means of awareness. Are you seriously suggesting that a person can be conscious in no particular form and by no particular means?!? How is that even conceivable? In fact, it isn't, because to conceive of being conscious, one must conceive of it in a particular form, which in turn requires a particular means of awareness (e.g., vision requires the eye, the optic nerve and visual cortex, etc.)

I wrote, "Suppose I were to accuse you of murder without offering any evidence for it, either in terms of who the victim is, or how, where or when you were alleged to have committed the murder. And suppose I then demanded that you prove that you didn't commit a murder. Well, of course, you couldn't satisfy my demand, because you couldn't 'prove a negative' in that sense of the terminology."
Nonsense. By definition: “Good people cannot commit murders” / “I am a good person” / Ergo, “I cannot commit murder”. That satisfies the condition “Prove that you did not commit the murder.” If you then ask “Well, prove that you really are good,” I will say, “Sure…but that’s a different condition and a different demand”, which is the same sort of infinite regress you can get with any sort of syllogism, including “All men mortal” / “Socrates is a man” / Ergo, “Socrates is mortal”. You could say “That doesn’t satisfy me; prove that all men actually are mortal; now prove that Socrates actually is a man”, etc. As long as we define our terms the way we wish, we can prove the non-existence or non-occurrence of something.
Not true. Proof rests on concrete evidence. Knowledge isn't based on arbitrary definitions. For example, if you were prosecuting me for murder, you would have to produce concrete evidence sufficient to prove my guilt beyond a reasonable doubt. Similarly, if you were my attorney and were going to exonerate me, you would have to show that the evidence is insufficient to establish my guilt. You couldn't simply say, "Good people do not commit murders; my client is a good person; therefore, he didn't commit this murder."

I wrote, "What Christopher is saying in relation to your example is that to believe in the actual existence of intelligent extraterrestrial life ought to require some proof. I assume that if the scientists you refer to have no proof whatsoever that intelligent extraterrestrial life exists, then they don't yet believe in its existence; at most, they believe in its likelihood, and are looking for evidence that it actually does exist."
Wrong. They believe that it actually exists. The “likelihood” is that they might be able to detect it.
Claude, are you using "believe" in the sense of "strongly suspect" (e.g., "I don't know for a fact that he murdered her, but I believe he did."). If you are, then I would agree with you. I was using "believe" in the stronger sense of a "claim to knowledge."

You wrote, "we don’t find consciousness without a living biological organism; we don’t find living biological organisms without some degree of consciousness."

I replied, "Not true. Plants are living organisms that have no consciousness. What you intended to say, I take it, is that we don't find animal life without some degree of consciousness, which is true."
Quite wrong. See below link: . . .
Interesting link. From what I can gather, I would disagree with these biologists' concept of what it means to be conscious. They are evidently equating consciousness with goal-directed activity, which I don't think is sufficient to establish its existence. You quote some of the biologists as follows:

QUOTE: “To a growing number of biologists, the fact that plants are now known to challenge and exert power over other species is proof of a basic intellect. ‘If intelligence is the capacity to acquire and apply knowledge, then, absolutely, plants are intelligent,’ agrees Leslie Sieburth, a biologist at the University of Utah in Salt Lake City.” END QUOTE

I don't think the mere ability to challenge and exert power of other species is sufficient to establish consciousness. And, although intelligence is the capacity to acquire and apply knowledge, it is doubtful that plants possess 'knowledge' in any normally understood sense of that term.
Plants are not mere automatons; plants are not machines. They are living organisms that have awareness of their environment. Plants absolutely are conscious – even if they are not self-conscious or display feelings.
I agree that plants are not automatons or machines; they're clearly living organisms, but even though they're able to interact with their environment in a goal-directed, self-sustaining manner, that doesn't mean that they are consciously aware of their environment.

I wrote, "You mean that consciousness is neither created nor destroyed? I don't think so. The evidence indicates that consciousness arose with the emergence of animal life, and did not exist before its emergence."
You have no evidence of that. You just have definitions.
Not true. Again, I'm not simply tendering an arbitrary definition. Consciousness is a faculty of living organisms (and I would further restrict it to animal life). Prior to the emergence of life on earth, there was no evidence of living organisms, nor of entities that possess consciousness.

