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Wednesday, April 23, 2014

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Perhaps, saying "Frodo Baggins" refers to Frodo Baggins isn't logically kosher. Because in so far as Frodo Baggins is a fictional character our thought process goes like this: "Suppose that Frodo Baggins is a member of the set of hobbits, while keeping in mind that outside of the story there is no such member of the set of Hobbits". So, in real life "Frodo Baggins" does not refer to Frodo Baggins, since we are keeping in mind that he is fictional, and therefore, there is no Frodo Baggins to refer to. But in order to enjoy the story, one places oneself in the world of the story where there is a Frodo Baggins to refer to, making the reference kosher. And one can imagine oneself making the necessary inferences required in the story, such as "Frodo has hairy feet", just as if Frodo Baggins were real.

Bill,

I'm sure I left a comment here, but it has not appeared. In any case, another comment. You say (tagging the points in the last section).

(A) Form abstracts from semantic content.

(B) The specific meaning of a name is irrelevant to the evaluation of the validity of an argument in which the name figures.

(C) But of course it is always assumed that names are used in the same sense [i.e. meaning] in all of their occurrences in an argument.

(D) So only in this very abstract sense is meaning relevant to the assessment of validity.

I really find this confusing. You say in (B) that the meaning of a name is not relevant to assessing validity. Yet in (D) you say that meaning is relevant (albeit in 'some abstract sense') to assessing validity. Isn't this a contradiction?

In (C) you say that it is always assumed that names are used in the same meaning in all of their occurrences in an argument. But then why should that assumption matter? You have already said that the meaning of a name is not relevant to assessing validity. If it is not relevant, then it is not relevant. And if form 'abstracts from semantic' content, as you say in (A), and if validity depends on logical form alone, why should the meaning of a name be relevant to assessing validity?

I'm really lost.

Ed,

I grant that my exposition above is poor and confusing, but I don't think I am contradicting myself.

All politicians lie; Obama is a politician; ergo, Obama lies. All politicians lie; Reid is a politician; ergo, Reid lies.

These arguments have the same form; the form is valid; so both arguments are valid.

Now here is one key idea that you may or may not agree with: if an argument is valid, it is because its form is valid, and not vice versa. Validity of an argument is grounded in its logical form. This grounding relation is asymmetrical.

This grounding relation is neither causal nor narrowly logical. I'll bet you'll balk!

Each of the above sample arguments features a proper name. Clearly, the meaning of these names plays no role in the assessment of validity. Suppose the sense of 'Obama' is given by: the most brazen political liar in U.S. history. Part of my point is that that specific sense plays no role in the determination of validity. The same goes for the specific sense of 'Reid.'

But if being a proper name is a semantic property, then every proper name has this property. So every name has at least the sense of being a name. And so it has the sense of having some particular sense or other -- assuming that names have sense.

Now consider: All politicians lie; Frodo is a politician; ergo, Frodo lies. This too is a valid argument since it has the form of the first two. It doesn't matter that 'Frodo' is empty, i.e., lacks a referent. If per impossibile it also lacks a sense, so that it lacks both Sinn and Bedeutung and yet remains a name, then that wouldn't matter either.

But 'Frodo' has to be a name. It has to have at least that much meaning. It can't be a syncategorematical expression like 'and' or 'or.' Nor can it be a concept-word (Begriffswort, in Frege's jargon).

Let me try to explain what Bill is getting at (not that he did not get at it).

'John is tall'; 'Mary is tall'. These two sentences have the same Logical Form (LF) in the following sense. Replace all non-logical terms with *appropriate* variables in a consistent way: i.e., the same expressions with the same variables throughout the same argument narrative.

Well, there are two types of non-logical terms in both sentences: i.e., singular terms-names ('John', 'Mary'); predicate ('tall'). Names are to be replaced by lower case term variables; predicates with upper case variables. When the suitable replacements are accomplished, both sentences have the form 'Fx'.

Notice that "meaning" comes in only in a generic way: i.e., meaning determines which expressions are singular terms/names and which are predicates. If you don't know the meaning of the token expressions you cannot decide which variables replace which terms. However, you do not need to know the specific meaning of any particular term: e.g., you do not need to know the difference in meaning between 'John'/'Mary' or between 'tall'/'short'. All you need to know is that the former pair are names, whereas the later are predicates.

More complex logical forms are given by introducing the logical-terms (by enumerating them all or by providing several and defining the rest). I think this sums up what I think Bill means by logical form.


Thank you, Bill and Peter. This in no way addresses my difficulty, however. My difficulty is about what constitutes 'instantiating a form'. The form in question is this:

a is F
a is G
some F is G

How do we decide which argument, with concrete terms replacing the placeholders, instantiates the form?

Let me quote Mark Sainsbury.

“'If p then q' is supposedly a 'valid logical form', from which it should follow that every instance is true, indeed, is valid, a truth of logic. However, the alleged instance of '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 suppose 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”.

Sorry for the long quote, but it is quite important. In the schema above, the letter ‘a’ occurs twice. It is a ‘middle term’. There is therefore a requirement that, as Sainsbury says, each substituted token is understood as making an equal contribution to validity.

Hence IMO it is incorrect for Bill to say “the specific meaning of a name is irrelevant to the evaluation of the validity of an argument in which the name figures”. I agree that the meaning of the name which substitutes for the first placeholder a is irrelevant. That is so obvious it hardly needs stating. But the meaning of the equiform token that replaces the second placeholder is not irrelevant. It must have the same meaning as the first token, otherwise the argument is not valid. In the example Bill quotes in the original post above, it is stipulated that the different occurrences of the name ‘Frodo Baggins’ have different meanings.

I agree that when the same proper name occurs consecutively, by convention the name has the same meaning. But that in no way affects my point.

I am not saying anything controversial or contentious. Strawson apparently made the same point in 1957 (“Propositions, Concepts and Logical Truths”, Philosophical Quarterly 7. Mark Sainsbury (who wrote a whole book on Logical Form) deals with it in some depth.

Could some of the confusion here be because the issue can be diced in two ways?  One way is Sainsbury's, outlined by Ed above.  A second way is to say that validity of argument form is indeed a syntactic issue, but that an instance of a valid argument form is truth-preserving only if its terms are univalent.  Thus, the argument form a is F, a is G, ergo some F is G is valid, full stop.  Its instance, FB is a hobbit, FB is not a hobbit, ergo some hobbit is not a hobbit delivers falsehood.  Therefore a premise is false or some term is polyvalent.  If we insist that the premises are true and hobbit is univalent then FB must be polyvalent.  This may be the more useful dicing for Ed's theory because it provides a way of inferring that a proper name is polyvalent. Conversely, if we know that FB is polyvalent then we know that the above argument is not guaranteed to be truth-preserving. We do better by disambiguating the distinct meanings of FB and using an argument of a different form.

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