Ever since the seminal work of Paul Grice, tautologies such as Business is business have been discussed from a number of angles. While most approaches assume that tautological utterances have to do with the operation of conversational maxims, an integrated analysis is still lacking. This paper makes an attempt at analysing tautologies within the framework of Levinson, who proposes a distinction between three pragmatic levels, namely Indexical Pragmatics, Gricean Pragmatics 1, and Gricean Pragmatics 2. It is shown that (...) observations of Ward and Hirschberg on the exclusion of alternatives, the claim of Autenrieth that the second NP in nominal equatives is predicative, and the recent insights of Bulhof and Gimbel on `deep' tautology, may be fruitfully integrated within Levinson's framework. The gist of this paper is to show that tautologies are not as tautological as once thought, because implicatures influence their truth conditions. Data are drawn from the author's corpus of authentic German examples. (shrink)

We consider logical expressions built on the single binary connector of implication and a finite number of literals . We prove that asymptotically, when the number of variables becomes large, all tautologies have the following simple structure: either a premise equal to the goal, or two premises which are opposite literals.

We consider tautologies formed form a pseudo-random number generator, defined in Krajicek [11] and in Alekhnovich et al. [2]. We explain a strategy of proving their hardness for Extended Frege systems via a conjecture about bounded arithmetic formulated in Krajicek [11]. Further we give a purely finitary statement, in the form of a hardness condition imposed on a function, equivalent to the conjecture. This is accompanied by a brief explanation, aimed at non-specialists, of the relation between prepositional proof complexity (...) and bounded arithmetic. (shrink)

In the Tractatus, Wittgenstein conceives of tautology as 'saying nothing'. More precisely, he holds -- or so this essay contends -- that it says nothing in virtue of possessing a zero quantity of sense. Insofar as it is the limit of a series of propositions of diminishing quantity of sense, tautology resembles a degenerate conic section. But it also resembles the result of a summing together of equal and opposite linear vector quantities. Both of these models shape Wittgenstein's conception of (...) tautology in the Tractatus, though they are not fully reconciled. Many of the puzzling features of the Tractatus's view of logic arise from this failure to affect the needed reconciliation. These points are argued for by working through the development of Wittgenstein's views on these matters in the Wartime Notebooks and other pre-Tractatus writings. (shrink)

If S ⊆{0,1}; * and S ′ = {0,1} * \sb S are both recognized within a certain nondeterministic time bound T then, in not much more time, one can write down tautologies A n → A′ n with unique interpolants I n that define S ∩{0,1} n ; hence, if one can rapidly find unique interpolants, then one can recognize S within deterministic time T p for some fixed p \s>0. In general, complexity measures for the problem of (...) finding unique interpolants in sentential logic yield new relations between circuit depth and nondeterministic Turing time, as well as between proof length and the complexity of decision procedures of logical theories. (shrink)

Economics is a science - at least positive economics must be. And science is in part applied mathematics, in part empirical observations and tests. Looking at the history of economics, one cannot find much testing done before the twentieth century, and even the collection of data, even in the manner Marx engaged in, was not common in his day. It is true that economic policy is an older field, and in that field much information is deployed for the purpose of (...) prescribing a course of action. But this is not to say that the information procured for that purpose is either based on observation or has been tested. In the seventeenth century some alchemists and economists hoped to boost the economy by manufacturing gold, others feared inflation; and the British Parliament legislated against manufacturing gold. David Hume proved in the eighteenth century - quite a priori - that doubling the quantity of gold will only double the price of each commodity and he thus set things at rest for a while. Later the question was opened again when Marx, for example, showed historically how the gold robbed from the Americas started Europe's boom. Yet the theory - the quantity theory of money, as it is called - which Hume proved a priori, is still contested and still hardly tested to economists' satisfaction: is the price level fixed mainly by the amount of available money? Some economists answer yes, others no. (shrink)

The standard understanding of tautologies is that they are semantically vacuous. Yet tautological utterances occur frequently in conversational discourse. One approach contends that apparent tautological statements are either genuinely tautologous and thereby semantically vacuous or are what we term ¿pseudo-tautologies¿, i.e., sentences that only bear a formal syntactic resemblance to tautologies but are not in fact tautologous. Another approach follows Grice and asserts that the meaning of a tautological utterance derives from an inference made by the listener (...) from the utterance via universal rules of conversation to a non-tautological proposition. We deny both accounts for a subset of tautological utterances that are both content-bearing and truly tautological. Such ¿deep tautologies¿ acquire meaning not by shedding their tautological status, but by drawing attention to it. Since only non-vague noun phrases will support tautological statements of the form N is N, the use of a tautology of this form in conversational context will, by its use as a tautology, indicate the speaker¿s intention that the noun phrase be considered non-vague. (shrink)