I wrote, "And consciousness is certainly capable of being destroyed. It's destroyed whenever an animal dies."
I’m wondering at what point you’ll get tired of contradicting yourself. You’ve said elsewhere that “we know consciousness directly THROUGH INTROSPECTION” Right? Right! Can you know an animal’s consciousness through introspection? Yes or no? NO! You only know YOUR consciousness through introspection. Ergo, you have no idea what happens to an animal’s consciousness when its body dies. You will only have, one day, introspective knowledge of what happens to your consciousness when you die. That’s quite a different matter.
I said that we know consciousness directly through introspection. But we can know it indirectly in other human beings and animals by extrospection -- by observing sufficient similarities to warrant the inference that they too are conscious and have feelings. We also know that once an animal dies, its physical processes cease and it no longer exhibits any evidence of being conscious. Eventually, of course, the entire organism decomposes, and along with it the physical requirements of consciousnness, such as its sensory organs, brain and nervous system.

I wrote, "Yes, but consciousness still depends on matter; it cannot exist independently of it."
Question begging. You can’t assume as axiomatically true the very point that is in fact at issue.
Again, a consciousness requires a form and a means of perception, both of which cannot exist without a material basis in reality.
It’s also true that matter doesn’t exist independently of consciousness. You may attempt to provide proof if you believe it does.
Really! So inanimate matter is conscious?? The sun, the moon, the stars are all conscious? Remarkable.

I wrote, "Matter, by contrast, can exist independently of consciousness."
Question begging. How do you know matter can exist independently of consciousness?
Because I see that it can? Hello!

You wrote, "The notion that consciousness is a 'property' of the physical part of the organism implies that it is ultimately physical in nature and is ultimately reducible to and explainable by physical laws."

I replied, "But it has to be a property of a physical organism, because it requires a physical organism in order to exist."
Already discussed, disputed, and disproved. You know nothing about what consciousness “requires.” No one does. All we know is that we always find it accompanying a living organism, and living organisms accompany it. That relationship doesn’t indicate a “requirement.”
See above.

I wrote, "I would characterize consciousness as the subjective manifestation of the operation of the brain and central nervous system."
“Subjective manifestation” is simply another phrase for “experience” or “consciousness”. Again, you’ve merely repeated a definition – this time in slightly different words – without providing any new information.
Consciousness is "defined" ostensively. The point I was making is that consciousness a subjective manifestation OF THE BRAIN AND CENTRAL NERVOUS SYSTEM. I was stressing the latter, not the former.
Additionally, you were the one claiming that consciousness has a spatial location. The phrase, “Consciousness is the subjective manifestation of the brain + nervous system” does nothing to locate consciousness in a place.
Since consciousness IS a property of the brain and central nervous system, it is located in the same place as the brain and central nervous system.

I wrote, "Consciousness is known introspectively by direct experience . . ."
Consciousness is experienced directly via introspection. “To experience” consciousness and “to know what it is” are two different things.
I'm not sure what your point is. If a direct experience of consciousness is not sufficient to know "what" it is, then what kind of information do you require? What would satisfy you?

To be continued . . .



Post 43

Wednesday, January 30, 2008 - 11:49pmSanction this postReply
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Continuing from Post 42, I wrote, "Again, a consciousness requires sense organs and a brain in order to exist and function." Claude Shannon replied,
Again, sense organs and a brain require some degree of consciousness in order to function – and actually, even to exist AS a sense organ and a brain. “Brain/consciousness” and “sense-organ/consciousness” are complementary pairs.
Well, sense organs and a brain can certainly exist without being functional; a person who has just died still has a brain and sense organs, even though he no longer possesses any form of consciousness. Obviously, if his brain and sense organs are functioning as conscious receptors and as a means of cognition, they would require a process of awareness. But awareness is itself a manifestation of a functional brain and sense organs, on which it depends for its very existence.

I wrote, "A consciousness without a physical organism is a consciousness without the preconditions for experiencing the external world."
Concept stealing. “External World” presupposes the existence of consciousness. “External World” and “Internal World” come into existence together…that’s what “existence exists” means. It’s not a clarion call for the primacy of matter. You can’t have the “outside of a box” before you have the “inside of a box.” When you close a box, you simultaneously define an inside and an outside. An apt analogy for “subjective” and “objective.”
I agree. I meant "external world" from our own perspective, not from the perspective of an entity that lacks consciousness. To put it another way, a consciousness without a physical organism is a contradiction in terms; if it lacks a physical basis for perception and cognition, it lacks the preconditions for consciousness.

I wrote, "Without sensory evidence, one couldn't form concepts of any kind, including quantitative relationships."
No mathematician would agree with that. Neither would an ethicist.
Just to be clear, I meant that one needs at least some sensory evidence to form concepts, not that all abstractions must have concrete archetypes in order to be valid. For example, one needs sensory evidence of discrete instances in reality in order to grasp and form the concept of quantity. E.g., the referent of "five" is | | | | |. But once having the concept of number, one can abstract to much larger numbers than one could ever perceive directly. No one can directly perceive five million people, for example, but it is a perfectly valid concept nonetheless.

