Criticizing Objectivist Metaphysics


Renee Katz

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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.

Consciousness assumes that entites exist because if you are conscious of something, then there has to be a thing being perceived and a thing doing the perceving. 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.

Moreover the concepts "entity" and "action" are axioms. They can't be defined, they can't be reduced to other concepts, and they can't be denied without contradicting oneself.

In short, I am challenging Objectivism in metaphysics because it fails to make explicit these two concepts (entity and action) that are inherent in the concept of consciousness, and that it does not recognize them as basic axioms. I'd like to discuss this.

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Renee,

Welcome to OL!

About axiomatic concepts, you appear to have a mistaken impression. Neither of the three fundamental ones are standalone. They all depend on the others. (Although existence does not depend on consciousness, as an axiom it does.) In the past I have used the image of the fundamental axioms being like facets of the same gemstone. One can focus exclusively on an axiom so you can talk about it, but one cannot remove the facet from the gemstone.

Also, entity and action are parts of the law of identity, which all boils down to existence. To quote Rand (from Atlas Shrugged, Galt's speech, p. 934):

To exist is to be something, as distinguished from the nothing of non-existence, it is to be an entity of a specific nature made of specific attributes. Centuries ago, the man who was—no matter what his errors—the greatest of your philosophers, has stated the formula defining the concept of existence and the rule of all knowledge: A is A. A thing is itself. You have never grasped the meaning of his statement. I am here to complete it: Existence is Identity, Consciousness is Identification.

Did that help?

Michael

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Hi Michael, thank you for responding.

About axiomatic concepts, you appear to have a mistaken impression. Neither of the three fundamental ones are standalone. They all depend on the others. (Although existence does not depend on consciousness, as an axiom it does.)

I am not sure what you mean by this. What is the difference? Why does existence not depend on consciousness, but as an axiom it does?

Also, entity and action are parts of the law of identity, which all boils down to existence.
This is another issue of mine. In Objectivism Identity and Existence are not two different things, but I would disagree. I think that these are two different concepts. Identity means the sum of an entities attributes, the nature of an entity; but an entity doesn't have attributes apart from being perceived. I mean, a thing can't be red as opposed to blue without someone perceiving it. Attributes don't exist.

So yeah, basically I would say that entity and action (awareness) are implicit in the law of identity, and not the other way around. Why would entity and action be parts of the law of identity?

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Why does existence not depend on consciousness, but as an axiom it does?

Renee,

Actually, if you are talking about the idea of existence, they both depend on consciousness. But as a state, we perceive "out there" that there are things that exist without consciousness. A whole bunch of them. Even things with consciousness do not have our consciousness. So we conclude that in the grand scheme of things, we are not fundamental to out there. Once our consciousness is gone, out there continues. If out there goes away, we go away with it. But like I said, the idea of all this needs a consciousness to figure it out.

An axiom is an idea regardless of how you look at it. As an idea, it needs a consciousness. The whole shebang axiom-wise is like the gem stone I mentioned.

In Objectivism Identity and Existence are not two different things, but I would disagree. I think that these are two different concepts. Identity means the sum of an entities attributes, the nature of an entity; but an entity doesn't have attributes apart from being perceived. I mean, a thing can't be red as opposed to blue without someone perceiving it. Attributes don't exist.

So yeah, basically I would say that entity and action (awareness) are implicit in the law of identity, and not the other way around. Why would entity and action be parts of the law of identity?

Identity and Existence are two different concepts. They are called axiomatic concepts. They are merely dependent on each other. They are not standalone states, albeit different concepts. Something with identity must exist as part of this state, and existence means to exist as something with identity as part of this state. The two concepts merely focus on a different aspect of the same state.

Colors certainly do exist without anyone to perceive them. They are merely not identified in such a case, but they do exist. They are part of "out there."

Michael

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Colors certainly do exist without anyone to perceive them. They are merely not identified in such a case, but they do exist. They are part of "out there."

Well, that depends how you define color. The usual definition is that of our perception of physical things. We may relate that to certain properties of those things (the kind of photons that they reflect or emit), where we may assign certain colors to certain wavelengths, but instead of one particular wavelength combinations of different wavelengths may also give rise to the same color perception, so that a particular color is not an intrinsic property of the thing we perceive. It is defined by our visual system. Different visual systems generate different sets of colors (color-blind people, animals that can see ultraviolet light but on the other hand can't distinguish some colors that are different to us). Two things that in our eyes have exactly the same color may in the eyes of other organisms have quite different colors.

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Colors certainly do exist without anyone to perceive them. They are merely not identified in such a case, but they do exist. They are part of "out there."

Michael

The frequency of a photon is objective. The color experience it produces in a conscious viewing being is subjective.

I will not make any Helen Keller jokes. I will not make any Helen Keller jokes .....

Ba'al Chatzaf

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Why does existence not depend on consciousness, but as an axiom it does?

Renee,

Actually, if you are talking about the idea of existence, they both depend on consciousness. But as a state, we perceive "out there" that there are things that exist without consciousness. A whole bunch of them. Even things with consciousness do not have our consciousness. So we conclude that in the grand scheme of things, we are not fundamental to out there. Once our consciousness is gone, out there continues. If out there goes away, we go away with it. But like I said, the idea of all this needs a consciousness to figure it out.

An axiom is an idea regardless of how you look at it. As an idea, it needs a consciousness. The whole shebang axiom-wise is like the gem stone I mentioned.

Oh, I definitely agree that the concept of existence depends on consciousness, but I'm talking about their referents in reality. I thought that the order of the axioms was important because consciousness in reality can't exist without existence.
Identity and Existence are two different concepts. They are called axiomatic concepts. They are merely dependent on each other. They are not standalone states, albeit different concepts. Something with identity must exist as part of this state, and existence means to exist as something with identity as part of this state. The two concepts merely focus on a different aspect of the same state.

Colors certainly do exist without anyone to perceive them. They are merely not identified in such a case, but they do exist. They are part of "out there."

The physical processes that make up colors exist, but the actual colors as perceived by a conscious being don't exist.
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"

The physical processes that make up colors exist, but the actual colors as perceived by a conscious being don't exist.

They surely do exist. Are you saying you have not experienced what you have in fact experienced? They exist but they are subjective.

Ba'al Chatzaf

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Well, that depends how you define color.

Dragonfly,

Correct. In philosophical terms, there is no way a person without specialized instruments or specialized knowledge would even know what a photon was. So it does depend on your definition.

Let's put it this way. I do not suggest you go into the business of selling house paint to housewives. In such a case, I would predict enormous conflicts.

:)

The physical processes that make up colors exist, but the actual colors as perceived by a conscious being don't exist.

Renee,

Of course they do. They exist inside a brain. It helps if you start thinking metaphysical ("out there") and epistemological ("in here").

Just because the epistemological sensation of a color is not the metaphysical source (existent), that does not mean that one or the other does not exist. They both do. They are merely two different things, albeit related.

Confusion starts when we use the same word for both things. Language is a messy business.

Michael

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Renee,

I just saw that you have a HUGE discussion on axioms going on at another forum. I will try to read some of that if you like. If you have any specific comments or doubts from there you would like to raise here, I would be glad to examine it. I'm not the world's greatest genius and have been known to make a mistake once or twice a year, but I can give it my best shot. There are some heavy dudes around here who will probably get interested and join in, too, depending on what the issue is.

Meanwhile, here are two essays you might want to read just to get the juices flowing without a whole lot of hairsplitting. I do admit that these matters can get incredibly boring and almost pointless after a while. Sort of like chewing on razor blades. But you will not find that in the two essays below.

Axioms: The Eightfold Way by Ron Merrill

Implied Axioms by Fred Seddon

There are also the study essays for Chapter 6 of ITOE linked in the thread ITOE - Enlightenment study papers (scroll down to Chapter 6 and there are two essays linked).

That should do for starters.

Michael

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Hey Michael, if you are talking about the discussion that's going on at SOLO, then I'd rather not bother with it. I actually like the way this thread is going much better.

And yes, I will definitely read those articles. This topic could never be like chewing on razor blades. EVER. :)

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Hello All,

Maybe this is a good thread in which to raise my related question about axioms.

One basic thing I don't understand about Objectivism is how it deals with logical inferences. My strong impression has been that it holds that all of logic was essentially fully captured by Aristotle's treatment of syllogisms.

But how can one do even the simplest kind of logical inference when it comes to such things as, say, Euclidean geometry? How could those logically rigorous arguments possibly be handled by Aristotlean logic? Has anyone holding to Objectivist philosophy tried to address this issue?

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Hello All,

Maybe this is a good thread in which to raise my related question about axioms.

One basic thing I don't understand about Objectivism is how it deals with logical inferences. My strong impression has been that it holds that all of logic was essentially fully captured by Aristotle's treatment of syllogisms.

But how can one do even the simplest kind of logical inference when it comes to such things as, say, Euclidean geometry? How could those logically rigorous arguments possibly be handled by Aristotlean logic? Has anyone holding to Objectivist philosophy tried to address this issue?

Huh? I'm nearly mystified by what context would prompt these questions. Are you a student?

1. Objectivism holds that ~deductive~ logic was nailed down by Aristotle's treatment of syllogisms. This is clear both in Peikoff's 1974 lectures, "Introduction to Logic," and Kelley's more recent textbook, The Art of Reasoning. But logic also includes concepts/terms, propositions and definitions, and inductive logic. Aristotle had a lot to say that we still use regarding concepts and propositions. However, although he certainly could handle himself inductively, he didn't systematize his thoughts on the skill like he did deductive logic or concepts or propositions. That task had to be taken up by Bacon, Mill, and others, including the 20th century Aristotelian logicians, H.W.B. Joseph and Leonard Peikoff.

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.

REB

P.S. -- Michael, got your ears on, good buddy? How about moving this thread over to the Metaphysics folder?

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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-).

Here are some interesting facts: Aristotle's syllogisms are a proper subset of what is now called first order logic or first order predicate calculus. In the 19-th century,Freidrich Ludwig Gottlob Frege invented a logic based on hypothetical syllogism (modus ponens is the corresponding inference rule) and quantifiers. Cleaned up and with modern notation (available in any reasonable text on logic) this is the logic used by mathematicians in the vast majority of proofs they do. Here is the interesting part: First order logic is insufficient to prove the following theorem. Given a non-empty set of real numbers bounded above, this set has a least upper bound. This theorem is necessary for proving the existence of certain functions and theorems in integral calculus. The American logician C.S. Peirce claimed that second order logic is required to do this proof. This was later proved by Loewenheim. Bottom line: First Order Logic, therefore Aristotelean syllogistic logic is NOT sufficient to prove the existence of least upper bounds which is necessary to prove many of the important theorems of real variable analysis, that branch of mathematics upon which much of physics is based.

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

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Thanks, Roger and Bob,

for #13 and #14.

Our standard modern logic has come to be called classical logic. This logic expanded and revised the logic of Aristotle as it had been developed up to the time of Kant. Classical logic, as taught in texts such as R. L. Simpson’s Essentials of Symbolic Logic and W. V. O. Quine’s Methods of Logic, is the culmination of innovations by Boole, De Morgan, Jevons, Peirce, and above all, Frege (1879).

Standard modern logic is called classical to distinguish it from extensions of it in modal logics and from rivals of it, such as intuitionist logic, many-valued logics, paraconsistent logics, fuzzy logics, quantum logics, and relevance logics. This last and modal logic, as well as the ways in which classical logic improves on Aristotelian logic (e.g., existential fallacy), stand out as promising productive integration with Rand’s metaphysics and conception of logic.

Predications are conceptual identifications. Edward Zalta takes the discipline of logic to be “the study of the forms and consequences of predication” (2004, 433).* That conception of logic fits well with Rand’s conception of logic as “the art of non-contradictory identification.” The ramifications of Rand’s idea that “logic rests on the axiom that existence exists,” combined with her E-, I-, and C-axioms, need to be charted through the terrain of classical logic, modal logic, and relevance logic.

~~~~~~

* “In Defense of the Law of Non-Contradiction” in The Law of Non-Contradiction, Priest, Beall, and Armour-Garb, editors (Oxford). Two beginning works have addressed how predication can be taken under Rand’s thesis “existence is identity.” These are the final section (IX) of my 1991 Objectivity essay “Induction on Identity” (V1N3) and David Kelley’s paper “Concepts and Propositions” read at the 1996 summer seminar of the Institute of Objectivist Studies.

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Ms. Katz,

Your idea that action should be an axiom, additional to the three Rand selected, is a friendly innovation and one worth pondering. Rand held that existents exist with identities independently of our identifications, independently of our consciousness of those identities. She held that the primary form of existence is entity and that entities bear attributes, have actions and susceptibilities, and stand in relations (ITOE 15, 39). She packs that and more into her epigram Existence is Identity.

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)

Is it possible for there to be identification of the identities of existents without existents being entities bearing actions and susceptibilities? Is it possible for the existents that are conscious agents to be the only existents that act? Is it possible for the existents that are the intentional objects of consciousness to be susceptible to consciousness without themselves bearing actions?

Some additional thinking related to these questions and to the question of whether action should be added as an axiom in Rand's metaphysics can be read in the Q&A Section at the SOLO site in my thread "Dependency of Change and Entity."

I maintain that identity in the world and all-pervasive occasions of the fact that existence is identity obtain without consciousness in the world. A notion of such identity (and of the fact that existence is identity) that does not include the fact of action in the world without consciousness is not the nature of the identity in the world that we find. If action should be added as an axiom in addition to existence and identity, then it should be done so for reasons that do not require appeal to the fact that acts of consciousness are themselves actions.

Stephen

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Huh? I'm nearly mystified by what context would prompt these questions. Are you a student?

1. Objectivism holds that ~deductive~ logic was nailed down by Aristotle's treatment of syllogisms. This is clear both in Peikoff's 1974 lectures, "Introduction to Logic," and Kelley's more recent textbook, The Art of Reasoning. But logic also includes concepts/terms, propositions and definitions, and inductive logic. Aristotle had a lot to say that we still use regarding concepts and propositions. However, although he certainly could handle himself inductively, he didn't systematize his thoughts on the skill like he did deductive logic or concepts or propositions. That task had to be taken up by Bacon, Mill, and others, including the 20th century Aristotelian logicians, H.W.B. Joseph and Leonard Peikoff.

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....

Sorry if I came to present my issue in the wrong context -- I'm new to these parts, and so don't have a feel for what's considered appropriate.

Just to give you a quick summary of my background, I was once (from about 1968-1973) pretty seriously involved in studying Objectivism, and attended a number of lectures given by Peikoff, and a course at the New School by Binswanger on Objectivism. But one problem I had with the philosophy at the time was that I couldn't understand how it handled the entire question of logical inference.

There are a number of things you say that I take issue with, and which replicate the sort of problems I had with Objectivist thought way back in the early 70s.

Most importantly is your assertion that "~deductive~ logic was nailed down by Aristotle's treatment of syllogisms." In fact, Aristotle's syllogisms did NOT capture all of deductive logic by any means. In fact, it is demonstrably incapable of capturing the logic of the simplest kinds of mathematical deductive inference -- the very basis of virtually every theory in the hard sciences. While you're right to point out that Aristotle and the Greek philosophers were perfectly aware of Euclidean geometry, and the rigorous inferences that discipline involved, the logical techniques of Aristotle had no way of capturing those inferences. While Euclidean geometry proceeded from axioms via purely logical inference to prove all of the theorems of the geometry, no philosopher or logician until Frege in the late nineteenth century was able to describe the logic of those inferences. The fundamental thing that Aristotlean logic lacked was an ability to characterize logical inferences when those inferences involved relational predicates or properties. Yet in mathematics, it's virtually impossible to find a subbranch in which relational predicates are not utilized. Even the simple assertion, "for every integer there exists a larger integer" involves necessarily a relational predicate -- "x is larger than y".

Now one reason for my original post is that I remember quite distinctly Peikoff deriding essentially all of modern "symbolic" logic (in part because of the so-called "paradoxes of material implication"). He argued, as do you, that Aristotle had captured all of logic. He basically claimed that the modern "symbolic" stuff was based in confusions of various kinds. I have been wondering if Objectivist thought has moved beyond this in the many years since.

What I find interesting is that others in response to my post seem to have basically accepted as legitimate many forms of modern logic. Is this now acceptable in Objectivist thought? How about people like Peikoff -- have they come around on this? (I'd be pretty surprised in Peikoff's case, given his general extreme reluctance to accept modifications in Objectivist beliefs, once stated.)

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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)

What about wave-particle duality? This would seem to contradict the "law of identity".

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What about wave-particle duality? This would seem to contradict the "law of identity".

Not at all. The premise that a thing cannot behave like a wave and also behave like a particle was just wrong. This premise was based on our experience of the macroscopic world where we never observe that kind of behavior, so it seemed intuitively obvious. But intuition can be wrong. We can't just extrapolate our macroscopic experience to the level of elementary particles, although some people find that difficult to accept.

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Now one reason for my original post is that I remember quite distinctly Peikoff deriding essentially all of modern "symbolic" logic (in part because of the so-called "paradoxes of material implication"). He argued, as do you, that Aristotle had captured all of logic. He basically claimed that the modern "symbolic" stuff was based in confusions of various kinds. I have been wondering if Objectivist thought has moved beyond this in the many years since.

Aristotle's logic is a restricted subset of logic, as it is now understood. Aristotle's syllogisms did not handle n-adic relations, functional relations or extended operations on sets. There are several modalities that Arisotle did not deal with. Metalogical analysis of logical formalisms was also out of reach for Aristotle, so he had no completeness or incompleteness theorems. Aristotle did not deal with multivalued logics where there is a degree associated with the truth of proposition. These logics are appropriate for situations where information is not complete. And this is just a beginning to the list.

All beginnings are difficult. Aristotle formulated logic version 1.0.

Ba'al Chatzaf

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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?

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Now one reason for my original post is that I remember quite distinctly Peikoff deriding essentially all of modern "symbolic" logic (in part because of the so-called "paradoxes of material implication"). He argued, as do you, that Aristotle had captured all of logic. He basically claimed that the modern "symbolic" stuff was based in confusions of various kinds. I have been wondering if Objectivist thought has moved beyond this in the many years since.

Aristotle's logic is a restricted subset of logic, as it is now understood. Aristotle's syllogisms did not handle n-adic relations, functional relations or extended operations on sets. There are several modalities that Arisotle did not deal with. Metalogical analysis of logical formalisms was also out of reach for Aristotle, so he had no completeness or incompleteness theorems. Aristotle did not deal with multivalued logics where there is a degree associated with the truth of proposition. These logics are appropriate for situations where information is not complete. And this is just a beginning to the list.

All beginnings are difficult. Aristotle formulated logic version 1.0.

Ba'al Chatzaf

I don't disagree with you, though I myself am unclear just how applicable particular so-called non-classical logics, such as modal logic or multivalued logic, really are to real situations. And for what it's worth, axiom systems expressible in the language of Aristotle's logic, that is, that of unary predicates, actually are complete and even decidable, though he certainly never got to a point that that question was something he could prove, or perhaps even contemplate. I do believe that his system of logic was "complete" in the sense that there were no inferences he could not capture in his syllogistic system, given the restrictions in the type of predicates he employed.

But I can only say that your own views here seem to conflict with the Objectivist views I remember pretty distinctly from many years ago. Under those views, Aristotle's logic captured all of logical inference.

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'.

Edited by frankly1
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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.

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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.

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