The standard understanding of tautologies is that they are semantically vacuous. Yet tautological utterances occur frequently in conversational discourse. One approach contends that apparent tautological statements are either genuinely tautologous and thereby semantically vacuous or are what we term “pseudo-tautologies”, i.e., sentences that only bear a formal syntactic resemblance to tautologies but are not in fact tautologous. Another approach follows Grice and asserts that the meaning of a tautological utterance derives from an inference made by the listener (...) from the utterance via universal rules of conversation to a non-tautological proposition. We deny both accounts for a subset of tautological utterances that are both content-bearing and truly tautological. Such “deep tautologies” acquire meaning not by shedding their tautological status, but by drawing attention to it. Since only non-vague noun phrases will support tautological statements of the form N is N, the use of a tautology of this form in conversational context will, by its use as a tautology, indicate the speaker’s intention that the noun phrase be considered non-vague. (shrink)

It is commonly thought that the prevalence of moral dissent poses a problem for the moral cognitivist, forcing her to diagnose either a lot of misunderstanding, or a lot of unexplained observational error. Since mere misunderstanding can be ruled out in most cases of moral dissent, and since the diagnosis of widespread unexplained error is interpretively unstable, prevalent dissent has pushed many philosophers towards non-cognitivism. In this essay, I argue that once a diachronic, pragmatist theory of language along the lines (...) of the latest Wittgenstein is employed, a third interpretive option becomes available to the cognitivist. Besides the diagnostic options of misunderstanding and factual disagreement, she can argue that a given case of moral dissent is an instance of grammatical tension. This interpretation not only saves moral cognitivism, it also has some attractive theoretical implications. Among other things, it yields an elegant way of solving the current debate around moral particularism. (shrink)

This essay examines U.S. blackface performance in the twentieth century through the lens of Adorno’s mass culture critiques, specifically of jazz music. Despite being rooted in the divisive logic of antiquated live performance traditions, blackface as a racist glyph flourishes in the technologically mediated social environment of the twentieth century. By replacing Adorno’s critique of jazz with a direct investigation of blackface, the essay argues for a more materialist approach to minstrelsy studies that acknowledges both circulation and accumulation as oppressive (...) hegemonic forces. (shrink)

A t-tautology is a propositional formula which is a tautology in all fuzzy logics defined by continuous triangular norms. In this paper we show that the problem of recognizing t-tautologies is coNP complete, and thus decidable.

The paper asks: are all tautologies true in a language with truth-value gaps? It answers that they are not. No tautology is false, of course, but not all are true. It also contends that not all contradictions are false in a language with truth-value gaps, though none are true.

I present a new 33-ray proof of the Kochen and Specker “no-go” hidden variable theorem in ℋ3, based on a classical tautology that corresponds to a contingent quantum proposition in ℋ3 proposed by Kurt Schütte in an unpublished letter to Specker in 1965. 1 discuss the relation of this proof to a 31-ray proof by Conway and Kochen, and to a 33-ray proof by Peres.

In the paper I analyze two features of the genre of the pedagogical. First is a particular usage of “should” statements where one can identify an effect of erasing present normative behavior, while that which is postulated is turned into an unattainable ideal, or a value. Second, I analyze “presumptive tautologies” in the discourse of aims of education. I focus on negative dimensions of these two features and, using theoretical insights from Laclau and Rancière, I connect them to the (...) work of negativity in political ontology so that the relation between the pedagogical and the political can thus be re-articulated. (shrink)

Extending techniques of Dowd and those of Poizat, we study computational complexity of in the case when is a generic oracle, where is a positive integer, and denotes the collection of all -query tautologies with respect to an oracle . We introduce the notion of ceiling-generic oracles, as a generalization of Dowd's notion of -generic oracles to arbitrary finitely testable arithmetical predicates. We study how existence of ceiling-generic oracles affects behavior of a generic oracle, by which we show that (...) is not a subset of is comeager in the Cantor space. Moreover, using ceiling-generic oracles, we present an alternative proof of the fact (Dowd) that the class of all -generic oracles has Lebesgue measure zero. (shrink)

It is shown how the schema of equivalence can be used to obtain short proofs of tautologies A , where the depth of proofs is linear in the number of variables in A .