I wrote, "No one has ever seen a golden mountain either."
I have.
In reality? -- an actual mountain of solid gold? I don't think so.
But I know for a fact that you have never seen a perfect circle, because a perfect circle cannot exist in material reality (unlike a golden mountain, which, of course, can easily exist). Ergo, no one has ever perceived a perfect circle. You can THINK a perfect a circle; you cannot perceive one.
On the contrary, I have a book about plane geometry, which features a perfect circle. I am looking at it right now, and can perceive no imperfections. Now, you might say, but if you got a strong enough magnifying glass, you would definitely see some imperfections. Perhaps, but for the purposes of geometrical demonstration, the standards of perfection are less precise, and by those standards, in which there are no obvious imperfections, the circle is indeed perfect.

Earlier you wrote, "We do not arrive at the notion of 'perfect circle' by 'abstracting' from actual circles (which are all imperfect). You can’t abstract from the imperfect to the perfect since the 'perfect' does not exist except in the head of the mathematician." Well, you can arrive at the notion of a perfect circle by ignoring the imperfections of actual circles and considering only the essential shape. If you had no perceptual experience of shape, you couldn't arrive at the idea of a particular shape, just as if you had no perceptual experience of color, you could arrive at the idea of a particular color.

I wrote, "If we define proof as 'the derivation of a conclusion from antecedent knowledge,' then epistemological axioms cannot and need not be proved, but that doesn't mean that they don't require validation. Validation is a broader concept than proof. As Professor Peikoff notes, validation 'subsumes any process of establishing an idea's relationship to reality, whether deductive reasoning, inductive reasoning or perceptual self-evidence. In this sense, one can and must validate every item of knowledge, including axioms.' (OPAR, p. 8) One validates axioms ultimately by a direct appeal to sensory evidence."
I don’t know what you mean by “ultimately.” That sounds like logical positivism, which reduced all sentences to “protocol sentences” that had to be verified by the senses in order to be validated as “true.” The axiom “A is A” or “A cannot be both A and non-A at the same time and in the same respect” need not be confirmed by any appeal to sensory evidence. Same applies to all axioms of logic, mathematics, and ethics.
Sensory evidence is required in order to form any concept, since with the exception of abstractions from abstractions, a concept is a mental integration of two or more particulars. Concepts of logic, such as the principle of identity, are abstractions from abstractions, but the lower-level abstractions on which they depend must be grounded in concrete reality. Mathematical concepts are ultimately based on a perception of discrete units, but are not limited to them. One can conceive of quantities far greater than one can perceive. As far as ethics is concerned, it is simply a code of values to guide one's choices and actions in the pursuit of an ultimate end -- one's own happiness. In other words, ethics is a simply means to an ultimate value, whose recognition depends on a perception of reality and of one's survival requirements. If one had no perceptual awareness of reality, one couldn't conceive of one's needs or how to achieve them.
Most axioms are validated pragmatically: e.g., do the they work? do they help to organize the data in a consistent and convenient way? can I solve problems if I assume XYZ as my starting points?
According to Objectivism, the epistemological axioms -- of existence, consciousness and identity -- are validated by recognizing that one must accept and use them in any attempt to deny them.
Finally (and for the record re Peikoff’s statement above), there is no such thing as “inductive reasoning.” All reasoning is deductive. Karl Popper proved that long ago, and he spent most of his life writing on the philosophy of logic and science. An inductive statement is an utterance that falls under the field of rhetoric, not logic. Induction is a form of “argument from analogy.”
I don't think induction is simply a form of rhetoric. Consider the following example: You heat water to a certain temperature and observe that it boils. Now it's reasonable to conclude that its boiling at a certain temperature is a property of the water itself. Every cook who heats water in order to boil it is engaged in a process of inductive reasoning. He knows from experience that water will boil at a certain temperature. Since he wants it to boil, he heats it in order to get it to that temperature. Further study reveals that water boils at a different temperature at sea level than at altitude, that it depends on atmospheric pressure, and that it involves a process of the water's molecules breaking free from their bonds. All of this knowledge is arrived at by a process of inductive reasoning, which is every bit as legitimate as deductive reasoning. In fact, inductive reasoning is required just in order to exist and function in the real world.

