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Tuesday, April 22, 2014

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Ed,

I agree with most of Bill's critical comments. However, beyond the details of Bill's comments, I think he highlights a fundamental tension in your project. The tension can be stated as follows: you are trying to reconcile

A. A Denotational Semantics, which essentially relies upon denotation (i.e., referential relations) as the basis for meaning and inferential structure (See SEP Article: "Proof-Theoretic Semantics"; 2012; by Peter Schroeder-Heister);

B. A theory of fictional-names that has no ontological commitments.

These two tenets cannot be reconciled. A denotational semantics, by its very nature, requires *some* referents for names in order to define validity, truth, meaning, etc. Hence, a denotational semantics must have some ontological commitments, even if it is to Meinongian non-existents.

And, conversely, a theory of fictional names that lacks any ontological commitments cannot at the same time take advantage of a denotational semantics, since the later requires extensions for non-logical expressions.

I think Bill's fundamental point is that you have to choose between A and B. If you opt for B, then you may explore what is called an *inferential semantics* (See SEP essay cited above) instead of a denotational semantics as you have been trying. Inferential semantics provides meaning not based upon the usual extension of terms, but rather in terms of the inferential properties of expressions. That is what I think Bill was telling you regarding the validity of the Frodo argument.

1. What I mean by individuation.
>>Once again, you haven't told us what individuation is.

Not true. I explained it earlier in response to your questions in this post . I defined it as telling-which-character-is-being-talked-about.See also in points 7a, 7b and 7d of my comments on that post. “A fictional name like 'Frodo', in the sense it is used in The Lord of the Rings, tells us which character Tolkien is talking about”. It is a Moorean/datanic truth that at the end of LOTR, Tolkien tells us which of the hobbits fell into the fiery heart of Mount Doom.

Bill, do you agree that fictional names individuate in precisely this sense? I.e. they tell us which character (out of many possible characters) the author is talking about? This is fundamental. I agree that ‘individuate’ is a technical term, but it has a non-technical sense.

2. Validity and semantics.
>>now you take a turn that is reasonably resisted. You want to know what makes the Frodo argument valid. I say it is valid because it has a valid form: [...]It has nothing to do [my emphasis] with any semantic property of a substituend of the arbitrary individual constant, 'a.'

On the contrary. 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 is ‘nothing to do with any semantic property’ is incorrect.

3. Definition of validity.
>>Now if every sentence in which such a name figures is false (as you seem to believe), then there is no argument featuring purely fictional names that has true premises and a false conclusion. Therefore every such argument is by default valid (given the technical definition of validity that we both accept).<<

I should have been clearer about this. Validity is where the premisses cannot be true with the conclusion false. Although fictional statements aren’t true, I hold (unlike a direct reference theorist) that they could be true. Thus the following argument is not valid.

Bilbo Baggins is over 100 years old
Frodo Baggins is not over 100 years old
Someone is over 100 years old and not over 100 years old

This is because the first premiss could be true, namely when there was such a person as Bilbo Baggins, and if he was over 100 years old. For similar reasons, the second premiss could be true. But the conclusion couldn’t be true, because it is a contradiction. Such arguments are only valid when the fictional name is the same (and, as explained above, has the same sense). And this property of fictional names – namely the property that when used in the same sense in different propositions, those propositions imply the existence of a single individual satisfying the different predicates of the different propositions – explains their power of telling us which character is being talked about.

4. Summary.
So Bill, do you accept (1) my definition of individuation, namely in terms of ‘telling which’, (2) the need for a semantic (not a merely formal) conception of validity and (3) my modal definition of validity?

Peter,

That is a very helpful comment. It helps me see more of what might be going on here. I can understand how there could be an inferential semantics of the logical constants. But names, fictional or otherwise, are not logical constants. All names, whether or not they actually denote, have directedness (when they are thoughtfully tokened, and when they are not thoughtfully tokened, they are not names, strictly speaking.) And it is hard to see how directedness could accounted for inferentially.

So I think you are right: Ed is trying to do something impossible: provide an inferential semantics of names.