Representative democracy is often assessed from the standpoint of direct democracy. Recently, however, many theorists have come to argue that representation forms a democratic model in its own right. The most powerful claim in this direction is to be found within two quite different strands of thinking: the aesthetic theory of Frank Ankersmit and the savage theory of Claude Lefort. In this article, I show that while Ankersmit and Lefort converge in their critique of direct rule, they provide us with (...) two distinct models of democracy. Aesthetic democracy, I argue, in the end falls short as a democratic recuperation of representation. It reduces representation to delegation. Savage democracy proves more fruitful in this respect. It offers a representative view of politics without committing itself to the premises associated with political delegation. (shrink)

The tautological implications of “innate talents” are outlined. Analogies are drawn between the present review and the nature–nurture controversies of 40 years ago. Ferguson 's theoretical positions are proposed as a context in which to consider present and future attempts to resolve this long-standing issue.

We present a simple propositional proof system which consists of a single axiom schema and a single rule, and use this system to construct a sequence of combinatorial tautologies that, when added to any Frege system, p-simulates extended-Frege systems.

Herbrand’s theorem is one of the most fundamental results about first-order logic. In the context of proof analysis, Herbrand-disjunctions are used for describing the constructive content of cut-free proofs. However, given a proof with cuts, the computation of a Herbrand-disjunction is of significant computational complexity, as the cuts in the proof have to be eliminated first.In this paper we prove a generalization of Herbrand’s theorem: From a proof with cuts, one can read off a small tautology composed of instances of (...) the end-sequent and the cut formulas. This tautology describes the proof in the following way: Each cut induces a formula stating that a disjunction of instances of the cut formula implies a conjunction of instances of the cut formula. All these cut-implications together then imply the already existing instances of the end-sequent. The proof that this formula is a tautology is carried out by transforming the instances in the proof to normal forms and using characteristic clause sets to relate them. These clause sets have first been studied in the context of cut-elimination.This extended Herbrand theorem is then applied to cut-elimination sequences in order to show that, for the computation of an Herbrand-disjunction, the knowledge of only the term substitutions performed during cut-elimination is already sufficient. (shrink)

The paper presents a particular example of a formula which is a standard tautology of Łukasiewicz but not its general tautology; an example of a model in which the formula is not true is explicitly constructed. Analogous example of a formula and its model is given for product logic.

Graham Priest has asked whether the consequence relation associated with the Anderson–Belnap system of Tautological Entailment,1 in the language with connectives ¬, ∧, ∨, and countably many propositional variables as tomic formulas, maximal amongst the substitution-invariant relevant consequence relations on this language. Here a consequence relation is said to be relevant just in case whenever for a set of formulas Γ and formula B, we have Γ B only if some propositional variable occurring in B occurs in at least one (...) formula in Γ. (It follows that relevant consequence relations are atheorematic in the sense that whenever Γ B for some such consequence relation , Γ = ∅.) Here I write up in more detail the upshot of the conversation – returning an affirmative answer to Priest’s question – about this in the common room that Greg Restall and I were participating in last Friday [ = October 6, 2006], dotting some “i”s and crossing some “t”s (and adding the odd further reflection). (shrink)

In Cieśliński (J Philos Logic 39:325–337, 2010), Cieśliński asked whether compositional truth theory with the additional axiom that all propositional tautologies are true is conservative over Peano Arithmetic. We provide a partial answer to this question, showing that if we additionally assume that truth predicate agrees with arithmetical truth on quantifier-free sentences, the resulting theory is as strong as $$\Delta _0$$ Δ 0 -induction for the compositional truth predicate, hence non-conservative. On the other hand, it can be shown with (...) a routine argument that the principle of quantifier-free correctness is itself conservative. (shrink)

Few problems in the philosophy of evolutionary biology are more widely disseminated and discussed than the charge of Darwinian evolution being a tautology. The history is long and complex, and the issues are many, and despite the problem routinely being dismissed as an introductory-level issue, based on misunderstandings of evolution, it seems that few agree on what exactly these misunderstandings consist of. In this paper, I will try to comprehensively review the history and the issues. Then, I will try to (...) present the following “solution”, or, one might say, “dissolution”, of the problem, and consider the wider implications of formal, or schematic, explanations in science: yes, the principle of natural selection is a tautology, and so what? It is a promissory note for actual, physical, explanations in particular cases, and is none the worse for that. This is not a new argument, of course, but it does point up the importance of formal schematic models in science. (shrink)

Classes of linguistic paradoxes are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic.