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Monday, July 21, 2014

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I read through this, but I was a bit lost as to how it was supposed to be an objection to the idea that there are different modes of existence. Is it possible to summarize the main thrust of the argument a little? Was the idea that somehow it will lead to a regress, with an infinite number of modes of existence, instead of only two, as we would like?

Also, I don't understand the inference from, "I wrongly believe there is such a thing as Frodo", to, "There is a thing such* that I wrongly believe there is such a thing as it". How does one get this? I could say, "I wrongly believe there is such a thing as Frodo, therefore there is a thing such that I wrongly believe it to be Frodo", but even that is strange, because it seems to involve a change of form. (How does one quantify into an existential quantification?)

Anyway, even if one could infer this, I am not clear how a contradiction would follow unless the thing such that I believe it to be Frodo actually is Frodo. It is even tempting, on the basis of this observation, to solve the problem by saying that when I think about Frodo, there is indeed something I am thinking about, but it is not Frodo (from which it of course ought not to follow that I am not thinking about Frodo).

Penultimately, and this is a general problem I have with proposals to distinguish different senses of words like "is", "there is such a thing as", etc. -- it often seems the proposals are motivated only by the desire to avoid a paradox. One would accept them for the sake of being rational, and yet have no other reason to believe they are true. (I sometimes wonder if this is the case even with distinctions as between the "is" of identity and the "is" of predication, but that is my own hobby-horse.)

Finally, I think it is curious that the English, "there is such a thing as," allows for a kind of particular existential quantification, if one wanted to call it that (or statements of existence). Perhaps it is because of the versatility of the word "is", which may be made now singular, now plural, and so allows the quantificational statement to become, in English, particular or general. But in formal logic the form of the two statements, "There are such things as unicorns", and, "There is such a thing as Frodo", are quite different!

*[non sic, but the other phrasing is a bit strange, and I am not sure if it is grammatical]

Bill,

As I read him, I think that Ed's idea is that your view does imply that you can can derive (10) from (9) such that the claim

(8) Tom thinks that there is such a thing as Frodo, but he is wrong

is impossibly true. But because (8) is obviously possibly true, something has to give.

Ed,

I think you move too quick. You say, "If premiss (4) above were true, then from (8) we could derive 'there is such a thing such that Tom thinks that there is such a thing as it', which would mean Tom was right, rather than wrong."

But why would this mean that Tom was right? Tom thought that there was a Frodo, so we can derive

(P) There is an x such that x is thought to be Frodo by Tom, but there is no x such that x is Frodo.

But this is not problematic - I can see no contradiction. There is a contradiction here however:

(Q) There is an x such that x is thought to be Frodo by Tom, but there is no x such that x is thought to be Frodo by Tom.

But I can't see how you can derive (Q) from (8) and Bill's account. (Q) is just the spelled out version of (S)

(S) There is an x such that x is thought to be Frodo by Tom, but there is no such x.

And you might have thought that (S) is how you have to spell out expressions like 'Tom thinks that Frodo is real, but there is no such person!' on Bill's view, but this isn't right: they are spelled out as you find in (P).

>>BV: For this reductio ad absurdum to be formally valid, you need an auxiliary premise to the effect that 'For some x, x = b' asserts the existence of b. In other words, you must read the particular quantifier 'For some x, ___ x ___' as an existential quantifier, where an existential quantifier expresses existence […]
<<

Not at all! I used the expression ‘there is such a thing as b’. The word ‘exist’ does not appear. It states that, if you look through all the things falling under ‘thing’, you will find b as one of them. Conversely ‘there is no such thing as b’ states that if you look at every one of those things, you will not find b.

>>It is at least a question whether existence can be reduced to someness!

Possibly, but the question is irrelevant to my argument.

>>BV: Now you've lost me completely. There is clearly a difference between (1) -- Tom is thinking of Frodo -- and 'Tom thinks that there is such a thing as Frodo.' I don't understand why you shifted to the latter sentence.

The purpose was to show that at least one proposition of apparently relational (logical) form clearly doesn’t express a relation at all.

>>If Tom is thinking of Frodo, then Tom is thinking of something; but it doesn't follow that this thing exists.

Again, I deliberately avoid the use of the term ‘exist’. The question is whether ‘Tom is thinking of something’ implies ‘some thing is such that Tom is thinking of it.

