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Davy

Modern versus Traditional logic

42 posts in this topic

As I understand it, Objectivism uses the so-called "traditional" logic of syllogisms rather than the modern mathematical logic introduced by Frege/Russell. From the Objectivist view, are there important philosophical differences between the two logics? It seems to me that modern logic is still "Aristotelian" (in the sense that none of the traditional logic is denied) and is in fact a superset of the old logic in that it's able to analyse a much wider range of arguments (although it's more difficult to learn).

Edited by Davy
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There is nothing in Rand’s definition of logic, nor in her metaphysics and epistemology taken all together, that implies her concept of logic is incompatible with all developments in logic beyond Aristotle.* There is no incompatibility between Objectivism and the modern, standard first-order predicate logic with quantification and identity. In the modern propositional logic, Objectivism may need to take issue with the standard theory of material implication; it perhaps should embrace instead a form of relevance logic (a genre of non-standard modern logic). The work needed to settle that last point one way or the other is work not yet done by Objectivist thinkers.

. . .

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. See also.

~~~~~~~~~~~~~~~~

Remark

Rand’s metaphysics and epistemology may favor certain developments in two nonclassical logics: modal logic and relevance logic. But within our classical logic itself, it is unlikely that Rand’s 1957 metaphysics and the conception of logic she situates in it have any definite ramifications for second-order logic, only for elements up to first-order predicate logic with quantification and with identity.

Said of any existent, “A is A” can mean either “A is being A, specifically, A is predicatively being A the way it is and not in other ways” (Metaph. 1041a10–26) or it can mean “A is the same as A”. The latter can be divided into the merely verbal, as when we say “a belly is a tummy” or it can be more than merely verbal interchangeability, as when we say “a triangle is a trilateral” or “the morning star is the evening star.”

It is because identity has various bearings in the real that it has various bearings in logic. These would include the license of substituting like for like and the proscription of equivocation. Truth is preserved under the former, spoiled under the latter.

Another bearing of identity in logic is the logical relation of identity, which is usually denoted by the equals-sign in the texts (Copi’s Symbolic Logic, 158–68; Quine’s Methods of Logic, 268–73). Logic assimilates this relation by adding two axioms to those sufficient for the logic of (logical) quantification. One of those additional axioms is: for any a, a = a.

Within the syllogistic, we have the identity formula “Every A is A”. This was being used by logicians at least by the time of Albert the Great (13th cent.). They used it, for example, to prove the convertibility of "No B is A" to "No A is B". They added "Every A is A" to "No B is A" to infer "No A is B", relying on one of Aristotle’s forms of syllogism (first mood of the second figure):

No L is M

Every S is M

No S is L

No B is A

Every A is A

No A is B

(See Kneale and Kneale’s The Development of Logic, 235–36; also.)

The workings of identity in logic can sometimes look like a barren exercise. But these workings are for true thinking about the way the world is.

See also "Philosophy of Modal Logic" here.

~~~~~~~~~~~~~~~~

PS – Davy, welcome to OL. I like your portrait. When you next drop into the Abbey, please give him 10 seconds of silence from me.*

Edited by Stephen Boydstun
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As I understand it, Objectivism uses the so-called "traditional" logic of syllogisms rather than the modern mathematical logic introduced by Frege/Russell. From the Objectivist view, are there important philosophical differences between the two logics? It seems to me that modern logic is still "Aristotelian" (in the sense that none of the traditional logic is denied) and is in fact a superset of the old logic in that it's able to analyse a much wider range of arguments (although it's more difficult to learn).

There is a little about the difference between term logic and modern logic here.

Advances in term logic have been made by Fred Sommers in recent years. See here. His book The Natural of Natural Language lays it out and also discusses modern logic. The book is not widely available and expensive, unless you can borrow it from a library. Alternatively, George Englebretsen's book Something to Reckon With presents Sommers' term logic very well. Also Englebretsen's book (co-written) Philosophical Logic: An Introduction to Advanced Topics presents Sommers' term functor logic in Chapter 8, which you can see online with Amazon's Look Inside feature.

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Thanks for the feedback guys. I noticed that Peikoff's logic course seems to favour the traditional (pre Frege) logic, whereas modern philosophy students might not meet it at all; I haven't actually studied philosophy in a formal setting, but in most modern logic texts the 'old' logic doesn't seem to get much coverage, if any.

@ Merlin, I'm aware of Sommer's Term Logic (David Kelley devoted a chapter to it in the earlier editions of 'The Art of Reasoning') and prefer it to the standard predicate calculus - anyone giving it a try could hardly fail to agree, although it may not be up to mathematical reasoning. Thanks for the links.

You're probably aware of the work by Jewish philosopher/Logician Avi Sion (A Vision?). Loads of stuff on his site but I wish he would include a few more concrete examples in his texts which are incredibly dry and abstract. In 'Critique of Modern Logic' he says:

Modern symbolic logic gives the impression that it is extending the scope of formalization, by its symbolizations, but it is in fact doing nothing of the kind. It is just abbreviating language. I admit that such abbreviation is occasionally not without utility: it allows us to display a lot of data in a small space, and thus more readily perceive its patterns. But it can also be counterproductive, in many ways (see ch. 1).

This is just plain wrong. The scope of formalization has been extended enormously by modern logic.