- Bill
(Edited by William Dwyer on 1/30, 11:54pm)


Post 44

Thursday, January 31, 2008 - 5:14amSanction this postReply
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William Dwyer writes:

Just to be clear, I meant that one needs at least some sensory evidence to form concepts, not that all abstractions must have concrete archetypes in order to be valid. For example, one needs sensory evidence of discrete instances in reality in order to grasp and form the concept of quantity. E.g., the referent of "five" is | | | | |. But once having the concept of number, one can abstract to much larger numbers than one could ever perceive directly. No one can directly perceive five million people, for example, but it is a perfectly valid concept nonetheless.


I respond:

The cardinal integer five is -the class of all sets which are in one to one correspondence with the set of stroke marks
{| | | | |}-. A specific instance of the cardinal integer five instance is the aforementioned set of stroke marks, which is NOT the ordinal integer five. The cardinal integer five is a predicate which applies to certain sets of objects. The cardinal integer five has no referent in the world outside of your brain and mine. Classes of sets (particularly infinite or unlimited classes) have no existence in the physical world. In fact, mathematics done in the purely abstract mode has zero empirical content.

It is interesting that mathematicians must become "closet Platonists" in order to ply their trade. Most mathematicians I know (including myself) believe in the existence of mathematical objects when they are doing mathematics. When I am -talking about mathematics- in a detached way, I come to my senses (quite literally) and I know that my beloved objects and relations are ghostly spooks in my attic (so to speak)

There are no infinite anythings in the real (physical) world, but mathematics is replete with infinite sets and classes (e.g. the theory of transfinite numbers).

Bob Kolker


Post 45

Thursday, January 31, 2008 - 8:24amSanction this postReply
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I wrote, "Just to be clear, I meant that one needs at least some sensory evidence to form concepts, not that all abstractions must have concrete archetypes in order to be valid. For example, one needs sensory evidence of discrete instances in reality in order to grasp and form the concept of quantity. E.g., the referent of "five" is | | | | |. But once having the concept of number, one can abstract to much larger numbers than one could ever perceive directly. No one can directly perceive five million people, for example, but it is a perfectly valid concept nonetheless.

Robert Kolker replied,
The cardinal integer five is -the class of all sets which are in one to one correspondence with the set of stroke marks
{| | | | |}-. A specific instance of the cardinal integer five instance is the aforementioned set of stroke marks, which is NOT the ordinal integer five.
I'm sorry, I should have said that "a" referent of "five" is | | | | |; there is, in reality, no such thing as pure five. The number "five" refers to any set of five units.
The cardinal integer five is a predicate which applies to certain sets of objects. The cardinal integer five has no referent in the world outside of your brain and mine.
Not according to the Objectivist epistemology. Just as the concept "man" refers to any individual man (any person), so the concept "five" refers to any set of five units. To be sure, the concept "five" does not exist ontologically; it exists mentally, but its referents do.
Classes of sets (particularly infinite or unlimited classes) have no existence in the physical world. In fact, mathematics done in the purely abstract mode has zero empirical content.

There are no infinite anythings in the real (physical) world, but mathematics is replete with infinite sets and classes (e.g. the theory of transfinite numbers).
Mathematical infinity refers to the potential for extending a series without limit. It does not, and cannot, refer to actual infinity; there is no such thing.

- Bill

(Edited by William Dwyer on 1/31, 12:44pm)


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Post 46

Thursday, January 31, 2008 - 10:35amSanction this postReply
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W.D. says


Mathematical infinity refers to the potential for extending a series without limit. It does not, and cannot, refer to actual infinity; there is no such thing.


I reply:

In fact, the theory of transfinite numbers and set theory (as formalized under ZFC) regards infinities as completed (actual) entities and not merely a potential for "adding just one more".

Which is why G. Cantor generated so much opposition to his theory. Ultimately his approach has been accepted by the greater part of the mathematical profession. David Hilbert once wrote "from this Paradise which Cantor has made for us, no one shall expel us".

The Objectivist understanding of mathematics, particularly as articulated by Rand and Peikoff is just plain wrong. The Objectivist view of mathematics is just about as good as the Objectivist view of physics (especially in the quantum era) which is to say it is not very good.

Bob Kolker




Post 47

Thursday, January 31, 2008 - 12:54pmSanction this postReply
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I wrote, "Mathematical infinity refers to the potential for extending a series without limit. It does not, and cannot, refer to actual infinity; there is no such thing."

Robert Kolker replied, "In fact, the theory of transfinite numbers and set theory (as formalized under ZFC) regards infinities as completed (actual) entities and not merely a potential for 'adding just one more'."

I don't understand this. A "completed (actual) entity" is one whose limits have been reached. An infinite series is one without a limit. Isn't this a contradiction?

