Criticizing Objectivist Metaphysics


Renee Katz

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If Rand said "A leaf cannot be a stone at the same time" I don't see how this is any different than saying a wave cannot be a particle at the same time. She says nothing about mutual exclusion, etc.

A leaf cannot be a stone at the same time? Check your premises...

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  • 3 weeks later...
2. Aristotelians (and others) have known how to handle Euclidean geometry arguments for over 2000 years. Beginning with certain assumptions and definitions, Euclidean geometry uses deductive syllogisms (Aristotelian logic) to arrive at an enormous number of conclusions. Euclidean deductive arguments ~are~ Aristotelian deductive logic applied to the study of points, lines, planes, and volumes. (This is not a definition, just a half-assed description.) I recall being told when I took Basic Symbolic Logic in college that, if I had taken and understood Euclidean geometry, I would have no trouble with the college course. Indeed, that was so -- same song, second verse, you might say.

Here is a reference you will need to answer a subsequent question: http://en.wikipedia.org/wiki/Syllogism

This article conveniently lists all of the valid categorical syllogisms in one place and provides examples of each valid categorical syllogism.

O.K. We have the database containing all the valid categorical syllogisms in place. Now the challenge.

Take in hand a universally accepted translation of -Euclid's Elements-. I would recommend the Heath translation which includes all kinds of reference notes and analysis of the proofs. Look at Prop 47, Book I. This is the famous Pythagoras Theorem for right angle triangles. The sum of the squares on the legs of a right triangle equals the square on the hypotenuse. O.K. Are you with me? Now using the list of valid categorical syllogisms given in the base line reference (the Wiki article) produce a proof of Prop 47 using only categorical syllogisms. Tough you say? You bet. But I am an easy fellow. Try proving the following:

Prop 2 using only valid categorical syllogisms. Prop 2 states (using the Heath translation): To place at a given point (as an extremity) a straight line equal to a given straight line. The proof given by Euclid (as translated by Heath) does not use a single valid categorical syllogism. Not one. I am challenging you to replace Euclid's proof for this simple proposition with a proof that uses only valid categorical syllogisms (a la Aristotle as given in -Prior Analytics-).

[snip comments on calculus and modern logic]

I do not deny that anyone capable of doing Aristotelean syllogistic has the wits necessary to prove Euclid's theorems. But I also say, valid categorical syllogisms were not the way Euclid's theorems were proven. Hence the above challenges. Syllogistic logic, therefore, is NOT NECESSARY to do Euclid's geometry. And in light of the problem of the existence of least upper bounds, the syllogistic logic of Aristotle is NOT SUFFICIENT to do the necessary mathematics required by physics (basically, integral calculus). I would go even further to say that casting Euclidean proofs in the form of valid categorical syllogisms is not worth the effort. Logic based on the hypothetical conditional (which is now expressed as propositional calculus) and beefed up with quantifiers to get first order logic is good for many of the proofs in modern mathematics and physics and is a hell of a lot easier (Google <Natural Deductiion>). Or put in a less charitable way, the Aristotelian Syllogistic is as necessary as buggy whips to get about.

Ba'al Chatzaf

Sorry, but none of this makes any sense to me. I aced Euclidean geometry, and I don't recall using any logical processes other than straightforward deduction from axioms, definitions, and previously established results.

You offer Euclid's Proposition 2 as a challenge. OK.

Given and having constructed the following:

1. Given segment BC and outside point A.

2. Connect A and B, making segment AB.

3. Make circle 1 on B with radius AB.

4. Make circle 2 on A with radius AB.

5. Make make circle 3 on B with radius BC.

6. Extend chord DB from intersection D of circles 1 and 2, through B to point G on circle 3.

7. Make circle 4 on D with radius DG.

8. Extend chord AD from D to A to point L on circle 4.

===================================

Prove that segment AL = segment BC:

1. BC = BG (radii of the same circle are equal)

2. DL = DG (radii of the same circle are equal)

3. DA = DB (Proposition 1)

4. AL = BG (from 2 and 3: equal segments diminished by the same amount are equal)

5. AL = BC (from 1 and 4: segments equal to the same segment are equal)

Despite the need for constructing 4 circles and 2 (or 3) line segments, the deductive process is relatively simple, requiring only two deductions. So, I did not have to stand on my head or get out the "buggy whip" in order to lay out the proof.

And the deductions are both categorical syllogisms, with the categorical premises being "All equal segments diminished by the same amount are equal" and "All segments equal to the same segment are equal". So, as I said before, Euclidean geometry is carried out by basic Aristotelian deductive logic.

Now, Aristotle would be the first to admit that more is needed in order to establish Euclid's propositions than deductive logic. One must discover or intuit the deductive pathway, perhaps by "thinking backward" from the intended conclusion, to figure out what is needed in order to establish the conclusion. But this is nothing new or controversial.

If I missed anything in the 8 preliminary steps or the 5 proof steps, I'm sure you'll let me know. :-)

REB

P.S. -- I wouldn't mind tackling Proposition 47 sometime when I'm not so busy. But I expect that it will be just somewhat "busier" and more long-winded than the proof for Proposition 2, not different in essence. Since you offered Proposition 2 as an acceptable stand-in, I will take your challenge as having been answered, in principle.

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Not at all. The premise that a thing cannot behave like a wave and also behave like a particle was just wrong.

I'm sorry, but are you agreeing or disagreeing with me? Doesn't the 'law of identity' say that it cannot do this?

No. A coin can be a gambling device and also be a means of payment. A thing can be two different things a the same time if these two things are not mutually exclusive characteristics, so there is no contradiction. An elementary particle can behave like a particle and also behave like a wave. You don't see this combination in the macroscopic world, where these characteristics seem to be mutually exclusive (and that is the source of confusion), but experimental evidence shows that this is not true at atomic scales.

In general, I agree with Dragonfly's comments, here and elsewhere in this thread. However, I think that a bit more precision would be helpful. And I do have one specific objection to make about the above.

First, the objection: it has demonstrated that entities in the macroscopic world do exhibit both particle-like and wave-like properties or behaviors. My favorite example is the compression-rarefaction phenomenon in freeway traffic flow that can be observed perceptually from planes and helicopters. These are all individual automobiles driven by individual human beings, but also moving in wave-like patterns. You can also observe this in long lines at the Post Office or DMV. :-(

Secondly, a clearer statement of the Law of Contradiction is that a thing cannot be both A and non-A at the same time and in the same respect. That is, it cannot have a given characteristic and NOT have that characteristic at the same time and in the same respect. Viz., an elementary particle cannot both have mass and NOT have mass at the same time and in the same respect. An elementary particle cannot both possess wavelike properties and NOT possess wavelike properties at the same time and in the same respect.

An leaf actually living now cannot be a dead leaf at that time or in that respect. However, it WILL BE a dead leaf LATER (different time) -- and it IS POTENTIALLY a dead leaf NOW (different respect).

DB's silly attempts to ridicule the Law of Identity and the Law of Contradiction, notwithstanding, they have withstood far more competent attempts than his to invalidate them.

REB

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First, the objection: it has demonstrated that entities in the macroscopic world do exhibit both particle-like and wave-like properties or behaviors. My favorite example is the compression-rarefaction phenomenon in freeway traffic flow that can be observed perceptually from planes and helicopters. These are all individual automobiles driven by individual human beings, but also moving in wave-like patterns. You can also observe this in long lines at the Post Office or DMV. :-(

That is not the same thing. The waves you see in a traffic flow are formed by varying movements of a large number of individual cars. In fact this is true for all waves in classical physics: these are formed by varying movements of a large number of (non-wavelike) particles: sound waves, waves in the water etc. (for light waves the ether was hypothesized for this reason). But the individual cars are not wave-like, it is only through their collective behavior that waves are created, and that is the essential difference with the microscopic world, where individual electrons (or photons) can exhibit both particle behavior and wave-like behavior.

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First, the objection: it has demonstrated that entities in the macroscopic world do exhibit both particle-like and wave-like properties or behaviors. My favorite example is the compression-rarefaction phenomenon in freeway traffic flow that can be observed perceptually from planes and helicopters. These are all individual automobiles driven by individual human beings, but also moving in wave-like patterns. You can also observe this in long lines at the Post Office or DMV. :-(

That is not the same thing. The waves you see in a traffic flow are formed by varying movements of a large number of individual cars. In fact this is true for all waves in classical physics: these are formed by varying movements of a large number of (non-wavelike) particles: sound waves, waves in the water etc. (for light waves the ether was hypothesized for this reason). But the individual cars are not wave-like, it is only through their collective behavior that waves are created, and that is the essential difference with the microscopic world, where individual electrons (or photons) can exhibit both particle behavior and wave-like behavior.

Wave and Particle are modes of description, not literal properties. The underlying entities/processes that make us perceive light do not have properties that are meaningful at our scale of existence (macroscopic). We are prisoners of our size. Our understanding of the world is shaped and influenced by our size. Our ideas and concepts are acquired in a man-scaled context. We stretch our man-scaled ideas (wave, particle) to apply to teeny tiny things in a metaphorical manner (aided by some fancy mathematics). Physics could readily be conceived of as a metaphorical mode of understanding the world, as opposed to a literal mode of understanding the world. Even our words for understanding, grasp, conceiving are used metaphorically. I like Heinlein's made up word "grok". It does not have baggage (in a manner of speaking) as do some of our other words.

Ba'al Chatzaf

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Consciousness assumes that entities exist because if you are conscious of something, then there has to be a thing being perceived and a thing doing the perceiving. Consciousness assumes that the entities act because without action or motion, consciousness doesn't work. Consciousness IS action. In order to be a aware, you have to DO something; the perception of reality is an ACTIVE process.

Jolly good. All forms of knowing involve interaction between the Knower and the Known (as you have ably pointed out). Here is a question for you. It is possible for the Knower and the Known to be one and the same?

Ba'al Chatzaf

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Wave and Particle are modes of description, not literal properties. The underlying entities/processes that make us perceive light do not have properties that are meaningful at our scale of existence (macroscopic). We are prisoners of our size. Our understanding of the world is shaped and influenced by our size. Our ideas and concepts are acquired in a man-scaled context. We stretch our man-scaled ideas (wave, particle) to apply to teeny tiny things in a metaphorical manner (aided by some fancy mathematics).

Bob,

This is as I think. It goes the other way, too. We are hopelessy tiny specks in the big scheme of things, yet "ideas and concepts are acquired in a man-scaled context." I tried to argue this perspective once on another forum and was called everything but loony, and this was only because they did not think of that term.

In fact, I believe philosophy, as opposed to science, is conditional to this size consideration. Size is one of the main ways science extends from philosophy.

Michael

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  • 5 weeks later...
If I missed anything in the 8 preliminary steps or the 5 proof steps, I'm sure you'll let me know. :-)

REB

Point out where you used categorical syllogisms. Starting with BaRBaRa and going to the others.

My point is, that categorical syllogisms are rarely used in a mathematical context. And for good reason. The categorical style is constipated. Mathematics runs on conditional modes, not categorical modes. Different tune, different trope although they are all music.

Ba'al Chatzaf

Edited by BaalChatzaf
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"It is in the nature of that leaf-stone to be itself; that is, a leaf-stone"

It was a fossil. Since when is the impression an object makes in plastic medium, the object itself?

Ba'al Chatzaf

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If I missed anything in the 8 preliminary steps or the 5 proof steps, I'm sure you'll let me know. :-)

REB

Point out where you used categorical syllogisms. Starting with BaRBaRa and going to the others.

My point is, that categorical syllogisms are rarely used in a mathematical context. And for good reason. The categorical style is constipated. Mathematics runs on conditional modes, not categorical modes. Different tune, different trope although they are all music.

Ba'al Chatzaf

Simple! Barbara, all the way...

BC and BG are radii of the same circle.

Radii of the same circle are equal.

1. So, BC and BG are equal.

DL and DG are radii of the same circle.

Radii of the same circle are equal.

2. So, DL and DG are equal.

DA and DB are sides of equilaterial triangle (ADB).

Sides of an equilaterial triangle are equal. (Proposition 1.)

3. So, DA and DB are equal.

Equal segments diminished by the same amount are equal.

AL and BG are equal segments (DL and BG) diminished by equal amounts (DA and DB). (2 and 3)

4. So, AL and BG are equal.

Segments equal to the same segment are equal.

BC and AL are equal to the same segment (BG). (1 and 4)

5. So, AL and BC are equal.

Naturally, once we automatize the various definitions and propositions and the ways in which they are deductively related, we don't repeat all these steps explicitly. The deductions are abbreviated. For instance, in a single step of a proof, say #5, you refer to steps 1 and 4 and draw on the principle that segments equal to the same segment are equal. Just because this is abbreviated, however, does NOT mean that you are NOT using deductive logic, with categorical syllogisms.

Also, I must say that it does NOT appear "constipated" to me, to illustrate the categorical deductive structure of a Euclidean proof. Making the implicit explicit is illuminating, not constipating. To me, anyway. I guess I'm only in charge of ~my~ mental bowel habits. :-)

REB

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  • 1 month later...
Basically my dissent involves the three basic axioms: Existence, consciousness, and identity. I don't think they're wrong or that they're in the wrong order, but I think that consciousness rests on two crucial concepts: entity and action. I think that these concepts are implicit in consciousness and that without them consciousness is a floating abstraction.

That is analogous to Aristotle's understanding of substance (thing-hood) and essence (a thing at work being itself). He saw substances are being form + matter. See also Aristotle's locution -entelechia- (being at work staying itself).

Aristotle effectively created the basic philosophical vocabulary that we use today, regardless of whether he was right or not. He is somewhat analogous to Shakespeare who single handedly doubled the vocabulary of the English language of his time. We are still using Shakespearian tropes, words and phrases.

So even when we disagree with Aristotle, we disagree in the terminology he largely created.

Ba'al Chatzaf

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  • 2 weeks later...

Ba'al:

~ I know I'm going to be sorry I got into this, but...

~ ('Basic') arithmetic is rarely used in (especially your level) 'Mathematics', ergo...?

~ I've clearly overlooked something in my readings on electron/photon experiments; has there been an experiment showing the single entity manifested simultaneously as BOTH a 'particle' AND 'wave'...in the same respect, er, experiment? --- I see this 'wavicle' prob as akin to seeing the heads/tails of a coin: different perspectives (observational experiments) show different, but never simultaneously both, aspects. (And, who's going to say that a coin has no 'identity'?)

LLAP

J:D

Edited by John Dailey
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  • 1 month later...
I'm still wondering if standard Objectivist philosophy nowadays allows that Aristotle's logic was deficient in its ability to capture, say, mathematical deductive inference.

Indeed, could it even capture this following inference?

Premise: There is some person who loves every person.

Conclusion: For every person, there is a person who loves them.

Note that the inference in the opposite direction is not logically legitimate.

Note too, this inference involves a non-unary, relational predicate, 'x loves y'.

If it is a requirement that the premise is true, then why is the conclusion not allowed? It seems to me that you created a contradiction and then denied it is a contradiction.

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  • 5 years later...

Posted 05 October 2007 - 12:22 PM

Stephen Boydstun, on Oct 5 2007, 12:01 PM, said:snapback.png

She writes:
"To exist is to be something, as distinguished from the nothing of non-existence, it is to be an entity of specific attributes. . . . Existence is Identity, Consciousness is Identification.
"Whatever you choose to consider, be it an object, an attribute or an action, the law of identity remains the same. A leaf cannot be a stone at the same time, it cannot be all red and all green at the same time, it cannot freeze and burn at the same time.
". . . . An atom is itself, and so is the universe; neither can contradict its own identity; nor can a part contradict the whole." (AS 1016)

Yeah, I like most people would at least agree that things are what they are at any specific moment in time. But the "A=A," Law of Non-Contradiction, Objectivist notion of identity seems like too narrow a definiton for identity, I think. Why can't an identity be any relationship where one thing connects with another, both as "A=A" and "A is similar to A" (or B or C or whatever it connects closely [or even distantly] to). This would make identity a wider concept, one more general and seemingly more fundamental. To me all things seem interconnected somehow, both within and outside the mind.

Because we don't know an object or entity or thing only at one specific moment in time, but at many moments in time (being that change seems inevitable through the active state of our lives and/or consciousness), why can't identity be a synthesis of these two ideas? Just like existence doesn't fix down any exact idea in its definiton, because it is everything (or subsumes everything?), why do identities have to concretize things only to thier exact, "denotative" definitions? In art, for example, I find it refreshing when there are several layers of interpretation that can be suggested for a meaning-- that doesn't have to take away from any essential meaning in the work, or even the denotative list of subject matter, materials, techniques etc used to create the effect-- these layers instead seem to add to the meaning of art, help give it more nuance, or a larger, more penetrating identity.