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As I understand it, Objectivism uses the so-called "traditional" logic of syllogisms rather than the modern mathematical logic introduced by Frege/Russell. From the Objectivist view, are there important philosophical differences between the two logics? It seems to me that modern logic is still "Aristotelian" (in the sense that none of the traditional logic is denied) and is in fact a superset of the old logic in that it's able to analyse a much wider range of arguments (although it's more difficult to learn).

Modern (post-Boolean) logic differs from Aristotelian logic in this: Modern Logic does not assume universal propositions have existential import. In the statement All Politicians are Liars, If true, Aristotelian logic would infer that there exists a politician. Whereas the proposition All Unicorns are Blue would be false since there are no Unicorns. The Aristotelian approach cannot handle empty classes.

See http://en.wikipedia.org/wiki/Existential_import#Existential_import

Ba'al Chatzaf

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Great posts, Baal and Stephen. I was just looking into relevance logic seriously for the first time yesterday. If you've got any suggestion on where to start, outside the SeOP articles, I'd appreciate it.

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Stephen, I've been reading another thread "what use is Aristotle's logic?" which led me to Harry Binswanger's article in which he states:

The problem is not merely that no book has been written to incorporate the discoveries of Ayn Rand in epistemology. Nor is the problem merely that modern errors in epistemology are present in the current logic texts. The problem is that the modern texts proceed from the linguistic, formalistic context of contemporary philosophy. As a result, the logic texts currently in print generally range from misleading to worthless; many of them are actually destructive of logical thinking.

It seems to me that Binswanger is suggesting that there is an incompatibility between Objectivism and the modern logic, am I wrong? or have I hit on another schism here? I'm curious as to how modern logic can be "destructive of logical thinking".

Anyway, I've read the first chapter of Joseph's "Introduction to Logic" at archive.org and have ordered a copy from Amazon.

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Ryan,

Regarding #6:

. . .

I mentioned above that standard modern logic, which is an enlargement (and some correction) of logic beyond its development by Aristotle, is called classical to distinguish it from its further extensions and from its rivals. Logics that only extend classical logic will have modified some of “the classical logical constants, interpretation rules, axioms, or inference rules such that all the tautologies, theorems, valid inferences and laws of elementary logic still hold, along with some additional ones” (RL 40–41). Such are modern modal logics (Garson 2006; Priest 2001). The rivals of classical logic make modifications to “logical operators [constants], interpretation rules, axioms, or inference rules such that not all the tautologies, theorems, valid inferences, and laws of classical or elementary logic still hold” (RL 41). Such is relevance logic (Mares 2004; Priest 2001) or paraconsistent logic (Priest 2006).

The logics in rivalry with classical logic are contestants on the field of specifying which inferences, among our inferences in the vernacular, are valid. One inference certified in classical logic that many students find repugnant is the taking as valid any inference from false premises to a true conclusion. Paraconsistent logics and relevance logics are systematic formulations of logic in which such inferences come out as invalid. I should mention, too, that various informal fallacies of classical logic come to be formal fallacies within various nonclassical logics (RL 218).

. . .

References

Garson, J. W. 2006. Modal Logic for Philosophers. Cambridge.

Mares, E. D. 2004. Relevant Logic: A Philosophic Interpretation. Oxford.

Priest, G. 2001. An Introduction to Non-Classical Logic. Cambridge.

——. 2006. Doubt Truth to Be a Liar. Oxford.

Relevance Logic (American name) is the same as Relevant Logic (British name).

Davy, regarding #7:

In the text you quote, the deficiencies mentioned could apply to modern presentations of logic, without being an indictment of modern developments (19th and early 20th centuries) in logic per se. Dr. Binswanger’s final clause goes too far in my experience. None of the logic books below, from my personal library, are destructive of thinking, at least not when approached by one equipped with Rand’s ideas about logic.*

Introduction to Logic – Irving Copi

The Art of Reasoning – David Kelley

Symbolic Logic – Irving Copi

Methods of Logic – W. V. Quine

Intermediate Logic – David Bostock

Set Theory, Logic and Their Limitations – Moshé Machover

Modal Logic for Philosophers – James Garson

An Introduction to Non-Classical Logic – Graham Priest

Relevant Logic: A Philosophical Interpretation – Edwin Mares

Classical Mathematical Logic – Richard Epstein

Edited by Stephen Boydstun
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Anyway, I've read the first chapter of Joseph's "Introduction to Logic" at archive.org and have ordered a copy from Amazon.

This book can be gotten as an epub free(!!!!) from the Guttenberg Project.

I have it loaded on my Kobo.

Ba'al Chatzaf

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As I understand it, Objectivism uses the so-called "traditional" logic of syllogisms rather than the modern mathematical logic introduced by Frege/Russell. From the Objectivist view, are there important philosophical differences between the two logics? It seems to me that modern logic is still "Aristotelian" (in the sense that none of the traditional logic is denied) and is in fact a superset of the old logic in that it's able to analyse a much wider range of arguments (although it's more difficult to learn).

Yes and no. There are formal logical systems where the law of the excluded middle does not hold. There are the so-called paraconsistent logics where the law of non-contradiction does not hold. There are multi-value logics in which truth values other than TRUE and FALSE exist. Among these probability based logic and "fuzzy" logic. Then there are a large variety of modal logics where modalities other truth or falsity exist. The chief players in these are possibility and necessity. There are finite logics and logics with infinite modes of inference are possible.

