Roger Wertheimer

View more Abstract If logical truth is necessitated by sheer syntax, mathematics is categorially unlike logic even if all mathematics derives from definitions and logical principles. This contrast gets obscured by the plausibility of the Synonym Substitution Principle implicit in conceptions of analyticity: synonym substitution cannot alter sentence sense. The Principle obviously fails with intercepting: nonuniform term substitution in logical sentences. ‘Televisions are televisions’ and ‘TVs are televisions’ neither sound alike nor are used interchangeably. Interception synonymy gets assumed because logical sentences and their synomic interceptions have identical factual content, which seems to exhaust semantic content. However, intercepting alters syntax by eliminating term recurrence, the sole strictly syntactic means of ensuring necessary term coextension, and thereby syntactically securing necessary truth. Interceptional necessity is lexical, a notational artifact. The denial of interception nonsynonymy and the disregard of term recurrence in logic link with many misconceptions about propositions, logical form, conventions, and metalanguages. Mathematics is distinct from logic: its truth is not syntactic; it is transmitted by synonym substitution; term recurrence has no essential role. The ‘=’ of mathematics is an objectual relation between numbers; the ‘=’ of logic marks a syntactic relation of coreferring terms.

Analyses of quotation have assumed that quotations are referring expressions while disagreeing over details. That assumption is unnecessary and unacceptable in its implications. It entails a quasi-Parmenidean impossibility of meaningfully denying the meaningfulness or referential function of anything uttered, for it implies that: 'Kqxf' is not a meaningful expression 'The' is not a referring expression are, if meaningful, false. It also implies that ill formed constructions like: 'The' is 'the' are well formed tautologies. Such sentences make apparent the need for what is commonly explicit, a genuine referring expression, a noun phrase, usually a description, to which the quotation is appositional. A quotation is not itself a word, though it may contain such. The markers signal that the enquoted material is like a sentence-embedded color patch, material displayed to facilitate reference to something identifiable by/with it specified by the noun phrase it subserves.

Analyticity is a bogus explanatory concept, and is so even granting genuine synonomy. Definitions can't explain the truth of a statement, let alone its necessity and/or our a priori knowledge of it. The illusion of an explanation is revealed by exposing diverse confusions: e.g., between nominal, conceptual and real definitions, and correspondingly between notational, conceptual, and objectual readings of alleged analytic truths, and between speaking a language and operating a calculus. The putative explananda of analyticity are (alleged) truths about essential properties. Real definitions (a la Socrates) are the (alleged) explananda, not the explanans of analyticity. Their truth can be explained neither by conceptual definitions (a la Kant), nor by nominal definitions (a la Frege). The Quinean assault on synonomy is unsuccessful and in any case misplaced, because analyticity turns on the explanatory import of synonomy, not its existence. Synonym substitution in a logical truth cannot yield a necessary truth for it doesn't preserve logical form. Self-identity statements (for properties and/or individuals) differ in logical form from alter-identity statements.

The identity "relation" is misconceived since the syntax of "=" is misconceived as a relative term. Actually, "=" is syncategorematic; it forms (true) sentences with a nonpredicative syntax from pairs of (coreferring) flanking names, much as "&" forms (true) conjunctive sentences from pairs of (true) flanking sentences. In the conaming structure, nothing is predicated of the subject, other than, implicitly, its being so conamed. An identity sentence has both an objectual reading as a necessity about what is named, and also a metalinguistic reading as a contingency about the names. Either way the claim about the subject referent has no extralinguistic content. The necessity of alteridentity (non-self-identity) statements is "lexical", due to contingencies of the names' reference, much like the necessity of analytic statements, due to contingencies of the predicates' sense, and unlike the necessity of logical truths (e.g., self-identities) whose truth is secured by syntax alone. Both alter-identity and analytic sentences are readable as objectual necessities and metalinguistic contingencies. Epistemically, alter-identity statements are not essentially unlike analyticities. "Greece is Hellas"/"g=h" and "Greeks are Hellenes"/"(x)(Gx<=>Hx)" are equally (un)informative; so too for "Azure is cobalt"/"a=c" and "Everything azure is cobalt"/"(x)(Ax<=>Cx)". The real epistemic contrast is between proper names (terms without predicative sense) and terms with a predicative sense (names and predicates of properties). Proper names refer to concrete objects, property names refer to abstract objects. That contrast is metaphysical and thus epistemic.