Ed,

In response to Bill's question as to what do you mean by *fictional individuation of a name* you respond:

"I defined it as telling-which-character-is-being-talked-about."

The trouble with this definition is that when it comes to fictional names you hold that they systematically lack referential properties: hence, they lack any referent, since according to you there is no ontology of fictional characters. But, then, the 'about' in the above hyphenated phrase is empty: there is a name, but no referent of any kind. And so fictional names cannot individuate in the sense of telling which character is being talked about, since no such a character exists (in any shape or form).

As for the ambiguity of names, this is a well known problem that is traditionally solved by presupposing an indexing to disambiguate prior to running inferences. Since this assumption is well known, the practice of indexing is not made explicit unless it is necessary to do so.

I do not see how any of this answers Bill's claim that the validity of the Frodo-argument is based purely on identity of form rather than on referential semantics (in this case, Model Theory for First Order). And here I think once again I refer you to the idea that perhaps what you want is inferential semantics rather than denotational semantics.

You define validity as follows: "Validity is where the premisses cannot be true with the conclusion false. Although fictional statements aren’t true, I hold (unlike a direct reference theorist) that they could be true."

But now I am completely confused. If you think that sentences containing fictional name *could* be true, then this sounds to me like you are appropriating a possible world semantics for fictional names without explicitly saying so. O/w what does the 'could' mean here? Moreover, if it is possible that 'Frodo is a hobbit' is true, then in what sense is this sentence part of a fiction rather than simply a false history of the actual world which nonetheless could have been true?


Bill,

" I can understand how there could be an inferential semantics of the logical constants. But names, fictional or otherwise, are not logical constants."

I understand that. But Proof-Theoretic Semantics aims to extend beyond merely defining the logical constants to encompass non-logical terms. Computer programming, for instance, operates in something like this way.

The simplest way that occurs to me of carrying out (what I take to be) Ed's underlying idea is this. You define the logical constants inferentially in the usual non-realistic way (Natural Deduction being the underlying inferential system). Then you enumerate all the sentences in a fictional work in which a fictional name such as 'Frodo' appears. Call this a 'Frodo-Frame'. The Frodo-Frame defines the so-called "fictional character Frodo". Next you define the set of all sentences that can be inferred from the Frodo-Frame applying a suitable inferential system (such as Natural-Deduction again).
The set of all sentence included in the Frodo-Frame together with their consequences (using a suitable system) you define as the *inferential meaning* of the fictional name 'Frodo'. Validity, etc., are all definable in this manner without requiring any denotational or referential relations. The Frodo-Frame and its inferential extension *individuates* (in Ed's sense) the *use* of the term *Frodo* in all fictionally relevant discourse.

Does it work? I do not know. But this is a rough picture to which I believe Ed is committed.

(Peter) >>The trouble with this definition [i.e. telling-which] is that when it comes to fictional names you hold that they systematically lack referential properties: hence, they lack any referent, since according to you there is no ontology of fictional characters. But, then, the 'about' in the above hyphenated phrase is empty: there is a name, but no referent of any kind. And so fictional names cannot individuate in the sense of telling which character is being talked about, since no such a character exists (in any shape or form). <<

I claim that the following two ordinary language statements are perfectly true, indeed self-evidently true

(1) At the end of LoTR, Tolkien tells us which hobbit fell into the depths of Mount Doom. (From memory, he tells us it was Gollum).
(2) There are no such things as hobbits, and never were.


Do you think they are not true, or not self-evident?


>>you may explore what is called an *inferential semantics* [here http://plato.stanford.edu/entries/proof-theoretic-semantics ]

Thanks for the useful link. "Proof-theoretic semantics is an alternative to truth-condition semantics. It is based on the fundamental assumption that the central notion in terms of which meanings are assigned to certain expressions of our language, in particular to logical constants, is that of proof rather than truth."

That is clearly the direction I am coming from, but I want to explain the idea without complicated words like 'truth condition semantics'.

I wonder if a better approach would be to drop the exemplar of 'Lord of the Rings' and start with a text where there is uncertainty about whether it is true or not. e.g. the Gospels. We can sensibly ask whether Jesus existed or not, or whether the Gospels are true. Indeed there is a whole literature on the subject of whether the Gospels are true, partly true or a complete invention, down to the invention of Jesus as a character.