- Bill

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Post 48

Thursday, January 31, 2008 - 1:00pmSanction this postReply
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Dwyer:


I don't understand this. A "completed (actual) entity" is one whose limits have been reached. An infinite series is one without a limit. Isn't this a contradiction?


Kolker:

No. All of the known contradictions have been removed from set theory. It looks pretty clean now. The contradiction lies between you philosophical prejudices and the way the mathematical theories are. There are no known internal contradictions. You are exhibiting a frequently observed difficulty among Objectivists to comprehend what mathematics, especially modern mathematics based largely on set theory, is all about.

My recommendation: First learn the math. Then criticize it.

Bob Kolker


Post 49

Thursday, January 31, 2008 - 3:31pmSanction this postReply
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I didn't simply define it (arbitrarily) in such a way that a contradiction follows. I pointed out its necessary preconditions, which are that it requires a particular form and means of awareness.


 

 First you claimed to define consciousness; now, you claim that you weren’t really defining it, but rather “pointing out its necessary precondition”…which is not the same thing as a definition. It matters little; for what you have done here, as well as in the Evolution thread, is merely to <u>describe</u> consciousness (you will probably try to justify this practice by claiming that a mere description is really a higher-status thing – an “ostensive definition”!).


 

 A description is not the same as a definition. As for “necessary preconditions”, that could only happen if we move beyond a mere description (even if that mere description is given a deep-dish, high-falutin’ name like “ostensive definition.” We know that consciousness and biological organisms accompany each other; no one knows anything beyond that: no one knows HOW; no one knows WHY. Not even those great neuroscientists whose “incontrovertible evidence” you keep promising to cite, but somehow never get around to doing so.


 

 Are you seriously suggesting that a person can be conscious in no particular form and by no particular means?!?


 

 There are different degrees of consciousness: “self-consciousness”; “attention” (i.e., conscious of something else but not yourself); dreaming; “sleeping” (which is different from complete lack of consciousness).


 

 Proof rests on concrete evidence.

 

Math and logic are replete with proofs with no concrete evidence. Either the concrete evidence is missing entirely or it’s simply unnecessary. No one has to test the Pythagorean Theorem concretely by drawing right triangles in the sand with a stick (like the slave in Plato’s “Meno”). There is no “concrete evidence” proving the Law of Contradiction, or the Law of Excluded Middle.

 

Knowledge isn't based on arbitrary definitions.

 

There are different kinds of knowledge. Mathematical knowledge can certainly be based on arbitrary definitions. Lots of non-Euclidean geometry is based on arbitrary definitions (“Let’s pretend that NO two lines, drawn through two points, are parallel”; or, “Let’s pretend that ALL lines, drawn through two points, are parallel.”)

 

You couldn't simply say, "Good people do not commit murders; my client is a good person; therefore, he didn't commit this murder."

 

Quite untrue. Your defense attorney adjusts the kind of argument he uses to suit the kinds of arguments used by the prosecution. If the prosecution presents concrete incriminating evidence, your attorney either throws that evidence into doubt or presents concrete evidence to the contrary. If the prosecution presents arguments based on your character, the defense brings up arguments based on your character (such as witnesses to your character, who will attest under oath that “He is a good person / good people don’t commit murder / ergo, WD could not have committed murder.” That would be sufficient to establish your innocence if your goodness or lack thereof were the gravamen of the trial.

 

Claude, are you using "believe" in the sense of "strongly suspect" (e.g., "I don't know for a fact that he murdered her, but I believe he did."). If you are, then I would agree with you. I was using "believe" in the stronger sense of a "claim to knowledge."

 

Outside of math and logic, where we get to invent the definitions, no knowledge is completely certain. Outside of math and logic, all belief is of the “strongly suspect” variety.

 

I don't think the mere ability to challenge and exert power of other species is sufficient to establish consciousness. And, although intelligence is the capacity to acquire and apply knowledge, it is doubtful that plants possess 'knowledge' in any normally understood sense of that term.

 

There is no “normally understood” sense of the term “knowledge.” You are simply applying that term as it is experienced by an organism with self-consciousness, such as human beings.

 

I agree that plants are not automatons or machines; they're clearly living organisms, but even though they're able to interact with their environment in a goal-directed, self-sustaining manner, that doesn't mean that they are consciously aware of their environment.

 

It means precisely that. You confuse your general description with a definition; then you claim this “definition” has higher status than empirically verified knowledge. I’ll stick with the plant experts on this one.

 

Not true. Again, I'm not simply tendering an arbitrary definition.