The core of Aristotle's logic were the categorical statement (proposition) and categorical syllogism of which there are 19 valid forms.

Later developments in logic introduced conditional statements (if... then...).

As you point out Aristotelian logic can be rendered as a special subclass of first order logic.

All of the operations in Aristotelian logic can be restated as equations in Boolean algebra.

Ba'al Chatzaf

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It seems to me that those logics you mention fall more into the category of specialised tools rather than what we normally consider to be everyday (or scientific) reasoning, and some of them (the so-called "Deviant" logics) are controversial. I'm no expert, but for example, Intuitionist logic denies the law of the excluded middle when applied to some cases in mathematics which involve infinite sets.

I really can't conceive of any "non-Aristotelian" logic which would make sense in the real world, if "non-Aristotelian" means to deny any of the "laws of thought". How can logic be used to refute itself? Take quantum physics; because an electron can seem both to be, and not be, in one place, is it then reasonable to reject the law of non-contradiction on the grounds that contradictions exist "in reality"? But the motivation to rewrite the law of non-contradiction is prompted by that very law! In other words, the method of reviewing one's premises in the light of apparent contradiction is a cornerstone of Aristotelian logic.

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It seems to me that those logics you mention fall more into the category of specialised tools rather than what we normally consider to be everyday (or scientific) reasoning, and some of them (the so-called "Deviant" logics) are controversial. I'm no expert, but for example, Intuitionist logic denies the law of the excluded middle when applied to some cases in mathematics which involve infinite sets.

I really can't conceive of any "non-Aristotelian" logic which would make sense in the real world, if "non-Aristotelian" means to deny any of the "laws of thought". How can logic be used to refute itself? Take quantum physics; because an electron can seem both to be, and not be, in one place, is it then reasonable to reject the law of non-contradiction on the grounds that contradictions exist "in reality"? But the motivation to rewrite the law of non-contradiction is prompted by that very law! In other words, the method of reviewing one's premises in the light of apparent contradiction is a cornerstone of Aristotelian logic.

Indeterminacy exists "in reality" and is a not logical contradiction. Since one never knows where a particle is until it is detected, one detecst only a certain state or position when it becomes known. In that sense, there are no contradictions in reality. Indeterminacy is a potential. Once it is actualized one has a well behaved phenomenon. The spin of an electron before it goes through as Stern Gerlach apparatus could be up, could be down with equal probability. Once through and before it is perturbed again its spin is definite as the measurement reveals. At the level of the very small, things are in states that we simply do not perceive in the World of the Large.

Classical Physics assumes that the states of the world are deterministic and the only place for probability is to measure our ignorance of some of the states.

If quantum computers are ever successful and perform computational feats beyond the range of current technologies then the basic indeterminacy of world we be easier for we Clumsy Big Bags of Mostly Water to contend with.

Ba'al Chatzaf

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As I understand it, Objectivism uses the so-called "traditional" logic of syllogisms rather than the modern mathematical logic introduced by Frege/Russell. From the Objectivist view, are there important philosophical differences between the two logics? It seems to me that modern logic is still "Aristotelian" (in the sense that none of the traditional logic is denied) and is in fact a superset of the old logic in that it's able to analyse a much wider range of arguments (although it's more difficult to learn).

Back when there were mastodons and I was a senior in high school taking The Basic Principles of Objectivism, I bought The Principia Mathematica by Russell and Whitehead. When I saw that it took them eight pages to get to the Law of Identity, I put it down and never looked back and eventually sold the book.

Now, I see that I have to broaden my horizons.

For one thing, since then, when all I knew was English and German, I have had classes in Japanese and Arabic and taught myself enough Tibetan to translate coin inscriptions. The point is that when we speak of "natural language" we seem to be speaking only of modern English. Anglo-Saxon had four tenses. We say: help, helped, helped. German is helfen, half, geholfen. Old German and Anglo-Saxon was helpan, half, hulf, yholfen. There was a past tense in there that we dropped. I taught myself enough classical Greek to translate my own citations for publications about numismatics. I never understood what "middle aorist" is supposed to be in a declension. I grew up with Hungarian. As an adult, much later, I discovered that the language has a dozen cases: nominative, genitive, accusative, dative, ablative, vocative (easily enough, but also) inessive, adessive, progressive, regressive... The point is, again, just what do those logicians mean by "natural language."??

I found the Wikipedia on "Relevance Logic." I look forward to revisiting this later and benefiting materially from the discussion here so far.

And just as a note, my community college curriculum in criminal justice (2007) required a semester of symbolic logic. I got an A. It was an easy C+ for most crim majors and hard to understand why it was required, except that if actually applied, it allowed the average officer on the street to theoretically be able to see through: "68% of incarcerated felons are Black, therefore Blacks are likely to be felons."

Edited by Michael E. Marotta
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The point is, again, just what do those logicians mean by "natural language."??

Defining natural language

Though the exact definition varies between scholars, natural language can broadly be defined in contrast on the one hand to artificial or constructed languages, such as computer programming languages like Python and international auxiliary languages like Esperanto, and on the other hand to other communication systems in nature, such as the waggle dance of bees. Although there are a variety of natural languages, any cognitively normal human infant is able to learn any natural language. By comparing the different natural languages, scholars hope to learn something about the nature of human intelligence and the innate biases and constraints that shape natural language, which are sometimes called universal grammar.

Linguists have an incomplete understanding of all aspects of the rules underlying natural languages, and these rules are therefore objects of study. The understanding of natural languages reveals much about not only how language works (in terms of syntax, semantics, phonetics, phonology, etc.), but also about how the human mind and the human brain process language. In linguistic terms, natural language only applies to a language that has developed naturally, and the study of natural language primarily involves native (first language) speakers.

While grammarians, writers of dictionaries, and language policy-makers all have a certain influence on the evolution of language, their ability to influence what people think they ought to say is distinct from what people actually say. The term natural language refers to actual linguistic behavior, and is aligned with descriptive linguistics rather than linguistic prescription. Thus non-standard language varieties (such as African American Vernacular English) are considered to be natural while standard language varieties (such as Standard American English) which are more prescribed can be considered to be at least somewhat artificial or constructed.

This is interesting
here
The Stanford Natural Language Processing Group ...

where Deep learning has recently shown much promise for NLP applications. Unlike most approaches in which documents or sentences are represented by a sparse bag-of-words vector, our work in the intersection of deep learning and natural language processing handles variable sized sentences in a natural way and captures the recursive nature of natural language. We explore recursive neural networks for parsing, paraphrase detection of short phrases and longer sentences and sentiment analysis. Our approaches go beyond learning word vectors and instead learn vector representations for mulit-word phrases which are useful for different applications.

This page led me to this dudes website: here, which deals with "Parsing Natural Scenes and Natural Language with Recursive Neural Networks"

Interesting stuff.

Adam

Edited by Selene
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Though the exact definition varies between scholars, natural language can broadly be defined ...

Thanks, Adam! I have to insist, that just as nothing can be "super (supra) natural", neither can any language be unnatural. I know a few computer languages and studied more. I appreciate the point: they are artificially constructed, but so is a Super Dome stadium and such a structure cannot violate the laws of nature, even if the stadium was not built by beavers or bees. So, too, with so-called "natural language." With that caveat as a delimiter, thanks, again for the pointers. It's complicated. I appreciate that.

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Though the exact definition varies between scholars, natural language can broadly be defined ...

Thanks, Adam! I have to insist, that just as nothing can be "super (supra) natural", neither can any language be unnatural. I know a few computer languages and studied more. I appreciate the point: they are artificially constructed, but so is a Super Dome stadium and such a structure cannot violate the laws of nature, even if the stadium was not built by beavers or bees. So, too, with so-called "natural language." With that caveat as a delimiter, thanks, again for the pointers. It's complicated. I appreciate that.

No problem. I tend to struggle with some of these symbolic semantics primarily because of the "language" that it is necessary to learn in order to fully process the article or analysis, but in many instances it is worth the struggle.

I really enjoyed the parsing natural scenes website. Pictures worth anything from a few words to a thousand words??? lol

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Indeterminacy exists "in reality" and is a not logical contradiction. Since one never knows where a particle is until it is detected, one detecst only a certain state or position when it becomes known. In that sense, there are no contradictions in reality. Indeterminacy is a potential. Once it is actualized one has a well behaved phenomenon. The spin of an electron before it goes through as Stern Gerlach apparatus could be up, could be down with equal probability. Once through and before it is perturbed again its spin is definite as the measurement reveals. At the level of the very small, things are in states that we simply do not perceive in the World of the Large.

Classical Physics assumes that the states of the world are deterministic and the only place for probability is to measure our ignorance of some of the states.

If quantum computers are ever successful and perform computational feats beyond the range of current technologies then the basic indeterminacy of world we be easier for we Clumsy Big Bags of Mostly Water to contend with.

Ba'al Chatzaf

Ok, well my point was more about the lack of reflexive thinking which can lead to self-refuting arguments. Some commentators have suggested that the results of quantum physics imply that the 'old' logic is somehow false or incomplete, yet they are using it in order to come to that conclusion.

I'm curious as to what you mean by "Indeterminacy exists "in reality"". Indeterminacy is a function of our knowledge (or lack of it), but it seems to me that you're claiming that it's an inherent property of an object.

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There is nothing in Rand’s definition of logic, nor in her metaphysics and epistemology taken all together, that implies her concept of logic is incompatible with all developments in logic beyond Aristotle.* There is no incompatibility between Objectivism and the modern, standard first-order predicate logic with quantification and identity. In the modern propositional logic, Objectivism may need to take issue with the standard theory of material implication; it perhaps should embrace instead a form of relevance logic (a genre of non-standard modern logic). The work needed to settle that last point one way or the other is work not yet done by Objectivist thinkers.

Rand did not exactly reject post-Fregean logic.She just didn't know about it.

There is clearly still a tendency amongst O-ists to side with Aristotle, as the Binswanger quote demonstrates:-

The problem is not merely that no book has been written to incorporate the discoveries of Ayn Rand in epistemology. Nor is the problem merely that modern errors in epistemology are present in the current logic texts. The problem is that the modern texts proceed from the linguistic, formalistic context of contemporary philosophy. As a result, the logic texts currently in print generally range from misleading to worthless; many of them are actually destructive of logical thinking.

..as it also demonstrates, there isn't much of an objective, rational critique of post-Fregean logic to be found, just a swinging I-don't-like-it-so-it's-wrong.

Likewise, there isn't much of a case *for* Term logic. Term logic has well known shortcomings:-

Predicate logic was designed as a form of mathematics, and as such is capable of all sorts of mathematical reasoning beyond the powers of term logic. Predicate logic is also capable of many commonsense inferences that elude term logic. Term logic cannot, for example, explain the inference from "every car is a vehicle", to "every owner of a car is an owner of a vehicle." Syllogistic reasoning cannot explain inferences involving multiple generality. Relations and identity must be treated as subject-predicate relations, which make the identity statements of mathematics difficult to handle. Term logic contains no analog of the singular term and singular proposition, both essential features of predicate logic.

...and modern research into it is a case of playing catch-up. Where is the real *advantage* to it?

really can't conceive of any "non-Aristotelian" logic which would make sense in the real world, if "non-Aristotelian" means to deny any of the "laws of thought". How can logic be used to refute itself? Take quantum physics; because an electron can seem both to be, and not be, in one place, is it then reasonable to reject the law of non-contradiction on the grounds that contradictions exist "in reality"? But the motivation to rewrite the law of non-contradiction is prompted by that very law! In other words, the method of reviewing one's premises in the light of apparent contradiction is a cornerstone of Aristotelian logic.

There aren't any serious suggestions to rewrite PNC specifically in the light of quantum mechanics. Electrons are where

they are observed to be. They could have been somewhere else. Modal logic can handle the could-have-been ([]P & []~P is not a contradiction). It aprioristic to argue that electrons can't possibly be behvaving that way because the non-modal, bivalent logic Randians prefer can't model it.

Ok, well my point was more about the lack of reflexive thinking which can lead to self-refuting arguments. Some commentators have suggested that the results of quantum physics imply that the 'old' logic is somehow false or incomplete, yet they are using it in order to come to that conclusion.

That is very loosely argued. The specific claim is that distributivity is not a feature of quantum logic. AFAIK, distributivity was not appealed to to get to that conclusion. If you know better, you should write a paper.

I'm curious as to what you mean by "Indeterminacy exists "in reality"". Indeterminacy is a function of our knowledge (or lack of it), but it seems to me that you're claiming that it's an inherent property of an object.

You cannot prove that indeterminacy does not exist in reality by appealing to a definition, any more than you can

prove god exists in reality be defining God as a necessarily existing being. To understand reality, one has to employ

ones senses.

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Predicate logic was designed as a form of mathematics, and as such is capable of all sorts of mathematical reasoning beyond the powers of term logic. Predicate logic is also capable of many commonsense inferences that elude term logic. Term logic cannot, for example, explain the inference from "every car is a vehicle", to "every owner of a car is an owner of a vehicle." Syllogistic reasoning cannot explain inferences involving multiple generality. Relations and identity must be treated as subject-predicate relations, which make the identity statements of mathematics difficult to handle. Term logic contains no analog of the singular term and singular proposition, both essential features of predicate logic.

The Term logic developed by Sommers in recent decades is at least as powerful as predicate logic, see "Something to Reckon With".

Electrons are where they are observed to be. They could have been somewhere else.

Really? and how do you know that?

You cannot prove that indeterminacy does not exist in reality by appealing to a definition, any more than you can

prove god exists in reality be defining God as a necessarily existing being. To understand reality, one has to employ

ones senses.

Which definition was I appealing to? Physicist E.T. Jaynes has written extensively about what he calls "the mind projection fallacy" - the tendency to assume that lack of knowledge about how things really are as meaning that they're indeterminate. In his book "Probability Theory: The Logic of Science" in a section titled "But what about quantum theory?", Jaynes writes:

Those who cling to a belief in the existence of "physical probabilities" may react to the above arguments by pointing to quantum theory, in which physical probabilities appear to express the most fundamental laws of physics. Therefore let us explain why this is another case of circular reasoning. We need to understand that present quantum theory uses entirely different standards of logic than does the rest of science. In biology or medicine, if we note that an effect E (for example, muscle contraction, pho-totropism, digestion of protein) does not occur unless a condition C (nerve impulse, light, pepsin) is present, it seems natural to infer that C is a necessary causative agent for E. Most of what is known in all fields of science has resulted from following up this kind of reasoning. But suppose that condition C does not always lead to effect E; what further inferences should a scientist draw?

At this point the reasoning formats of biology and quantum theory diverge sharply. In the biological sciences one takes it for granted that in addition to C there must be some other causative factor F, not yet identified. One searches for it, tracking down the assumed cause by a process of elimination of possibilities that is sometimes extremely tedious. But persistence pays of; over and over again medically important and intellectually impressive success has been achieved, the conjectured unknown causative factor being finally identified as a defi nite chemical compound. Most enzymes, vitamins, viruses, and other biologically active substances owe their discovery to this reasoning process.

In quantum theory, one does not reason in this way. Consider, for example, the photoelectric effect (we shine light on a metal surface and find that electrons are ejected from it). The experimental fact is that the electrons do not appear unless light is present. So light must be a causative factor. But light does not always produce ejected electrons; even though the light from a unimode laser is present with absolutely steady amplitude, the electrons appear only at particular times that are not determined by any known parameters of the light. Why then do we not draw the obvious inference, that in addition to the light there must be a second causative factor, still unidentified, and the physicist's job is to search for it?

What is done in quantum theory today is just the opposite; when no cause is apparent one simply postulates that no cause exists - ergo, the laws of physics are indeterministic and can be expressed only in probability form. The central dogma is that the light determines, not whether a photoelectron will appear, but only the probability that it will appear. The mathematical formalism of present quantum theory - incomplete in the same way that our present knowledge is incomplete - does not even provide the vocabulary in which one could ask a question about the real cause of an event. Biologists have a mechanistic picture of the world because, being trained to believe in causes, they continue to search for them and find them. Quantum physicists have only probability laws because for two generations we have been indoctrinated not to believe in causes - and so we have stopped looking for them. Indeed, any attempt to search for the causes of microphenomena is met with scorn and a charge of professional incompetence and `obsolete mechanistic materialism'. Therefore, to explain the indeterminacy in current quantum theory we need not suppose there is any indeterminacy in Nature; the mental attitude of quantum physicists is already sufficient to

guarantee it.

Edited by Davy
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The Term logic developed by Sommers in recent decades is at least as powerful as predicate logic, see "Something to Reckon With".

Which is to say it is no more powerful. Objectivists like Aristotelean logic because Rand used it, and

she used it because she knew of no alternative. It's like doing calculations with a quill pen

because that is what Newton would have done.

Electrons are where they are observed to be. They could have been somewhere else.

Really? and how do you know that?

I like to base my views on the best available theories. Of course they are still fallible. But better than

apriorism masquerading as empirical realism.

You cannot prove that indeterminacy does not exist in reality by appealing to a definition, any more than you can

prove god exists in reality be defining God as a necessarily existing being. To understand reality, one has to employ

ones senses.

Which definition was I appealing to?

"probability is subjective..it's just lack of information".

What is done in quantum theory today is just the opposite; when no cause is apparent one simply postulates that no cause exists - ergo, the laws of physics are indeterministic and can be expressed only in probability form. The central dogma is that the light determines, not whether a photoelectron will appear, but only the probability that it will appear. The mathematical formalism of present quantum theory - incomplete in the same way that our present knowledge is incomplete - does not even provide the vocabulary in which one could ask a question about the real cause of an event. Biologists have a mechanistic picture of the world because, being trained to believe in causes, they continue to search for them and find them. Quantum physicists have only probability laws because for two generations we have been indoctrinated not to believe in causes - and so we have stopped looking for them. Indeed, any attempt to search for the causes of microphenomena is met with scorn and a charge of professional incompetence and `obsolete mechanistic materialism'. Therefore, to explain the indeterminacy in current quantum theory we need not suppose there is any indeterminacy in Nature; the mental attitude of quantum physicists is already sufficient to

guarantee it.

Jaynes' opinions is belied by the facts. There has been considerable research into the question of (in)determinism. It just

is bringing up the answer he presupposes. Apriorism, in other words.

Edited by peterdjones
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What was Fred Sommer's objective. He wished to prove that the logic of terms (subject-predicate) logic as originated by Aristotle in Prior Analytics has received a bad rap. Aristotle formulated logic in terms of propositions that had the form subject (application) predicate where (application) = (some/all is/is not). This leads to the four categorical forms of scholastic logic, based on Aristotle but modified somewhat to conform to Latin grammar (rather than Greek). In any case Logic was associated with thinking in natural language (or at least natural languages that resembled Greek and Latin in their basic bauplan). Subject-predicate or as Sommers puts it term-functor-logic is keyed to reasoning in natural language mode. Its main defect is the inability to deal with relationals. In categorical logic of the traditional scholastic form one cannot make this argument: a horse is an animal. sven is the owner of a horse therefore sven is the owner of an animal. That is because the assertion x is an R of y (R a relation) does not have a categorical subject-predicate structure with the usual quantity-quality designators.

What Sommers set out to do (and did) was to show the Term Logic could be emended and modified to handle n-adic relations as well as modern propositional (or predicate) logic can.

I was brought up in the post-Frege tradition of modern predicate logic was was formulated on a much different basis than term logic. More on this later. It took me a week of reading Sommers' book -The Logic of Natural Language- to finally groove into Sommers' thinking.

Frege conceived of logic as being an organon (tool) for formal mathematics, not thought. He regarded natural language as tricky and ambiguous and often misleading. So he denigrated logic that was composed to tally with natural language expression. How he did this, I was deal with later, also.

In any case Fred Sommers has done the deed. He has shown that Term logic could be rehabilitated to cope with relations of order 2 and and higher. From an aesthetic p.o.v. (which is necessarily subjective) the Sommers notation is clunky and ugly and is not very suitable to support mathematical reasoning, which is based more on conditional logic than on the logic of categorical propositions.

More later. It is an interesting topic.

Ba'al Chatzaf

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Advances in term logic have been made by Fred Sommers in recent years. See here. His book The Natural of Natural Language lays it out and also discusses modern logic. The book is not widely available and expensive, unless you can borrow it from a library. Alternatively, George Englebretsen's book Something to Reckon With presents Sommers' term logic very well. Also Englebretsen's book (co-written) Philosophical Logic: An Introduction to Advanced Topics presents Sommers' term functor logic in Chapter 8, which you can see online with Amazon's Look Inside feature.

I second -Something to Reckon With-. It is an excellent book because It shows where and how Term Logic and the logic of conditionals and propositions diverged and why. The lynch pin to the divergence was Gottloeb Leibniz. He missed (by just a little) a way of dealing with relationals within the context of Scholastic Logic. His near miss opened the road to Frege (and later Russel and Whitehead) to formulate a system of logic suitable for mathematics, but very disconnected from thinking in natural language.

The real divergence in logic came with Frege and not Boole who never rejected the logic of terms (subject cupola predicate). While Boole did enlist the aid of simple algebra to deal with syllogistic he never formulated the system of propositional logic which originated with Frege in his -Begreffschriffte-. Frege is the man who broke the Path not Taken (by the scholastics).

Ba'al Chatzaf

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...Subject-predicate or as Sommers puts it term-functor-logic is keyed to reasoning in natural language mode. Its main defect is the inability to deal with relationals. In categorical logic of the traditional scholastic form one cannot make this argument: a horse is an animal. sven is the owner of a horse therefore sven is the owner of an animal. That is because the assertion x is an R of y (R a relation) does not have a categorical subject-predicate structure with the usual quantity-quality designators...

There is no such defect in subject-predicate logic. If there were, traditional logic couldn't even do "All men are mortal. Socrates is a man. Therefore all men are mortal."

Consider some typical "relational" propositions...

In "Sven is the owner of an animal"--which I would express less ambiguously as "Sven is an owner of an animal"--what is designated by "Sven" is also designated by "an owner of an animal." Sven is the same thing in reality as one of the members of the class "owner of an animal."

In "Chicago is south of Milwaukee"--which I would express as "Chicago is a city that is south of Milwaukee"--what is designated by "Chicago" is also designated by "a city south of Milwaukee." Chicago is the same thing in reality as one of the members of the class "city south of Milwaukee."

In "Socrates is the teacher of Plato," what is designated by "Socrates" is also designated by "the teacher of Plato." Socrates is the same thing in reality as the teacher of Plato. (For the purpose of the example, we are considering "the teacher of Plato" to be a single-member class. No doubt, he had other teachers, but Socrates was perhaps Plato's only philosophy teacher.)

Doing standard traditional logic with such propositions is completely unproblemmatic.

And actually, ~all~ categorical subject-predicate propositions are also "relational" propositions," and all relational propositions can (and should) be rewritten as categorical subject-predicate propositions, where the predicate's class is made explicit.

In "Socrates is a man", what is designated by "Socrates" is also designated by "man." Socrates is the same thing in reality as one of the members of the class "man."

The key, though, is to bear in mind that all of the various ~other~ relationships (including being-owner-of, being-a-city-south-of, being-the-teacher-of, being-a-member-of-the-class-of) reduce to the fundamental Identity-relationship of being-the-same-thing-in-reality-as.

"Ayn Rand is the author of Atlas Shrugged"--relational? Sure. Being-the-author-of-Atlas-Shrugged is certainly a relation, and there is a person who stands in that relation. But that relation, like all relations, defines a class of things--in this case, the single-member class "author of Atlas Shrugged," because one and only one person stands in the relation that defines that class.

So, "Ayn Rand is the author of Atlas Shrugged" most fundamentally should be understood as saying: "Ayn Rand IS THE SAME THING IN REALITY AS the author of Atlas Shrugged." All of propositional logic can be dealt with in this way.

"Is the same thing in reality" is what "is" means, when you strip away all the ambiguities. (Are you listening, Bill Clinton?)

It even works when you state the foregoing as a subject-predicate categorical proposition: "Is the same thing in reality" is the same thing in reality as the meaning of "is." Or, compressing the relationship to a simple copula: "Is the same thing in reality" is the meaning of "is." (But I repeat myself....)

To me, this insight is the bridge between what is valid of traditional "what" logic and modern "relational" logic.

"Chicago is (south of Milwaukee)" can be converted to "Chicago (is south of) Milwaukee" and back again, with no loss of meaning or perspective or understanding. So can "Chicago is (the same thing in reality as one of the cities south of Milwaukee) and "Chicago (is the same thing in reality as) one of the cities south of Milwaukee."

No, we don't have to use the stilted, clunky, verbose formulations involving "is the same thing in reality as," but it's very important to bear in mind, and to be able to apply it when necessary, in cases of confusion, ambiguity, and the like.

Also, using propositions to express the identity or "what" of something is a more fundamental cognitive function than using propositions to embody and display more specific existential relations. To that extent, modern logic is formulated in terms of non-essentials and is thus more prone to error in deal with fallacies, paradoxes, immediate inference, etc. that involve the issue of truth-value in relation to existential import.

REB

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...Subject-predicate or as Sommers puts it term-functor-logic is keyed to reasoning in natural language mode. Its main defect is the inability to deal with relationals. In categorical logic of the traditional scholastic form one cannot make this argument: a horse is an animal. sven is the owner of a horse therefore sven is the owner of an animal. That is because the assertion x is an R of y (R a relation) does not have a categorical subject-predicate structure with the usual quantity-quality designators...

There is no such defect in subject-predicate logic. If there were, traditional logic couldn't even do "All men are mortal. Socrates is a man. Therefore Socrates is mortal."

Consider some typical "relational" propositions...

In "Sven is the owner of an animal"--which I would express less ambiguously as "Sven is an owner of an animal"--what is designated by "Sven" is also designated by "an owner of an animal." Sven is the same thing in reality as one of the members of the class "owner of an animal."

In "Chicago is south of Milwaukee"--which I would express as "Chicago is a city that is south of Milwaukee"--what is designated by "Chicago" is also designated by "a city south of Milwaukee." Chicago is the same thing in reality as one of the members of the class "city south of Milwaukee."