For example, in Rand's examples above, a leaf could exist in petrified or decaying form within a stone, red and green in an impressionist painting blend to brown when standing at a certain distance from a painting-- so that brown is both red and green at the same time. If you wanted to isolate the red and the green to their specific shapes, one could move even further in within the red shape and perhaps see green specks, as long as those specks were dominated and surrounded by a red more intense so that in backing up again they disappear to red. And doesn't liquid nitrogen literally both freeze and burn our skin at the same time? Again I'm not denying that things are what they are at any moment in time, but shouldn't identity, to be posited as a useful axiomatic concept, have an extended definition... like to any/all relationships? Isn't what we are trying to get out of identity the idea that there is some way to expain A as A because it connects to this or that content in some way, not simply because it can only be one thing at any moment in time?

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Wouldn't the idea above morph Rand's ideas of "measurement ommission" in Intro to Objectivist Epistemology, to also include within its process "mesurement inclusion," much like how we use both induction and deduction to form an idea, if there isn't just one specifc identity in anything we are trying to define?

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Responding to an earlier post by Roger Bissel, what he says about the Law of Non-Contradiction is absolutely logical--a thing cannot both be itself and not itself at the same time in the same context (although he explains it much better than this). What I would ask then, is the Law of Non-Contradiction the only thing encompassed within the idea of identity? Could it also include the idea that all things are interconnected somehow? Would this make the concept more useful? more accurate? more all-emcomssing to better ground its axiomatic nature?

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Welcome to Objectivist Living, Dan!

Some quick thoughts:

Rand's notion of identity was pretty inclusive. She tried to explain perceptual similarities in terms of identical dimensions common to similar things having different magnitudes along those dimensions. That was an endorsement of simple substitutional identity, such as is normally meant by the formula A=A. But she also packed specific natures into her notion of identity, so that the nature of a leaf, that it cannot freeze and burn at the same time (in the same little bit of it, I imagine), is part of her meaning of A=A or "A thing is itself" or "A thing is what it is."

Stephen

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Welcome to Objectivist Living, Dan!

Some quick thoughts:

Rand's notion of identity was pretty inclusive. She tried to explain perceptual similarities in terms of identical dimensions common to similar things having different magnitudes along those dimensions. That was an endorsement of simple substitutional identity, such as is normally meant by the formula A=A. But she also packed specific natures into her notion of identity, so that the nature of a leaf, that it cannot freeze and burn at the same time (in the same little bit of it, I imagine), is part of her meaning of A=A or "A thing is itself" or "A thing is what it is."

Stephen

And yet there are properties of things that are not permanent and change over time. White bread is not forever white. Sometimes it turns green and moldy. Sometimes it turns brown (when it is toasted).

So how does A is A deal with the reality of change?

Ba'al Chatzaf

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Good question Ba'al-- I wonder how you'd respond to that Stephen. Stephen when you talk about Rand's inclusion of "perceptual similarities in terms of identical dimensions common to similar things having different magnitudes along those dimensions," it sounds like your'e talking about the difference between "kinds" and "degrees" of something, like vertical vs. horizontal categorization. Is this a fair assessment? I guess I'm trying to understand your "identical dimesions common to similar things" idea. "Identical" from what I gather of how she/you are using the A=A notion, means one thing is exactly like another thing in some way. I'm not sure that really holds physically speaking, since for example, two cups of the same kind, although they will have a similarity of shape and a common function (normally for drinking), if examined physically, they have different space-time placements for one, and probably a lot of minute differences in their microscopic compositions, and of course cups can be used for very different things-- e.g. one for drinking and the other for holding objects. If the idea of identity is simply made more general to include any/all relationships-- that things have to relate somehow, but not pin identity's axiomatic nature to any exacting contexts (yet stemming from it's one exception--that things also are what they are at any specific moment in time [since this doesn't seem to contradict physics]), then I think it alleviates having to tie the axiomatic notion of identity to our perceptual processes, and still allows us to say that, for example, that there is no "mind-body" dichotomy, because all things have to relate somehow, no matter if we are able to define those relations. I'm not arguing that Rand's notion was pretty inclusive (I think it was the best idea of its time), but pretty inclusive is not all-inclusive-- I think axiomatic concepts need to be all-inclusive.

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Stephen is our Resident Scholar. You should get a good answer in due course.

Ba'al Chatzaf

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