Motto:

"There are none so blind as those who will not see." --

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Thursday, October 31, 2013

Deep Thought of the Day: Meinongianism

There are plenty of sound arguments against Meinongianism, the only question is whether they exist.

Sunday, October 27, 2013

A Counterexample to Social Externalism?


Suppose there are two linguistic communities of (roughly) equal size, dispersed throughout a large area. Both speak dialects of the same language. One community uses the term 'arthritis' to refer exclusively to a painful condition of the joints, the other uses it to refer to any painful condition in one's limbs. There is a certain smaller region in which members of both communities are to be found, and in (roughly) equal numbers. There is, however, no “overlap”: Each speaker fully adopts the convention of his or her community, they do not sometimes adopt one usage and sometimes another. The dialects are alike in every other respect. Along comes Wyman, who does not speak the language. Wyman, however, comes to learn it, and eventually speaks it, to all appearances, just as the two communities do. But he is nevertheless unaware of the difference in usage with respect to the term 'arthritis'. One day he tells his doctor, “I have a horrible case of arthritis in my thigh.” One community would judge that what Wyman said was false; and the other, that it was true. Both could not be right.

The question is: What did the term 'arthritis' mean on that occasion? Which of the two communities' incompatible usages could it have been that determined what 'arthritis' meant in Wyman's mouth? He was unaware of any difference between the two communities, both are equal in size and equally prevalent in his area, and he interacted just as much with both. To say that Wyman “really” counts as a member of one community rather than the other, and thus that the term “really” had one meaning rather than the other, seems arbitrary. And externalists cannot say that 'arthritis' had both meanings, for then what he said would have been both true and false. If externalists were to say that it was indeterminate which meaning it had, they must admit that some matters are indeterminate—which, though many may be happy to do, might not be coherent. That the statement had no meaning is something I can understand, though I find it implausible for this case; but could it really be that it's determinate that it had one or other of those meanings, but not determinate which? But however that may be, I'm interested to see what my readers think.


Tuesday, October 22, 2013

Truth-making and Reference-making: Appendix

Appendix


Some may have noticed that on my account, as it stands, bivalence will fail for empty nouns or noun-phrases. A false-maker for a sentence is defined as a reference-maker for its subject term which is not a reference-maker for its predicate term. If the subject term is empty, it has no reference, so false-makers are not defined for sentences of this kind. Neither are truth-makers, for a truth-maker for a sentence is defined as a reference-maker for its subject term which is also a reference-maker for its predicate term, for these sentences their subject terms have no reference-makers. If we require that every true sentence has a truth-maker and that every false sentence has a false-maker, such sentences will come out as neither true nor false.

Many, I take it, will unhappy with this result. To reinstate bivalence, I'll introduce the concept of a negative reference-maker, in analogy with the concept of a false-maker for a sentence. A negative reference-maker is something that makes it the case that a term does not refer to anything. In the case of nouns and predicates, we could also call them empty-makers, for they make nouns and predicates empty.

I will now define this concept, calling what I have previously called reference-makers positive reference  makers. I say that a noun has the proper class V of all objects (excluding proper classes) as its negative reference-maker iff it has no positive reference-makers. Similarly for monadic predicates. For relations, I say that an n-ary relational has the proper class of all n-tuples as its reference maker if it has no n-tuple as a positive reference-maker.

We can now give revised definitions of false-makers for subject-predicate and relational sentences:

An object x is a false-maker for a subject-predicate sentence p iff x is a positive reference-maker for p's subject term but is is not a positive reference-maker for p's predicate term. The proper class V of all objects is a false-maker for a subject-predicate sentence p iff V is a negative reference-maker for p's subject term or p's predicate term (or both).

An ordered n-tuple o is a false-maker for an n-ary relational sentence p iff the objects ordered in o are each positive reference-makers for one of p's subject terms, but o is not a positive reference-maker for p's predicate term. A proper class C is a false-maker for an n-ary relational sentence p iff C is a negative reference-maker for one of p's subject terms, or for p's predicate term, or both.