In "Socrates is the teacher of Plato," what is designated by "Socrates" is also designated by "the teacher of Plato." Socrates is the same thing in reality as the teacher of Plato. (For the purpose of the example, we are considering "the teacher of Plato" to be a single-member class. No doubt, he had other teachers, but Socrates was perhaps Plato's only philosophy teacher.)

Doing standard traditional logic with such propositions is completely unproblemmatic.

And actually, ~all~ categorical subject-predicate propositions are also "relational" propositions," and all relational propositions can (and should) be rewritten as categorical subject-predicate propositions, where the predicate's class is made explicit.

In "Socrates is a man", what is designated by "Socrates" is also designated by "man." Socrates is the same thing in reality as one of the members of the class "man."

The key, though, is to bear in mind that all of the various ~other~ relationships (including being-owner-of, being-a-city-south-of, being-the-teacher-of, being-a-member-of-the-class-of) reduce to the fundamental Identity-relationship of being-the-same-thing-in-reality-as.

"Ayn Rand is the author of Atlas Shrugged"--relational? Sure. Being-the-author-of-Atlas-Shrugged is certainly a relation, and there is a person who stands in that relation. But that relation, like all relations, defines a class of things--in this case, the single-member class "author of Atlas Shrugged," because one and only one person stands in the relation that defines that class.

So, "Ayn Rand is the author of Atlas Shrugged" most fundamentally should be understood as saying: "Ayn Rand IS THE SAME THING IN REALITY AS the author of Atlas Shrugged." All of propositional logic can be dealt with in this way.

"Is the same thing in reality" is what "is" means, when you strip away all the ambiguities. (Are you listening, Bill Clinton?)

It even works when you state the foregoing as a subject-predicate categorical proposition: "Is the same thing in reality" is the same thing in reality as the meaning of "is." Or, compressing the relationship to a simple copula: "Is the same thing in reality" is the meaning of "is." (But I repeat myself....)

To me, this insight is the bridge between what is valid of traditional "what" logic and modern "relational" logic.

"Chicago is (south of Milwaukee)" can be converted to "Chicago (is south of) Milwaukee" and back again, with no loss of meaning or perspective or understanding. So can "Chicago is (the same thing in reality as one of the cities south of Milwaukee) and "Chicago (is the same thing in reality as) one of the cities south of Milwaukee."

No, we don't have to use the stilted, clunky, verbose formulations involving "is the same thing in reality as," but it's very important to bear in mind, and to be able to apply it when necessary, in cases of confusion, ambiguity, and the like.

Also, using propositions to express the identity or "what" of something is a more fundamental cognitive function than using propositions to embody and display more specific existential relations. To that extent, modern logic is formulated in terms of non-essentials and is thus more prone to error in deal with fallacies, paradoxes, immediate inference, etc. that involve the issue of truth-value in relation to existential import.

REB

Prove the Pythagorean theorem using only the categorical logic os syllogisms.

That should be an amusing exercise for you.

See Euclid Book I and redo Book I using only the 19 valid categorical syllogisms that Aristotle and his successor at the Lyceum identified. Aristotle did not do syllogisms in the 4 th figure. 4 more valid forms were added to the 15 that Aristotle identified.

It is time to put up or be somewhat more still.

Ba'al Chatzaf

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<p>The basic problem with Aristotle's approach was existential import.  Here is an example   statements of type A:  all S are P  imply statements of type I:  some S are P.  Now consider the type A: assertion  all Unicorns are white.  This must be true.  otherwise its contradictory the type O: statement some Unicorns are not white is true.  If that were the case then there would exists something that is  (1)  a Unicorn  and (2)  non- white.  which would mean there exists a Unicorn.  O.K.  So the statement all Unicorns are White must be true.  But this implies the the type I statement some Unicorns are white.  (see any reference to the traditional square of opposition for this).  Well,  from this it follows there is something that is (1) a Unicorn and (2) is white.  Which means there is something that is a Unicorn.   The insistence on existential import leads to nonsensical proofs for the existence of God as well as Unicorns.</p>

<p> </p>

<p>George Boole cured this  by introducing categorical logic in which the rule of existential import was relaxed.  This simplified the square of opposition considerably.  Good by to alternation,  sub alternation  The only links left in the square are for contradictories:  A and O  and I and E.  </p>

<p> </p>

<p>Ba'al Chatzaf </p>

<p> </p>

<p>P.S. and some notes.  In categorical logic there are four categorical statement types in standard form:</p>

<p> </p>

<p>A:  all S are P</p>

<p>E:  no S are P</p>

<p>I    some S are P</p>

<p>O  some S are not P.</p>

<p> </p>

<p>A categorical syllogism consists of three statements.  </p>

<p>The first premise contains the predicate P and a middle term M</p>

<p>The second promise contains the subject S and the middle term M</p>

<p>The conclusion contains the minor term S and the major term P  </p>

<p> </p>

<p>There are umpteen textbooks on Aristotle's logic. The give all the rules necessary for identifying the valid syllogistic forms with existential import. They deal with conversion, obversion, contraposition and distribution of the middle terms.  See <br />

http://en.wikipedia.org/wiki/Categorical_syllogisms  for a quick review of the traditional logic of categorical syllogisms.</p>

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