Page 283 - Encyclopedia of Philosophy of Language

nong's 'theory of Objects'—which Russell regarded as lacking that 'robust sense of reality' no less essential to a logician than to a zoologist. The capital letter in 'theory of Objects' signals that the word is used in a technical sense; the theory is about the objects of thought. According to Meinong some but not all Objects have Being—they either exist or, in the case of abstract Objects, subsist. But Objects as such are 'beyond being and notbeing'; that is, it is possible to think about something, and say true things about it, even if there is no such thing. 'The golden mountain is golden' and even 'the round square is round,' according to Meinong, are not false (as Russell would have it), or truth-valueless (as Frege's discussion might suggest), but true.
Some deviant logicians have been attracted by Fre- ge's presupposition theory, others by Meinong's the- ory of Objects. The first party urges the merits of a nonbivalent logic in which the relation of pre- supposition may be formally represented. Smiley uses Bochvar's 3-valued logic for this purpose; Woodruff prefers Kleene's strong matrices. (Van Fraassen sug- gests remaining classical syntactically while adopting his nonbivalent presuppositional semantics.) The other party sympathizes with Meinong's objection that the Russellian approach betrays a 'prejudice in favor of the actual.' What the classical logician, and even the 3-valued presupposition theorist, sees as ref- erence failure, the Meinongian logician construes as reference to an object which happens not to be real.
Even those who, reasonably enough, are alarmed by talk of unreal objects and the impossible inhabi- tants of impossible possible worlds, however, may have some sympathy with the thought that it may be inappropriate to treat fictional discourse, or discourse about prepositional attitudes, on a par with those cases of reference failure which result from mistake or inadvertence, as alike defective.
This intuition might however be accommodated by other routes, requiring recourse neither to Mei- nongianism nor to any other nonstandard 'logic of fiction' (Woods', for example, analogous to a modal system, in which the operator 'O' is read 'Once upon a time...'). The first step is to distinguish discourse in fiction from discourse about fiction. The latter can be acknowledged as straightforwardly true or false if construed as implicitly preceded by 'It says in the story that — ' The former may be best regarded not as unsuccessful fact-stating discourse, but simply as not making assertions at all. This would put fictional dis- course, in the sense of 'discourse in fiction,' no longer in need of non-standard logical treatment, because ruled, with good reason, outside the scope of logic altogether.
Discourse about propositional attitudes, which may also involve nondenoting terms (as: 'The Vikings believed that Thor made thunder when he was angry,' 'Meinong believed that the round square was round
as well as square') obviously cannot be plausibly claimed not to be bona fide assertion-making dis- course; and it must be conceded that a Russellian treatment leaves something to be desired. Such dis- course may however be accommodated without the alarming ontological commitments of Meinongianism by adopting Burdick's construal of belief, etc., not as of some peculiar nonextensional object, but as of the ordered pair of an ordinary object and a predicate representing a 'mode of presentation.' In this treat- ment, beliefs, as we say, about nonexistent objects are construed as beliefs of the null set under a certain description ('The Vikings believed of <A, "God of war") that he made thunder when angry'). Though it requires ascent to the formal mode in the introduction of modes of presentation, this maneuver maintains extensionality and avoids Meinongian ontological extravagance.
3.4 Semantic Paradox
If the liar sentence, This sentence is false' is true, what it says is the case, so it is false; while if it is false, since that is what it says, it is true. The classical, regimentalist line, paradigmatically represented by Tarski, is, maintaining the assumption that every legit- imate declarative sentence is either true or else false, to draw the conclusion that the liar sentence is illegit- imate. Semantically closed languages, therefore, which contain the means to refer to their own sen- tences and to predicate truth or falsity of them, are eschewed; in a well-behaved formal semantics the truth-predicate is deemed systematically ambiguous, with 'true-in-the-object-language' construed as a predicate in the °meta-language, 'true-in-the-meta- language' as a predicate of the meta-meta-language, etc. 'This sentence is false,' simpliciter, is not legit- imate; 'this sentence is false-in-O' is a sentence of M, and not paradoxical. And Tarski's 'T-schema':
S is true if and only if p
where the expression on the left names a sentence, and the expression on the right is that sentence itself, can be sustained, relativized to a language ('S is true-in-O iffp').
Others, however, draw the conclusion that it is not the semantic closure of natural languages but bival- ence that is at fault. This motivated Bochvar's 3- valued logic. It also motivates Kripke's diagnosis, and his resort to Kleene's 3-valued logic. According to Kripke, the truth-predicate is univocal, but only par- tially defined, undefined, in particular, for 'ungrounded' sentences like 'this sentence is true' and 'this sentence is false.' But repudiation of bivalence avoids the liar but not the strengthened liar: if the sentence 'this sentence is either false or truth-valueless' (or, 'this sentence is not true') is true, it is either false or truth-valueless; if it is false or truth-valueless, it is true. Kripke can, indeed, avoid the strengthened liar
Deviant Logics
261