With these definitions ready to hand, we can see that sentences containing empty nouns or empty predicates come out as false rather than truth-valueless. "Nessie [a.k.a. the Loch Ness Monster] exists" comes out as false because the term 'Nessie', being empty, has the proper class V of all objects as its negative reference-maker, and so "Nessie exists" has V as its false-maker. Moreover, since "Nessie exists" has V as its false-maker, "It's not the case that Nessie exists" has V as its truth-maker. On the other hand, "Nessie is non-existent" comes out as false--if we construe 'non-existent' as a real predicate, then since 'Nessie' has V as its negative reference-maker, "Nessie is non-existent" has V as its false-maker. To me this seems intuitively to be the correct result: 'Nessie' is empty, so nothing is true of its referent--not even that it is non-existent--for it has no referent, so there's no "it". Nothing could possibly be non-existent.

However, "It is not the case that Nessie is non-existent" is true--since "Nessie is non-existent" has V has its false-maker, "It is not the case that Nessie is non-existent"has V as its truth-maker. Yet though "It is not the case that Nessie is non-existent" is true, it does not follow that "Nessie exists" is true--given that 'Nessie' does not refer, "Nessie exists" cannot be true for reasons just explained. What this shows is that "x is non-F" and "it is not the case that x is F" are  not in general equivalent expressions, for the former entails the latter, but not conversely: In some situations where its not the case that x is F, "x is non-F" can nevertheless be false due to the fact that there is no such thing as x. We thus have the following three results:

1. 'Exists' is a meaningful predicate which is necessarily true of everything;
2. 'non-existent' is a meaningful predicate which is necessarily true of nothing; and
3. there can still be false positive existential sentences and true negative existential sentences.

Not bad results to get, if I do say so myself.

Truth-making and Reference-making: Part 3

Part 3: Philosophical Implications


I think my approach has the advantage that it can explain why necessary truths don't have everything as a truth-maker. Granted, "The Earth has exactly one moon --> the Earth has exactly one moon" is true no matter what, but it does not therefore have everything as a truth-maker. By my definitions, a truth-maker for that material conditional is either a false-maker for its antecedent or a truth-maker for its consequent. As the antecedent and consequent are the same in this case, and as it is in fact true, every truth-maker for "the Earth has exactly one moon" will be a truth-maker for our conditional, and nothing else will. Truth-making, on my account, is not trivial for necessary truths, not even for paradigm cases of tautologies. A different instance of the Law of Identity, say "Sacramento is the capitol of California --> Sacramento is the capitol of California", will have (a) different truth-maker(s) from the previous instance. We can call such sentences 'analytic' if we like, in the sense that their meaning fixes their truth value--they could not have the same meaning, but a different truth value--but on this view it would be wrong to say that they are true solely in virtue of meaning. They have truth-makers, and they are not trivially made true by everything, nor will even different logical truths of the same form necessarily have the same truth-makers.

Another advantage of my account is that it enables one to dispense with a primitive, cross-categorical relation between objects (including sets) and truths. We can, if we wish, instead define necessitation in terms of truth-making (which itself is defined in terms of reference-making): An object x necessitates p iff x is a truth-maker for p. I count this as an advantage because we can now explain why an object necessitates the truth of p via reference-making, which itself can be explained via meaning, which itself 
can be explained via the use and/or causal history of terms. On an account like that of D. M. Armstrong, it would appear to be brute that an object necessitates a truth-bearer. Brute facts are not always a bad thing--"Explanation comes to an end somewhere", as Wittgenstein said. But, first, it seems odd that there should not be an explanation for the obtaining of the necessitation relation, when we are trying to account for how the truth of truth-bearers is grounded in reality. To explain it in terms of necessitation by objects, and then offer no explanation as to why objects necessitate the truths they do, seems little better than taking truth to be a primitive property which just happens to attach to some truth-bearers and not others. Second, it also seems odd  that an account of why truth-bearers are true would say nothing about how their truth depends on the reference and structure of their components. My account is designed to do exactly that, and in virtue of doing that it can explain why objects make true the truth bearers they do--which, in my opinion, is perhaps the only kind of explanation of this that can be had, and perhaps also the only kind of explanation of it that we should desire. 

My account is neutral with respect to the existence of facts or states of affairs. Objects and sets are the only entities that it posits as truth-makers. If the relation of reference-making that holds between nouns or predicates and objects or sets counts as a fact, or a state of affairs, then of course my account will not work without such entities; but given them, it needs no others. All other predicational, relational, truth-functional and quantificational sentences can be accounted for in terms of my definitions. And if the reference-making relation does not count as a fact or state of affairs, then my needs none of them at all.