Ed,

I apologize for saying that you haven't told us what individuation is. And I agree that in your sense, fictional names do individuate. If they didn't, then we would have a situation in which 'Frodo,' say, is not uniquely about Frodo.

I can't think of a work of pure fiction in which one and the same name is about two or more characters.

So we could avoid 'individuate' by saying that every purely fictional name is about exactly one character. Would you agree that this is the Moorean fact you are pointing to?

(Bill) >>And I agree that [..]

I am shocked, truly shocked.

>>I can't think of a work of pure fiction in which one and the same name is about two or more characters.

There is one which I used as an example in a 2004 draft of my book. There is a short story by L.P. Hartley (a great, and undervalued English writer of the 1930s) in which two characters have the same name. This was clearly of importance to the writer – I have two separate editions of the same story, in the later of which the double name is changed from ‘Harry’ to ‘Freddy’. It was clearly important to Hartley. I think (a long time since I read it) it was because, while the identity of the different Harrys is clear to the reader, it is not clear to some of the people in the story, which involves us, the readers, appreciating that while the same name has a different reference for us, it has the same reference for some of the characters. (I think it was that one of the characters says ‘Harry killed himself’, and another character gets the reference wrong, thinking a different character killed himself. It doesn’t matter.)

>> So we could avoid 'individuate' by saying that every purely fictional name is about exactly one character. Would you agree that this is the Moorean fact you are pointing to?

I could agree to that, except that there are clear exceptions to this, such as the story I just mentioned.

(Peter) >> But this is a rough picture to which I believe Ed is committed.

This is correct. But I am seeking a way to introduce this idea to an audience which is generally literate and intelligent, but who will find the terminology or jargon of mathematic logic difficult to approach.

On reflection I think it might be dangerous to introduce any of these ideas through the medium of technical language or technical ideas.

I like Bill’s idea of introducing the idea by saying that the same fictional name (generally), being about exactly one character. That would do for an introduction. But then you have the problem of what ‘about’ really means. Doesn’t it automatically suggest an ‘aboutness’ relation? I then want to argue that we can eliminate the term ‘about’ by appealing to inference. For example

(*) A man called ‘Gerald’ and a boy called ‘Eustace’ were standing by a fountain. Gerald had a drink.

You can say that the two sentences are ‘about’ Gerald if you want. Or you can appeal to the notion of inference. Anyone who understands the second sentence clearly has to understand that the two sentences, taken together, imply that some man had a drink. That is the ‘inferential meaning’ of the proper name ‘Gerald’, as it occurs in that mini-story. Now it is still open to the realist to explain validity in terms of Meinongian reference to non-existent individuals. But then I invoke the Razor: if we can explain the inference in a way that doesn’t multiply entities, i.e. to understand the name ‘Gerald’ = to understand what inferences it generates, then we have an explanation which does not multiply entities in the way that the Realist explanation does. Which is to be preferred (even the Realist believes in the Razor, i.e. not without necessity, although he thinks in some cases it is necessary, whereas the non-realist does not).

I still need to understand Bill’s ‘logical form’ objection. This is mostly because I do not understand what he means by ‘logical form’. I.e. in the argument

Holmes is a cute puppy of mine
Holmes is a famous judge
:. Some cute puppy of mine is a famous judge

does Bill think that the proper name in the first premiss is a token of the same name as the proper name in the second premiss? If it is, then he needs to explain how the argument is not valid. Clearly it isn’t, since the premisses are true and the conclusion false.

Ed,

Both occurrences of 'Holmes' are tokens of the same type. This implies that one of the premises is true and the other false. The argument is valid. We know from Logic 101 that a valid argument can have a true premise, a false premise, and a false conclusion.

I don't need to explain how the argument is not valid, since the argument IS valid.

You think that argument is not valid because you think it has four terms thus falling afoul of quaternio terminorum.

>>Both occurrences of 'Holmes' are tokens of the same type.

By which you mean they are identically spelled, regardless of meaning, correct? See my comment on your later post.

