Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

Validity and Semantics: Will the Real Frodo Baggins Please Stand Up?

London Ed writes,

It is a well-known and puzzling fact that proper names are ambiguous. According to the US telephone directory, Frodo Baggins is a real person (who lives in Ohio). But according to LOTR, Frodo Baggins is a hobbit. Not a problem. The name ‘Frodo Baggins’ as used in LOTR, clearly has a different meaning from when used to talk about the person in Ohio. So the argument below is invalid:

Frodo Baggins is a hobbit
Frodo Baggins is not a hobbit
Some hobbit is not a hobbit.

This is because both premisses could be true, but the conclusion could not be true. So your claim that the validity of arguments using fictional names has ‘nothing to do with any semantic property’ is incorrect.

Well, ex contradictione quodlibet.  Since anything follows from a contradiction, the conclusion of the above syllogism follows from the premises.  So the above argument is valid  in that it instantiates a valid argument-form, namely:

p
~p
—
q

Obviously, there is no argument of the above form that has true premises and a false conclusion.  So every argument of that form is valid or truth-preserving.

You invoke a Moorean fact.  But we have to be very clear as to the identity of this fact.

It is a Moorean fact that proper names, taken in abstraction from the circumstances of their thoughtful use, are not, well, proper. They are common, or ambiguous as you say.  It is no surprise that some dude in Ohio rejoices under the name 'Frodo Baggins.'  

But so taken, a name has no semantic properties: it doesn't mean anything.  It is just a physical phenomenon, whether marks on paper or a sequence of sounds, etc. Pronounce the sounds corresponding to 'bill,' 'john, 'dick.' Is 'dick' a name or a common noun, and for what?  How many dicks in this room?  How many detectives?  How many penises?  How many disagreeable males, 'pricks'?  How many men named 'Dick'?  Consider the multiple ambiguity of 'There are more dicks than johns in the room but the same number of bills.' 

A name that has meaning (whether or not it refers to anything) is always a name used by a mind (not a voice synthesizing machine) in definite circumstances.  For example, if the context is a discussion of LOTR, then my use and yours of 'Frodo' has meaning: it means a character in that work, despite the fact that in reality there is no individual named. And as long as we stay in that context, the name has the same meaning.

And the same holds in the context of argument.  In your argument above 'Frodo Baggins' has the same meaning in both premises.

You can't have it both ways:  you can't maintain that 'Frodo Baggins' is a meaningless string that could mean anything in any occurrence (a fictional character, a real man, his dog, a rock group, a town, etc.) AND that it figures as a term in an argument.

To sum up.  Whether a deductive argument is valid or not depends on its logcal form.  If there is a valid form it instantiates, then it is valid.  The validity of the form is inherited by the argument having that form.  But form abstracts from semantic content.  So the specific meaning of a name is irrelevant to the evaluation of the validity of an argument in which the name figures.  But of course it is always assumed that names are used in the same sense in all of their occurrences in an argument.  So only in this very abstract sense is meaning relevant to the assessment of validity.

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6 responses to “Validity and Semantics: Will the Real Frodo Baggins Please Stand Up?”

  1. Bill Solomon Avatar
    Bill Solomon

    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.

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  2. london ed Avatar
    london ed

    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.

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  3. BV Avatar
    BV

    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).

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  4. Peter Lupu Avatar
    Peter Lupu

    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.

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  5. Ed Avatar
    Ed

    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.

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  6. David Brightly Avatar
    David Brightly

    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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