 

That’s true. You are in fact tendering a general description of human self-consciousness, which you confuse for a definition. Then you move beyond that entirely by claiming that this general description gives you enough knowledge to tell us something about “preconditions.”

 

Consciousness is a faculty of living organisms

 

That’s a description, not a definition.

 

(and I would further restrict it to animal life)

 

Unwarranted assumption contradicting publicly verifiable facts about plant behavior by scientists who are experts in this field.

 

Prior to the emergence of life on earth, there was no evidence of living organisms, nor of entities that possess consciousness.

 

Huh? “Prior to the emergence of life on earth, there was no evidence of living organisms”? Profound. I like this one, too: “Prior to the emergence of wheat, there was no evidence of wheat products such as bread or pasta.”

 

I said that we know consciousness directly through introspection.

 

Yes, indeed. That’s what you said.

 

But we can know it indirectly in other human beings and animals by extrospection -- by observing sufficient similarities to warrant the inference that they too are conscious and have feelings.

 

“To know directly” and “to know indirectly” are two completely different ways of knowing. To those with normal color vision, we know the color red directly through a subjective experience; we know ultraviolet through inference.

 

We also know that once an animal dies, its physical processes cease and it no longer exhibits any evidence of being conscious.

 

That in no way means that consciousness has disappeared. It simply means that consciousness – whatever it is – was acting through the animal, making itself known to you by means of the animal. When a TV broadcast station dies, it ceases to function; the television signals it broadcast are still out there, radiating away.

 

Again, a consciousness requires a form and a means of perception, both of which cannot exist without a material basis in reality.

Again, matter and mind are polar opposites; they complement each other in Existence. With the exception of certain entities inexactly referred to as “particles”, matter requires the existence of consciousness in order to BE matter. All qualities, for example – hard, soft, green, red, loud, quiet, etc. – exist only as qualities to consciousness. Nothing is objectively “green” or “hard”. To some particles, neutrinos for example, nothing really exists: it’s all just empty space.

 

Really! So inanimate matter is conscious?? The sun, the moon, the stars are all conscious? Remarkable.

 

I’m glad you think so, but I didn’t say that. Once more: You have zero proof – except your own definitions – that matter can exist without consciousness…this doesn’t mean that matter is conscious; it means that matter requires its complement, consciousness, in order to BE matter.

 

Question begging. How do you know matter can exist independently of consciousness?

 

Because I see that it can? Hello!

 

No, you don’t see that it can. You BELIEVE that it can. Belief is something very different from perception.

 

Consciousness is "defined" ostensively.

 

“Ostensive definition” = “mere description.” This is useful in the primitive beginnings of a discipline when you don’t have any actual knowledge about the thing you’re trying to study. It’s one of the hallmarks of pre-scientific societies that its members forever remain in the grip of ostensive definitions. It’s one of the hallmarks of scientific societies that its members move beyond them to actual empirical knowledge of the thing they are studying.

 

The point I was making is that consciousness a subjective manifestation OF THE BRAIN AND CENTRAL NERVOUS SYSTEM.

 

Brain and nervous system are simply the means by which this other thing called consciousness makes itself known. There is no identity between brain and consciousness, nor does the material brain have a higher metaphysical status than non-material consciousness. Without consciousness, there are no “sense organs”; just dead wiring.

 

Without light, there is no such thing as “red.” If you take a red apple into a darkened room, it’s incorrect to say “It’s a red apple but the lights happen to be out.” If the lights are out, the red no longer exists. If consciousness is gone, even the term “sense organs” is a contradiction: there’s nothing to sense and nothing to do the sensing.

 

I'm not sure what your point is. If a direct experience of consciousness is not sufficient to know "what" it is, then what kind of information do you require? What would satisfy you?

 

Only someone ensnared by his own arbitrary “definitions” could doubt that there was something to know about some fact of reality beyond one’s mere experience of it.

 

You’re like the cleric in the play “Galileo” by Bertolt Brecht. Galileo shows the multiple moons of Jupiter to the cleric through his telescope. The cleric says, “Yes, I see them; but the real question is, are they logically necessary?” Since the definition of “Jupiter” does not involve the predicate “has multiple moons”, one is therefore entitled, according to this brand of nominalism, to ignore the empirical finding. This is what you did with the plant article above, as well as with several challenges I made to you to provide empirical evidence regarding consciousness. Your subjective experiences – whether you refer to them as “ostensive definitions” or not – don’t count as knowledge.