My account is also neutral with respect to the existence of properties, including relations, and for much the same reasons as just stated. If reference-making counts as a genuine relation, then of course my account needs genuine relations to work, but it will need no others for the purposes of explaining truth-making. One may need to posit genuine properties for other reasons, but they are not items that my account is committed to. My account, then, is metaphysically chaste: If it requires any potentially dubious entities, it requires only the least amount necessary to achieve its purposes. I hope it should thus  be acceptable to philosophers of a variety of metaphysical persuasions.

For some final thoughts on truth-makers for negative truths, please see the Appendix.

Sunday, October 13, 2013

Truth-making and Reference-making: Part 2

Part 2: A Quasi-Formal Account


I will now define truth-makers for truth-functional compounds and quantified sentences. To define truth-makers for them, we  will also require the notion of a false-maker: We say that x false-maker for a subject-predicate sentence p iff x is a reference-maker for p's subject term but is not a reference-maker for p's predicate term.  For relational sentences, an ordered n-tuple o is a false-maker for an n-ary relational sentence p iff the objects ordered in o are each reference-makers for one of p's subject terms but o is not a reference maker for p's predicate term. 

We then define:

1a) An object x is a truth-maker for ~p iff x is a false-maker for p. A set s is a truth-maker for ~p iff some member of s is a false-maker for p. 

1b) An object x is a false-maker for ~p iff x is a truth-maker for p. A set s is a false-maker for ~p iff some member of s is a truth-maker for p. 


2a) An object x is a truth-maker for p & q iff x is a truth-maker for p and for q. A set s is a truth-maker for p & q iff some member of s is a truth-maker for p and some member of s is a truth-maker for q. 

2b) An object x is a false-maker for p & q iff x is a false-maker for p or for q. A set s is a false-maker for p & q iff some member of s is a false-maker for p or if some member of s is a false-maker for q. 


3a) An object x is a truth-maker for p v q iff x is a truth-maker for p or for q. A set s is a truth-maker for p v q iff some member of s is a truth-maker for p or if some member of s is a truth-maker for q. 

3b) An object x is a false-maker for p v q iff x is a false-maker for p and for q. A set s is a false-maker for p v q iff some member of s is a false-maker for p and some member of s is a false-maker for q. 


4a) An object x is a truth-maker for p --> q iff x is a false-maker for p or a truth-maker for q. A set s is a truth-maker for p --> q iff some member of s is a false-maker for p or if some member of s is a truth-maker for q. 

4b) An object x is a false-maker for p --> q iff x is a truth-maker for p and a false-maker for q. A set s is a false-maker for p --> q iff some member of s is a truth-maker for p and some member of s is a false-maker for q. 


5a) An object x is a truth-maker for p <--> q iff x is a truth-maker for p and for q, or if x is a false-maker for p and a false-maker for q. A set s is a truth-maker for p <--> q iff some member of s is a truth-maker for p and some member of s is a truth-maker for q, or if some member of s is a false-maker for p and some member of s is a false-maker for q. 

5b) An object x is a false-maker for p <--> q iff x is a truth-maker for p and a false-maker for q, or if x is a false-maker for p and a truth-maker for q. A set s is a false-maker for p <--> q iff some member of s is a truth-maker for p and some member of s is a false-maker for q, or if some member of s is a false-maker for p and some member of s is a truth-maker for q. 


6a) For a given, restricted domain of discourse: An object x is a truth-maker for a universally quantified sentence iff x is the only object in the domain and x is a reference-maker for the open sentence bound by the quantifier (I take open sentences to be predicates, and thus covered by what was said above). A set s is a truth-maker for a universally quantified sentence iff every member of s is a reference-maker for the open sentence bound by the quantifier.

6b) For a given, restricted domain of discourse: An object x is a false-maker for a universally quantified sentence iff x is not a reference-maker for the open sentence bound by the quantifier. A set s is a false-maker for a universally quantified sentence iff some member of s is not a reference-maker for the open sentence bound by the quantifier.