Consider:

This parcel of land on the Thames is a bank.
A bank contains money
*This parcel of land on the Thames contains money

The two tokens of ‘bank’ are tokens of the same type, if I understand you correctly. So does the Thames argument above instantiate the following valid form?

This is an F
Every F is G
This F is G

You seem to hold that if we substitute concrete tokens of the same type, then the resulting argument instantiates the form. And you also hold that to be a token of the same type means having the same spelling, and no more than that.

It’s the ‘and no more than that’ that I am having a problem with. I hold, and this is hardly an extreme or unorthodox position, that identically-spelled tokens can have (and often do have) different meanings, because meaning is a matter of convention. Sameness of spelling is never enough.

We can go some way towards resolving these difficulties by borrowing the notion of 'name-space' from programming language design. Ed already has this in his notion of 'story'. There is an implicit assumption that some sentences are to be 'taken together', as Ed says above, and others not. The cues for doing this are extra-linguistic, often having to do with spatial and temporal proximity. I agree with Bill that we validly derive a falsehood from the two sentences about 'Holmes'. This is prima facie evidence that the sentences come from distinct stories. But this is already going beyond what Ed has given us because we are relying on a notion of truth that we have brought in from outside Ed's theory. On second thoughts, I'm jumping the gun here. I think Ed has to give us a theory of truth at some point, but in this example we can say that we validly derive a sentence that merely contradicts another sentence such as 'no puppy is a judge', which we might take as a priori. The requirement on stories is consistency. But I think the name-space solution ultimately runs out of steam. We all have a 'background' story in which we fit all those sentences we don't explicitly label as fiction. But the name-clash problem is rife in the background story. English history is full of 'Essex's and 'Norfolk's (Earls and Dukes of said counties), for example, and Frodo Baggins the Ohioan can easily have a namesake in Nebraska. If we can't disambiguate (ugly word but handy) two equal names by attaching them to distinct name-spaces what resources are left to Ed to explain why we see them as distinct?

@Peter "If you think that sentences containing [a] fictional name *could* be true, then this sounds to me like you are appropriating a possible world semantics for fictional names without explicitly saying so. "

The statement 'there is a Roumanian in my attic' (uttered by me) is false, but it could be true. Similarly, Tolkien's claim that there was an age of the earth long ago when there existed a race of small humanoid creatures ('hobbits') is false, i.e. he was writing fiction, not history. But perhaps it could have been true. In which case Tolkien would not have been writing fiction.

There is clearly an ambiguity of scope here. When I say that some fictional sentence might not be fictional, I am not saying that it is possible that for some p, p is fictional and not fictional. Rather, for some p, p is in fact fictional (i.e. false) but could possibly not be fictional. Does that make better sense? The medievals distinguished 'sense of composition' from 'sense of division'. The sentence 'possibly someone who is sitting is not sitting' is false in the sense of composition, since it is impossible for the same person to be sitting and not sitting. But in the sense of division it is true, for it is clearly possible that Socrates, who is currently sitting down, could stand up.

1. I am not sure what is the problem with terms with multiple references ('bank'; 'Holmes'; etc.) with respect to validity or for that matter truth-values or any other semantic property. In everyday discourse, the context resolves the ambiguity. Otherwise, validity, truth, etc., cannot be assessed at all. In a formal language (or even semi-formal) ambiguities are resolved by the setting up of the language in the first place.

2. The logical form of a sentence is its form after all non-logical terms are replaced with suitable term variables. Thus, 'John is tall' and 'Mary is tall' have the same form because if the terms 'John', 'Mary', and 'tall' are replaced with suitable variables both sentence feature the form: 'Fa'.

3. Ed, : "...for some p, p is in fact fictional (i.e. false) but could possibly not be fictional." This seems to be a de-re reading. Several issues. First, you seem to appeal here to possible world semantics. i.e., while P is in fact false, there is a possible world in which it is true. But now you need to tell us what you mean by a sentence being true/false in the actual world as well as what it means for the same sentence to be true/false in a possible world. Second, this maneuver conflates merely false sentences with fictional ones.

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