Post 50

Thursday, January 31, 2008 - 4:12pmSanction this postReply
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Shannon:


Math and logic are replete with proofs with no concrete evidence. Either the concrete evidence is missing entirely or it’s simply unnecessary. No one has to test the Pythagorean Theorem concretely by drawing right triangles in the sand with a stick (like the slave in Plato’s “Meno”). There is no “concrete evidence” proving the Law of Contradiction, or the Law of Excluded Middle.





Kolker:


(Formal or Abstract) Mathematics has zero empirical content. It has nothing to say about the world. It is entirely about the consequences that can be derived logically from formal or abstract postulates.

The Pythagorean Theorem follows logically from the postulates of Euclidean Geometry. It does not hold in non-Euclidean spaces.

The question under discussion is whether or not some part of us survives death in reality. There is no empirical evidence whatsoever to support this proposition nor can it be tested empirically (by living people). It is an operationally meaningless question.


Bob Kolker




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Post 51

Thursday, January 31, 2008 - 7:21pmSanction this postReply
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I wrote, A "completed (actual) entity" is one whose limits have been reached. An infinite series is one without a limit. Isn't this a contradiction?"

Bob Kolker replied,
No. All of the known contradictions have been removed from set theory. It looks pretty clean now. The contradiction lies between your philosophical prejudices and the way the mathematical theories are. There are no known internal contradictions. You are exhibiting a frequently observed difficulty among Objectivists to comprehend what mathematics, especially modern mathematics based largely on set theory, is all about.

My recommendation: First learn the math. Then criticize it.
Look, "a completed actual entity" (your terminology) is by definition not one without a limit, unless you and I aren't speaking the same language. I'm simply asking you to make sense. If you're going to reply to something I've written, you should at least be able to state your position in a way that's not self-contradictory. I'm talking about your position -- your statement -- what you've written -- not what other mathematicians may have said.

Don't tell me to go read someone else. If you've got a point that you think is true, you should be able to state it coherently in your own words. You haven't done that. What you've stated amounts to a contradiction.

- Bill
(Edited by William Dwyer on 2/01, 12:40am)


Post 52

Friday, February 1, 2008 - 2:06amSanction this postReply
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The points are:
1. Set theory as formalized under the ZFC axiomatization has no known internal contradictions.

2. ALL of mathematics can be based on it including arithmetic, the theory of real variables, the theory of complex variables, the theory of vector spaces, the theory of lattices (which can be used to encapsulate propositional logic) etc. etc.


Now what is your problem with set theory and the mathematics based on it? It satisfies the one and only condition mathematicians absolutely require and that is logical (internal) consistency. That fact that the mathematics grates upon your philosophical expectations and aesthetic is irrelevant as far as the mathematics is concerned. Theoretical mathematicians work with systems that are logically consistent and which they consider interesting or pretty (that is a subjective aesthetic matter).

Furthermore, when the abstract mathematical systems with which you are obviously uncomfortable are interpreted in a way that is congruent with observed reality (so as to become applied mathematics) you get physics, which has produced the computer system on which we are currently conversing. In short, the physics works (i.e. is empirically validated). Did you know that Isaac Newton and G. Leibniz based their calculus on the notion of the infinitesimal which is infinitely small, yet not zero? From a logical point of view this is difficult to justify (it has been justified logically, by the way) but it produces differential equations which is the gut of physics and the physics works!

Now what is your problem?

PS: This issue arises quite frequently when I discuss with Objectivists matters mathematical. They just don't get it.

Bob Kolker



Post 53

Friday, February 1, 2008 - 2:16amSanction this postReply
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Dwyer:

Look, "a completed actual entity" (your terminology) is by definition not one without a limit, unless you and I aren't speaking the same language. I'm simply asking you to make sense. If you're going to reply to something I've written, you should at least be able to state your position in a way that's not self-contradictory. I'm talking about your position -- your statement -- what you've written -- not what other mathematicians may have said.


Kolker:

Mathemtics consists of what other mathematicians have said plus what I (and others) have added. Mathematics is a cumulative activity in which the work of A is built on the work of B. You quote Rand. I quote Cantor, Zermelo, Frankel and all the others who have built set theory. But why should I? Go look it up. The literature is vast and this medium, RoR with ascii font, is inadequate to express mathematics decently. Besides which if I complied with your request I would have to type in a book length explanation which I have neither the time (it would take months) nor inclination to do. If you want to criticize mathematics coherently, FIRST learn the math, THEN criticize it. The material is readily available. You can start by reading the article on set theory in the Wikipedia which has dozens of references into the literature. And it is all free of monetary charge. All it requires is some effort on your part.

PS: I do not give mathematics lessons for free. I have tutored folks on set theory, but I have been paid for it.