Our culture is conflicted about morally judging and condemning. We can't avoid it altogether, yet many layfolk today are loathe to do it for reasons neither they nor philosophers well understand. Their resistance is often confused (by themselves and by theorists) with some species of antiobjectivism. But unlike a nonobjectivist, most people think that (a) for us to judge and condemn is generally (objectively) morally wrong , yet (b) for God to do so is (objectively) proper, and (c) so too for certain persons in certain relations (e.g., self-condemnation, parental child rearing.) Certainly, religious (e.g., Christian) critics of judging and condemning without doubting the objective truth of their tradition's core moral teachings. Most puzzling is that (a) merely judging and condemning in one's heart may be improper, and (b) someone else with no more evidence or expertise might properly judge and condemn the same action. The answer is in condemning's complex structure of presuppostions. Condemning and judging are acts, and attitudes initiated by the act. Condemnation is motivated by two judgments presumed to justify it, a criticism of a target, and a judgment that the criticism justifies some negative response toward the target. Unlike nonpunitive penalties, punishments are motivated and explained by condemnation. Condemnation is an act of a hostile will, wishing some evil for its target, not (just) as a means to some good. Its root is in damning, an act akin to cursing. It declares a degraded status. The hostility makes it harder to justify condemnation than criticism, and punishment than nonpunitive penalties. Condemning claims objectivity and authority. It involves reflexive evaluation, regarding itself justified, approving its hostile feelings toward the target. Condemners presume themselves entitled to sit in judgment, pass judgment, and cast the condemned down. Those presumptions inhere in sitting in judgment, assuming jurisdiction. Unlike mathematical or scientific judgments, passing moral judgment seems to be a political act subject to extraepistemic constraints. "Who are you to judge?" may properly challenge your right to pass judgment.

The Socratic Paradox (that only Socrates is wise, and only because only he recognizes our lack of wisdom) is explained, elaborated and defended. His philosophical scepticism is distinguished from others (Pyrrhonian, Cartesian, Humean, Kripkean Wittgenstein, etc.): the doubt concerns our understanding of our beliefs, not our justification for them; the doubt is a posteriori and inductive, not a priori. Post-Socratic philosophy confirms this scepticism: contra-Descartes, our ideas are not transparent to us; contra-Verificationism, no criterion distinguishes sense from nonsense. The import of this scepticism for professional ethicists is examined.

Post-Fregean theorists use 'quotation' to denote indifferently both colloquially called quotations (repetitions of prior utterances) and what I call 'displays': 'Rot' means red. Colloquially, quotation is a strictly historical property, not semantic or syntactic. Displays are semantically and syntactically distinctive sentential elements. Most displays are not quotations. Pure echo quotations (Cosmological arguments involve "an unnecessary shuffle") aren't displays. Frege-inspired formal languages stipulate that enquotation forms a singular term referring to the enquoted expression (type). Formalist enquotations differ semantically and syntactically from natural language displays. Call them autonomes, and mark them with stars: *Rot* means red. In formal languages, an unenstarred expression has only one meaning, and an autonome has only one meaning viz., a name (or indexical) designating the unenstarred expression (type). Stars have semantic content and can’t disambiguate. Display punctuation only disambiguates; it says only: This material is displayed. Displays have a semantic function; their marks don't.nDisplays are not terms or lexical items. Displays are objects incorporable into utterances. Such incorporation enables them to be linguistically appropriated much as we appropriate speech-external objects by extrasentential supplementation (e.g., gesturing) to identify the extension of a term by ostending the object -- but now without any extrasentential supplement. Displays are always adjunctive to an (implicit or explicit) ostensionable term, a term whose extension is identifiable by ostending an object. The display-ostensionable term extension relations are various. A display may (1) be the term's referent, or (2) represent the term's extension by (a) replicating or (b) instantiating or (c) expressing the term's referent, or (e) instantiating the property the term predicates.