Talk:Logical form

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Additional information: Related task forces (core areas): Logic

Now I've created the article I see the article "argument form" is similar. My research on the history of the expression (Joyce, Wittgenstein, Russell, historically, most modern usage) suggests "logical form" is appropriate.

E.g.

In order to understand a sentence, it is necessary to have knowledge both of the constituents and of the particular instances of the form. It is in this way that a sentence conveys information , since it tells us that certain known objects are related according to a certain known form. Thus some kind of knowledge of logical forms, though with most people it is not explicit, is involved in all understanding of discourse. (Russell OKEW 53).

'If p then p' is supposedly a "valid logical form", from which it should follow that every instance is true, indeed, is valid, is a truth of logic. However, the alleged instance 'if John is sick then John is sick" may not be true if 'sick' is understood in one of its meanings on its first occurrence, another on the second. Logical forms presuppose a pattern of recurrence: they assume that for each schematic letter, each token of it is to be understood as making the same contribution to logical truth and validity. If we are to recognise a genuine instance of a logical form as valid, we must be able to recognise that replacements of equiform tokens of schematic letters make equal contributions. Hence the concept of logical validity requires the notion of a relation between tokens which obtains only on condition that they make the same contribution to validity, and whose obtaining can be manifest to reasoners." Sainsbury, Departing from Frege p.134.

Spinoza1111 06:22, 13 January 2006 (UTC)Is this at all what you are thinking of, buddy? For "more to follow". Fails to start with Frege, starts with Wittgenstein.

An open question in the philosophy of logic concerns the "ontological status" of logical form: in this, two questions arise: whether logical form corresponds to entities and whether any one logical form should be privileged as being in best correspondence to the world.

Wittgenstein's Tractatus was the most rigorous exposition of a case for the standing of logical form as grounded in ontology, because in the Tractatus the substance of the world corresponds to logical form. That is, because we can recognize in schematics such as "all a is b" the necessity for a myriad of atomic facts, because generalizations can be made from them if a logical form is followed, the world contains not one thing but many facts.

Wittgenstein, however, was almost immediately misinterpreted as having knowledge-that these facts corresponded to atomic sense data reports when a close reading of the Tractatus gives grounds only for a terribly abstract belief in some sort of multiplicity of substance, and not for its realization as sense data reports.

More recently, work by Quine et al. privileges certain kinds of logic, mostly two-valued, as having a higher ontological status than newer forms of logic such as "fuzzy" or "three-valued" logic. The overall critique of such "deviant" logics shows that they are notationally reducible to special-purpose tools for talking about an underlying two-valued metaphysic.

For example, the "three-valued" logic of true, false, or "indeterminate" is reduced in this critique to a two-valued way of talking about knowledge and as such not as ontologically significant as two-valued logic.

The conservative view finds significance, in some cases, even in the fact that parentheses must be used and it reports, in some cases, that their elimination in Polish logic doesn't eliminate the need to evaluate operators "in order", a fact or factoid which in the conservative view corresponds to an ontological necessity.

An empirical fact which lends support to Quine's view is that all or most digital computers happen to have two states in their memory units and that DIGITAL computers constructed of n-value elements are rarities. In response, the deviant logician would remark that actual people deal in 8 bit bytes and that older "analog" machines were in a modern reading, fuzzy or infinite valued machines.

Dangerously, the two-valued conservative view becomes ethnocentric, because it privileges the greater proximity, say, of Russell's notation of Principia Mathematica, to "reality" for no good reason.

However, the fact remains that a speaker of an n-valued language all the way down (in which the concepts of truth and falsity become, let us say, lime, coconut, lime in de coconut, and drink and fold up in a four valued logic) can after some pain communicate with a well-meaning two-valued missionary.

This is what is meant by "logical form", a ground of communication. The theory of translation and conflicts of law both demand a clearer answer in an era of globalization from philosophical logic as to whether, for example, a language of guilty versus not guilty, isomorphic to true and false by a simple transformation, is applicable when either translating texts or in international law.

Quine was clearly concerned that removing Aristotelean logic, and its direct successor Western modern logic, from centrality, would open a Pandora's box of mutual incomprehensibility (as in the case of the Scots law verdicts guilty, not guilty and unproven). But he may have been just confused by the fact that as soon as a common minimal logical form is agreed-upon, whether consciously by philosophers or unconsciously by lawyers and such riff raff, it in turn is spoken-of immediately in the philosopher's native tongue, which appears to return privilege to a particular way of speaking.

Only a Kantian purity of heart can remind itself that "all a is b", (x)(a(x) -> b(x)), or lime in the coconut are each just syntactical paths to a reality which, if it exists, is Taoist and in this way prior and unspeakable. Wittgenstein had this purity of heart ("wovon Mann nicht sprechen kann, daruber must Mann schweigen), but Quine's genuine purity became to some readers ill-temper.

We can, sort of, teach logic. But part of its difficulty is the fact that the is-ness of logical form is invisible to lawyers and others who are in fact able to construct valid arguments and criticise invalid arguments, who have received B in Logic and who consider it useless. For most people, once drained of color and life, a and b, a or b, a implies b, become husks of meaning. Their only possible interest lies in deep translation and mutual understanding.