on Talmudic Logic

Lovejoy, 46 mentions that the two key questions that underlie Plato system are:

1) Why is there any World of Becoming, in addition to the eternal World of Ideas, or, indeed, to the one supreme Idea?
Arthur Lovejoy

Arthur Lovejoy
2) What principle determines the number of kinds of beings that make up the sensible and temporal world?

I think that Lovejoy identification of these two grounding questions is extremely helpful. But far from being pure, speculative, pristine, philosophical questions, they squarely rest on Orphic presuppositions (See Macchioro).

But aside from this, Louis Jacobs, 6 introduces an enlightening, at least for me, yet simple description of  the Aristotelian syllogism, that efficiently connects it, or reveals its dependence upon the question (2) above. Jacobs says:
'in the Syllogism the inference concerns the relationship between genus and species; we are saying that since Socrates belongs to the class man then he must share the characteristics of that class.'
The Aristotelean Syllogism, which deals only with names, involves the reference between the subject and the predicate, whereby the relation between the minor and  major premises is the relation of the species to the genus, both being nothing but names...
Let us insert here a short digression to quote a incendiary proposal of Hume:
If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.
It is difficult to find any serious person today that would not laugh at this statement that considers that the only way of abstracting is by means of numbers. This blazing statement reduces everything to counting. Now, lets come back to our main discussion.

Collingwood (Method 204-5) comes to the rescue in clarifying what Jacobs means by 'names':
The business of language is to express or explain; if language cannot explain itself, nothing else can explain it; and a technical term, in so far as it calls for explanation, is to that extent not language but something else which resembles language in being significant, but differs from it in not being expressive or self-explanatory. Perhaps I may point the distinction by saying that it is properly not a word but a symbol, using this term as when we speak of mathematical symbols. The technical vocabulary of science is thus neither a language nor a special part of language, but a symbolism like that of mathematics. It presupposes language, for the terms of which it consists are intelligible only when defined, and they must be defined in ordinary or non-technical language, that is, in language proper. But language proper does not presuppose technical terms... Thus the technical element in scientific language is an element foreign to the essence of language as such. So far as scientific literature allows itself to be guided by its natural tendency to rely on technical terms, scientific prose falls apart into two things: expressions, as a mathematician speaks of expressions, made up of technical terms, which signify scientific thought but are not language, and the verbal definitions of these terms, which are language but do not signify scientific thought.

R. Jacobs
John Milton (Artis Logicae, [Columbia Ed.], 301) stated exactly the same thing with clarity:
... words are symbols and signs of simple notions (voces symbola sunt et notae simplicium notionum)
Thus the Syllogism deals with symbols. And specifically, Greek thought, has this intrinsic tendency to counting, enumerating, taxonomizing, which is completely alien to Jewish thought. This particularly Greek way of looking to logic, is I believe, sometimes suffocating as it pushes to divide and classify all knowledge (which in risk sciences leads to dead-ends as Ulrich Beck remarks while talking about risk's systemic interdependencies). The problems of vagueness, definitions, and the limits of concepts comes next, bogging quite a bit the intellectual enterprise.

I plan to review R. Jacobs' 'Studies in Talmudic Logic and Methodology', and specifically
  • Qal Wa-Homer: the ontology precedes the hermeneutics. The syllogism considers (therefore it ontologically pressupposes) the relation between major and minor premises, or genus and species. While the syllogism doesn't appraise the truthfulness of the premises, however it takes them for granted (pressupposes) in the sense they must exist for the syllogism to be relevant at all. So, the syllogistic ontological grounding necessitates of a subject matter that is: 1) amenable of being described by premises, i.e. genus and species, 2) of having relationships between the premises to the conclusion. Therefore the subject matter must be organized as genus/species for the syllogism to operate. Is speciatiation a universal ontological rule for knowledge? It might be logically suffocating to suppose so! Here the older-than-syllogism qal-wahomer enters. Qal-wahomer is indicated by terms such as: 'all the more so', 'surely so', and 'much more'. It lies not in an ontological space of genus-species, but in one of laws and principles, i.e. in a nomological space. As such, qal-wahomer navigates the space of applicability of laws or principles to particular instances: qal-wahomer functions as a logical instantiator of a nomological space. Some scholars label qal-wahomer as a a fortiori (more strongly) argument. But by classifying it this way, they make it a mere ranking technique, and thus place it within the Aristotelian syllogistic space, overlooking the ontological ground (i.e. nomological) of qal-wahomer. These are some examples that explain my point: 'If $30/hr is good, $50/hr is better', or 'An untuned engine gets 8 km/liter; if tuned, it should get more'. This is not qal-wahomer, but just a simple rule of three.
  • Sebhara: there are 2 types: Jacobs, 37
    • 'self-evident truth', commonsensical reasoning, that must be accepted by virtue of its being self evident.
    • 'reasoned argument' type: that can be rejected.
    • Campbell (Phil Rhet) might call these intuitive evidence.
  • Binyan 'Abh
  • Reductio ad Absurdum
  • Ha-kol: it's identical to the Aristotelian syllogism.

to be continued

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