PPS: If you have mathematical proof of a contradiction in set theory as formalized in the ZFC axiom system, publish it. You will become world famous over night. You will even get an article in the NYT science section.

Bob Kolker

(Edited by Robert J. Kolker on 2/01, 4:44am)


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Post 54

Friday, February 1, 2008 - 3:19amSanction this postReply
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And thus, it would seem, we have mathematicians in the same position as ivory tower philosophers, who would nit and pick nits for their own sake, claiming internal consistancy as their only relevance [and in the real world bringing out such idiocy as string theory, which by its own internals, cannot be proven, examplified, and must be 'taken by faith'].....
(Edited by robert malcom on 2/01, 3:20am)


Post 55

Friday, February 1, 2008 - 4:41amSanction this postReply
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reply to #54

String Theory (which is really a class of theories) is an attempt to overcome some of the difficulties in achieving a theory that can deal with all of the physical force. It is a class of physical theories and not purely formal mathematical endeavor. As a physical theory it has failed since it has yet to make a testable prediction.

On the other hand, purely formal mathematical theories have nothing whatsoever to say about the physical world. They are exercises in abstract form and logic. They are intellectual exercises pure and simple.

Applied mathematical theories are formal theories plus interpretations which map the mathematical objects and operations to physical objects and measurements. Such theories do have something to say about the world. For example, the theory of functions of a real and complex variables produces the theory of differential equations which is the gut of technique for dealing with changes in physical state as a function of time and space. They are the main cutting tool of physics and they work very well. Newton invented differential equations to describe matter in motion and make testable predictions. He succeeded to a high degree of precision.

We are having this computer mediated conversation because differential equations have made it possible.

Bob Kolker


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Post 56

Friday, February 1, 2008 - 11:09amSanction this postReply
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Bob,

Would you please read and respond to what I actually said?! I am not criticizing formal mathematics as a mathematical system. I was responding directly to YOUR statement, which on its face is self-contradictory. I wrote, "If you're going to reply to something I've written, you should at least be able to state your position in a way that's not self-contradictory. I'm talking about YOUR position -- YOUR statement -- what YOU'VE written -- not what other mathematicians may have said."

In Post 47, you referred to "infinities as completed (actual) entities and not merely a potential for 'adding just one more'." How can an an infinity, something without a limit, be a completed actual entity? If it has no limit, then, by definition, it can never be completed.

Are you now telling me that in order to resolve this contradiction, I have to spend months studying higher mathematics?

- Bill

Post 57

Friday, February 1, 2008 - 1:07pmSanction this postReply
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There are no known contradictions in set theory. The contradiction is in your head. Can I make it any clearer?

First, do you know what the word "infinite" means when applied to sets? You probably do not. A set has infinite cardinality if and only if it can be put into one to one correspondence with a proper subset of itself.

For example the set of integers has infinite cardinality.

Proof.

The correspondence n <-> 2*n puts the set of integers N into correspondence with the set of even integers E. Q.E.D.

Second, you have made no effort to understand what you are criticizing. That is not good scholarship.

Now either learn some set theory or forget about criticizing it.

Bob Kolker


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Post 58

Friday, February 1, 2008 - 1:32pmSanction this postReply
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Mr. Kolker said to Bill:
There are no known contradictions in set theory. The contradiction is in your head. Can I make it any clearer?
Don't worry about it, Bill, because set theory is all in his head (and the heads of others who have studied it).  As he said in post #50:
(Formal or Abstract) Mathematics has zero empirical content. It has nothing to say about the world. It is entirely about the consequences that can be derived logically from formal or abstract postulates.
He goes on to say in post #52:
Furthermore, when the abstract mathematical systems with which you are obviously uncomfortable are interpreted in a way that is congruent with observed reality (so as to become applied mathematics) you get physics...
Well, infinite sets can't be "interpreted in a way that is congruent with observed reality", as you have been trying to point out.
BTW, Mr. Kolker, when it comes to the rationalism that you are peddling, it's not that we Objectivists "just don't get it"; we don't want it.



Post 59

Friday, February 1, 2008 - 2:00pmSanction this postReply
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Well, infinite sets can't be "interpreted in a way that is congruent with observed reality", as you have been trying to point out.

It need not be "congruent with observed reality" to be mathematically and logically valid. That's one difference between mathematics and physics.

BTW, Mr. Kolker, when it comes to the rationalism that you are peddling, it's not that we Objectivists "just don't get it"; we don't want it.

That may be the reason there are no outstanding Objectivist mathematicians. The whole enterprise has to conform to "Introduction to Objectivist Epistemology" or they want nothing to do with it.


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