# Talk:Logical form

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## Similar article

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.

## Argument form merge into logical form.

It has been suggested that Argument form be merged into this article logical form.

The merger has been proposed a while ago already, however, as far as I can see there is substantial overlap between the two articles. Morton Shumwaytalk 10:31, 20 April 2011 (UTC).

Approve I would support that mergePhilogo (talk) 00:01, 8 February 2011 (UTC)
Support as it was not me who did the merger proposal. Close to identical articles, and 'argument form' in the sense of 'logical form of an argument' can easily be mentioned in the article. Morton Shumwaytalk 17:06, 22 April 2011 (UTC).

There being no objections I will merge the articles: but the result will need editing to remove redundacies. — Philogos (talk) 21:17, 22 April 2011 (UTC)

## General discussion (moved here from merger discussion, please stick to protocol WP:MERGE)

Both notions are vague, but it seems that argument form necessarily uses some notion of implication. [1] [2]. Or perhaps has a broader meaning, who knows. Vague philosophical stuff. [3]. At least in basic logic texts, they are equivalent: [4] (Well, I see Beall treats paraconsistency in that book as well, so perhaps not so basic.) Apparently to some logical form means using a formal language, while argument form may do without [5]. This intro logic book [6] also says they're the same notion, so I think we can ignore the idiosyncrasy of some philosophers and merge+redirect argument form here. Tijfo098 (talk) 19:56, 20 April 2011 (UTC)
The terms are not equivalent. The logical form of an argument is its argument form, but the logical form of a sentence/proposition/statement is not an argument form becuase it is not an argument. Re argument form necessarily uses some notion of implication see Corresponding conditional:-

In logic, the corresponding conditional of an argument (or derivation) is a material conditional whose antecedent is the conjunction of the argument's (or derivation's) premises and whose consequent is the argument's conclusion. An argument is valid if and only if its corresponding conditional is a logical truth. It follows that an argument is valid if and only if the negation of its corresponding conditional is a contradiction. The construction of a corresponding conditional therefore provides a useful technique for determining the validity of argument

— Philogos (talk) 21:01, 21 April 2011 (UTC)

Is that quote from a source or are you quoting a Wikipedia article? It's also strange that you supported a merge right above, given that you see them as different. I'm fine with pointing out whatever fine distinctions some see in the joint/merged article, as long as they are sourced; there's at least one source (D. Hitchcock [7]) among those I found that sees such a distinction, but frankly we'd have to quote an entire paragraph from it, because it's not clear to me what it's saying in order to rephrase it. Tijfo098 (talk) 06:31, 22 April 2011 (UTC)
D. Hitchcock's theory of argument form (as a broader notion than logical form) is about informal logic; see p. xvii in the intro. Hitchcock whose theory is discussed there by Pinto seems to be this guy. Tijfo098 (talk) 06:59, 22 April 2011 (UTC)
The quote was from the Wiki article (to save you looking it up). The terms logical form and argument form (cf argument schema) are distinct but that does not preclude merging the articles under logical form, sinc an argument form is an instance of a logical form. (Perhaps Mr Hithccock is useing the term argument form in a unconventional way.) This can be explained in one line in the merged argument. I'll insert that now pre any merge, so you can see what I mean.— Philogos (talk) 12:41, 22 April 2011 (UTC)
It is unclear whether Tijfo098 supports or opposes the proposed merge. — Philogos (talk) 12:41, 22 April 2011 (UTC)

### Argument form def

As written here it contradicts Tomassi [8], who sees logical form and argument form as equivalent. Like I wrote before (but apparently nobody read), Beall also defines them as synonymous. I admit it's entirely possible that someone defines it as written in this wiki article, but it requires citation, and the Tomassi-Beall-type usage should probably be mentioned as well. Tijfo098 (talk) 16:11, 22 April 2011 (UTC)

Hmm, I should have read the whole page in Beall, he does say something to that effect; I've edited the article. Tijfo098 (talk) 19:05, 22 April 2011 (UTC)

## merger

It is now necessary to edit the destination page again and delete the redundant content, editing until it looks good and consistent.— Philogos (talk) 21:29, 22 April 2011 (UTC)