>> BV: Now I think I see what you are up to. You take (1) Tom is thinking of Frodo to have the logical form of (9) Tom is thinking that Frodo exists. And then your point is that (9) does not entail (10) Frodo exists.
<<

Again no. I don’t use the term ‘exist’. Let’s be really really clear about this. However, I do take ‘Tom is thinking of Frodo’ to imply ‘Tom is thinking that Frodo is something’.

Note that if Tom is thinking about Frodo, then he must be entertaining or believing or imagining some proposition about Frodo. He must be thinking ‘Frodo is F’, for any F. But ‘Frodo is F’ entails ‘something is F’, no? And then I reply, to think that something is F doesn’t imply that anything is F. The scope of ‘anything’ is irrelevant here. It can range over just existing things, or additionally over fictional things, possible things, impossible things, whatever. These quibbles about ‘existence’ are irrelevant to my argument.

>>Clearly I can have either thought without the additional thought that the square in question exists or does not exist.

If you think ‘Trafalgar Square is in London’ then you are thinking that something (or some place) is in London, yes? And if you think ‘Scollay Square was a lovely place’, then you think that something (or some place) was a lovely place. But thinking that some place is in London doesn’t logically imply that anything is in London (perhaps it has turned into a waste land). Similarly for Boston.

@Leibovitz: “I don't understand the inference from, "I wrongly believe there is such a thing as Frodo", to, "There is a thing such* that I wrongly believe there is such a thing as it".”

The proposition "I wrongly believe there is such a thing as Frodo" has the form ‘—wrongly believe(s) there is such a thing as – ”. Ergo etc.

@Matt: “I think you move too quick”

I don’t think so. Spelling it out.

(a) (=4 above) The truth of a proposition of the form 'aRb' always implies the truth of 'for some x, x = b.'
(b) Tom wrongly thinks there is such a thing as Frodo
(c) ‘Tom wrongly thinks there is such a thing as Frodo’ has the form ‘aRb’.
(d) There is some x such that x = Frodo

But (d) clearly implies that Tom is right.

Ed,

Re: As for your (8) and ensuing discussion and replies to (Leibovitz, Matt) I am not certain that your account is correct. First (8) need not not have the form you state (aRb; where 'R' is understood as the relation "...wrongly thinks,,,". Why can't we assign (8) the following form:

(8) Tom thinks that there is such a thing as Frodo, but he is wrong

(8*) B(tp) & 'p' is False.

where 'B' is the (two place, in this case) belief-relation; 't' refers to Tom; 'p' is the proposition *There is such a thing as Frodo*).

If bivalence is in force, the the second conjunct of (8*) is to be interpreted:

(*) It is not the case that there is such a thing as Frodo;

or

(**) For every x, ~ Frodo = x)

And of course we are now back to the problem of the lack of a referent of 'Frodo'. But I think that the above is a more natural way of getting to the original problem than in the manner in which you construe (8) (which I have some trouble understanding).

@Peter: "First (8) need not not have the form you state"

Let's say it 'instantiates' the form I referred to. As we agreed a while back, a statement can instantiate more than one form. I am saying that "Tom wrongly believes there is such a thing as Frodo" instantiates (among other things) the form 'aRb' where R is 'wrongly believes there is such a thing as'.

I don't deny it also instantiates the form you mention.

Ed,

Granted. The difference is that while your too coerce logical form for (8) leads to problems noted by others, the more refined logical form I propose does not; or at least does not lead to the obvious problems yours does. And so based on this consideration alone, one should choose the one I propose guided by Okham's principle "Do not multiply problems beyond necessity!"

Ed,

Right, I see. Thanks for that. So here's an objection. (a) - (c) does not entail (d). We can agree with your (c) ‘Tom wrongly thinks there is such a thing as Frodo’ has the form ‘aRb’. But then we ought to distinguish two ways of parsing the expression according to that form, to wit:

(e) Tom wrongly thinks that 'there is such thing as Frodo' is true
(f) Tom wrongly thinks of Frodo that 'there is such thing as him'

The relatum in (e) is a proposition, and the relatum in (f) is Frodo. But by insisting on (e) as the correct way to parse your expression we can block your inference. We can grant that the proposition exists - it exists and is false. This isn't to deny that thoughts can relate to particular individuals, just to insist that when you are talking about thoughts that can be false propositions must be in view. Compare the way that the extension of a singular term is the entity referred to, but the extension of a sentence is its truth value. I think this is the sort of reason why Bill wants to keep the distinction between 'thinking that' and 'thinking about' in view.