7a) For a given, restricted domain of discourse: An object x is a truth-maker for an existentially quantified sentence iff x is a reference-maker for the open sentence bound by the quantifier. A set s is a truth-maker for an existentially quantified sentence iff some member of s is a reference-maker for the open sentence bound by the quantifier.

7b) For a given, restricted domain of discourse: An object x is a false-maker for an existentially quantified sentence iff x the only object in the domain and x is not a reference-maker for the open sentence bound by the quantifier. A set s is a false-maker for an existentially quantified sentence iff no member of s is a reference-maker for the open sentence bound by the quantifier.


There may be some additional complications concerning open sentences which are truth-functionally complex and/or which involve nested quantifiers, but I take it that they can be accounted for in much the same way as above. (And remember, I only said that this was a quasi-formal account.) In any case, this much should suffice for the purposes of Part 3

Truth-making and Reference-making: Part 1

Part 1: Introducing the Idea


In this post I introduce the idea of reference-making, which I take to be more-or-less undefined, and use it to account for the idea of truth-making for subject-predicate sentences. I take a truth-maker to be a reference-maker for a sentence. In Part 2 I'll give a quasi-formal account of how it can be applied to truth-functional compounds and quantified sentences, and in Part 3 I'll discuss some of its philosophical implications.

Let us say that the reference-maker for a noun or a noun-phrase is just what is ordinarily called its referent,  the thing that it "corresponds to" or '"picks out" in the world. Nothing interesting so far. For predicates, however, the idea is different: Just as sentences can  have many truth-makers--"Planets exist" being made true by each planet--on this view a predicate can have many reference-makers, without thereby becoming ambiguous (as nouns/noun-phrases would become if they had many reference-makers). This is a key difference between predicates and nouns/noun-phrases. We will therefore say that predicates have reference, but not that they have referents. We could say that every reference-maker for F is a referent of F, but that would be misleading in that it would suggest that F was ambiguous. (This is a terminological point introduced to prevent confusion. Nothing beyond that hangs on our choice of terms.) A reference-maker for a predicate is something that it is true of, or that satisfies it. Any red thing is a reference-maker for the predicate 'red' or 'is red'. In this 'red' and 'is red' differ from 'redness', whose reference maker, if any, is redness; i.e., the property of being red.

Since I take the relation of predicates to reality to be, in general, one-many, I think it would be a mistake to take the "referent" or the semantic value of a predicate to be its extension, the set of things of which it is true. On my view, any reference-maker for a predicate can be said to be a semantic value of the predicate. Still, most predicates of  a given language will have but one meaning.

What of relational predicates? Their reference-makers can indeed be taken to be sets, namely ordered n-tuples. Still, we will not identify "the" semantic value of a predicate with its extension (nor with the property, if any, that it expresses): A reference-maker for an n-ary predicate is any ordered n-tuple of which that predicate is true, not the set of all such n-tuples--unless that set is one of the things of which the predicate is true; but still it would only be only one reference maker among many.

We can now say what a truth-maker, which is a reference maker for a sentence, is for subject-predicate sentences. An object x ('object' being broadly construed as anything that exists) is a truth-maker for a subject-predicate sentence p iff x is a reference-maker for p's subject term and is also a reference-maker for p's predicate term. Similarly, for relational sentences: An ordered n-tuple o is a truth-maker for an n-ary relational sentence p iff the objects ordered in o are each reference makers for one of p's subject terms, and o is a reference-maker for p's predicate term. In Part 2, I'll extend this account to define truth-makers for truth-functional compounds and quantified sentences.

Monday, October 07, 2013

The Rational Man

The Rational Man

 By

Jason Zarri



A rational man took a stroll one day, 
and chopped some logic along the way.
Quoth he: "What should a logician say?
Does the law of bivalence hold fast come what may?
How could my mind know it, assuming it's true,
when with such abstract facts it has nothing to do?"

Repeating to himself the words 'what' and 'why,' 
he took little notice of passers-by.
Some laughed, some sang, some played, some cried,
but all the while he tried and tried
to discern what might happen once one has died.

As the day wore on, the skies grew dim,
the path rose up, and the air grew thin,
while he wondered at the heavens and the moral law within.
In his thoughts faint memories stirred, yet were silenced by the din.
One thing too painful to ponder: the life that could have been.