I was curious why someone created that separate article. Hurley, which was the only source cited in the argument form article defines it as "An argument form is an arrangement of statement variables and operators such that the uniform replacement of the variables by statements results in an argument." Hurley does not use the expression "logical form" at all in his book... Tijfo098 (talk) 23:06, 22 April 2011 (UTC)
If you read the Cam Enc of Phil article it explains that an argument form includes the logical form of each premis and the conclusion and then some more: i.e it shows which are the premises and which is the conclusion. There are various conventions for the latter, eg (a) each premiss on a new line, conclusion last on a new line preceded by a dot or the therefore sign. (b) premises first seperated by commas then forward slash followed by conclusion. The former step is acheived by showing the logical form of each premis and the conclusion. Formal languages were developed specifically to express such logical forms, (hence their name) and is such a way that the grammatical form of a sentence reflects its logical form. Thus was because with natural languages this was often not the case. (Much emphased by Frege) However it is not NECESSARY to use a formal language to set out a logical form (merely more convenient and precise): a natural; language can be used but this is less convenient and less precise. Formal languages are really a relativily recent development, but logicians had been discussing and setting out the logical forms of sentences for centures before their development. (If of interest this could be set out in the history page.) To illustrate the above take the old favourite:
• All Greeks are Men and all men are animals therefore all Greeks are animals.

The form of this (i.e. its argument form) can be set out as follows. First show which are the premises and which is the conclusion:

• All Greeks are Men, all men are animals/all Greeks are animals

Second, show the logical form of each premis and the conclusion:

• ALL A IS B, ALL B IS C / ALL A IS C

NB we have not used a formal language, but we have repalaced terms by place-holders. Using modern symbolism (developed post Frege - you should see HIS notation) we might write:

• $\forall$x(Fx→Gx), $\forall$x(Gx→Hx) / $\forall$x(Fx→Hx)

— Philogos (talk) 03:08, 26 April 2011 (UTC)

## Russell quote

Can anyone cite where Russell wrote: "Some kind of knowledge of logical forms, though with most people it is not explicit, is involved in in all understanding of discourse. It is the business of philosophical logic to extract this knowledge from its concrete integuments, and to render it explicit and pure."— Philogos (talk) 22:05, 22 April 2011 (UTC)

The ref cite in the article (free preprint linked, ya know) says it's from Russell, Bertrand. 1993. Our Knowledge of the External World: as a field for scientific method in philosophy. New York: Routledge. p. 53 [9] (Of course, that's a reprint of the 1914 stuff.) Tijfo098 (talk) 22:16, 22 April 2011 (UTC)
Thanks— Philogos (talk) 22:33, 22 April 2011 (UTC)

## Opening sentence

Although the opening sentence is based closely on the article in Camb. Enc of Phil and it was my edit, I don't like it much: I feel the following part it would not mean much to a lay reader

by abstracting from the subject matter of its content terms or by regarding the content terms as mere placeholders or blanks on a form

— Philogos (talk) 02:27, 26 April 2011 (UTC)

I am sorry to say this, but this page is very poorly written. The discussions above about Frege and Wittgenstein would be relevant if the page had more structure and sense.

Let me note a couple of things. First the opening sentence:

"In logic the logical form of a sentence (or proposition or statement or truthbearer) or set of sentences is the form obtained by abstracting from the subject matter of its content terms or by regarding the content terms as mere placeholders or blanks on a form."

This is biased, unclear and somewhat wrong. First, what is "truthbearer"? Is Kreisel's question forgotten? Or Goedel proof? The logical form has no connection with truth per se. Second, there is no logical form of a set, and therefore not for a set of sentences. A set of sentences can be interpreted as a (larger) sentence, and then has a logical form. Third, what does "abstracting from the content mean"? This is highly biased and wrong as it assumes that there is a logical form for at most natural language sentences. How can one "abstract from the content" the sentence "int main(){}" or "\forall x\exists y P(x,y)". Those are sentences and they have a logical form.

This is just the first sentence.