@Matt: "But then we ought to distinguish two ways of parsing the expression"

Your (e) is not a way of reparsing the proposition, but is rather a different proposition. One contains the name of Frodo the hobbit. The other, in virtue of the quote marks, contains the name of his name.


Peter "Granted. The difference is that while your too coerce logical form for (8) leads to problems noted by others, the more refined logical form I propose does not; or at least does not lead to the obvious problems yours does. And so based on this consideration alone, one should choose the one I propose guided by Okham's principle "Do not multiply problems beyond necessity!"

So you are agreeing with me that it doesn't have the problematic logical form then. That's fine, that's what I have been arguing all along. Some propositions have a misleading grammatical form, tempting us to misrepresent its logical form, leading us down all sorts of pathways into Meinongian jungles and the like, into esse intentionale, 'being' contrased with 'existing' and so on.

That's good.

Ed moves from 'Tom is thinking of Frodo' to 'Tom thinks Frodo is F' to 'Tom thinks there is such a thing as Frodo'. Bill objects to the second step, saying,

Clearly I can have either thought [about city squares] without the additional thought that the square in question exists or does not exist. To think about something is not eo ipso to think that the thing in question exists -- or to think that it does not exist.
I think I can see why Bill might say this, but in the final analysis I think it's wrong. Our relations with propositions can get convoluted. Consider the following tiny dialogue.
Al: I met this chap Soc in the pub. Soc is a philosopher.
Beth: Never heard of him.
Can Beth think about Soc? She can have thoughts like these,
There's a chap called Soc.
Soc is a philosopher.
Soc met Al in the pub.
But she can also distance herself from Al's speech. She doesn't have to take it at face value. She can think,
Al says he met a philosopher called Soc in the pub, but maybe there's no such person.
This might be seen as a thought about Soc unaccompanied by any commitment as to Soc's existence, as Bill says can occur. But it can also be seen as a thought about Al's speech in which there is no commitment to its truth or falsity. Beth can be seen as making a semantic ascent.

Suppose now that Beth trusts Al and has no reason to think he is spinning her a yarn. Before Al's speech she knew of no one called 'Soc'. Part of Ed's theory, as I understand it, is that new proper names have to be introduced by some minimal existential assertion such as 'There's a chap called Soc'. Without such an assertion, the bald statement 'Soc is a philosopher' seems 'semantically incomplete' and invites the response 'Who the **** is Soc?' This is the sense in which to think that Soc is a philosopher requires that we think there is someone called 'Soc'. There is a connection here with the predicate calculus proof rule of 'Existential Elimination'. This says that given ∃x.Fx we may introduce a new name 'a' and assert Fa. 'a' names a 'witness' to the existential assertion. This is the only way that a new name can be introduced into a proof in PC and it clearly requires an existential premise. Hence, in the last analysis, one cannot hold Fa without also holding ∃x.Fx.

David: ”Part of Ed's theory, as I understand it, is that new proper names have to be introduced by some minimal existential assertion such as 'There's a chap called Soc'.”

It’s not just part of my theory, it’s fundamental to it. Also fundamental is the claim that every singular assertion embeds an existential assertion. I.e. ‘Soc is running’ embeds ‘someone is running’. Thus a negative singular proposition such as ‘Soc is not running’, on my theory, although not in standard logic, has two causes of truth, namely (1) Soc exists but is not running and (2) Soc does not exist.

In standard logic, however, ‘not Fa’ implies ‘Ex, ~Fx’, so the negative singular proposition has only one, not two, causes of truth. This has the perverse result that ‘for some x, x=a ‘ is either necessarily true, or meaningless. We cannot translate ‘there is no such thing as Frodo’ into predicate calculus, although we can translate ‘Frodo does not exist’ by reading ‘exist’ as a predicate, i.e. translate it as ‘there is such a thing as Frodo, but Frodo is non-existent’ or something like that. This is clearly nonsense.

There are also varieties of non-standard logic, such as free logic, which attempt to grapple with the problem. Under standard free logic, ‘Fa’ does not imply ‘Ex Fx’. Under negative free logic (originally developed by Tyler Burge and promoted by Mark Sainsbury), ‘~Fa’ does not imply ‘Ex ~Fx’.

The London Ed theory is the only one which neatly and economically accounts for all the natural language inferences, and explains all the various puzzles connected with existence and reference statements. But of course I would say that.

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