The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom (...) is approximated by Herbrand’s Induction-Axiom Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (shrink)

We study the relationships between two clusters of axiomatizations of Kripke’s fixed-point models for languages containing a self-applicable truth predicate. The first cluster is represented by what we will call ‘\-like’ theories, originating in recent work by Halbach and Horsten, whose axioms and rules are all valid in fixed-point models; the second by ‘\-like’ theories first introduced by Solomon Feferman, that lose this property but reflect the classicality of the metatheory in which Kripke’s construction is carried out. We show that (...) to any natural system in one cluster—corresponding to natural variations on induction schemata—there is a corresponding system in the other proving the same sentences true, addressing a problem left open by Halbach and Horsten and accomplishing a suitably modified version of the project sketched by Reinhardt aiming at an instrumental reading of classical theories of self-applicable truth. (shrink)

Tarski avoids the liar paradox by relativizing truth and falsehood to particular languages and forbidding the predication to sentences in a language of truth or falsehood by any sentences belonging to the same language. The Tarski truth-schemata stratify an object-language and indefinitely ascending hierarchy of meta-languages in which the truth or falsehood of sentences in a language can only be asserted or denied in a higher-order meta-language. However, Tarski’s statement of the truth-schemata themselves involve general truth functions, and (...) in particular the biconditional, defined in terms of truth conditions involving truth values standardly displayed in a truth table. Consistently with his semantic program, all such truth values should also be relativized to particular languages for Tarski. The objection thus points toward the more interesting problem of Tarski’s concept of the exact status of truth predications in a general logic of sentential connectives. Tarski’s three-part solution to the circularity objection which he anticipates is discussed and refuted in detail. (shrink)

Consider the following sentence schemata: (1) The proposition that P is F; (2) The property of being Q is F; (3) The relation of being R is F, where `P' is a schematic letter for a sentence, `Q' and `F' are schematic letters for a nonrelational predicate, and `R' is a schematic letter for a relational predicate. For example, if we substitute `Snow is white' for `P', `famous' for `F' in (1), `round' for `Q', `instantiated' for `F' (...) in (2), `a father of' for `R', and `asymmetric' for `F' in (3), then we obtain the following particular sentences. (shrink)

-/- A schema (plural: schemata, or schemas), also known as a scheme (plural: schemes), is a linguistic template or pattern together with a rule for using it to specify a potentially infinite multitude of phrases, sentences, or arguments, which are called instances of the schema. Schemas are used in logic to specify rules of inference, in mathematics to describe theories with infinitely many axioms, and in semantics to give adequacy conditions for definitions of truth. -/- 1. What is a (...) Schema? 2. Uses of Schemas 3. The Ontological Status of Schemas 4. Schemas in the History of Logic Bibliography. (shrink)

This paper offers a new interpretation of John Austin’s views both on assertion and on adverbs, as result of which an expressivist thesis concerning the semantics for action sentences is advanced. First, Austin’s analysis of assertion based on various, specific assertive forces and his remarks on adverbs are systematically connected in order to obtain assertive schemata for action sentences. Finally, those schemata are put to work as the expression of inferential commitments implicit in argumentative practices of different sorts (...) (exculpatory, justificatory and illustrative) in the deployment of which, both logical contrariety and contradiction are exploited. (shrink)

Abstract: Introspection reveals that one is frequently conscious of some form of inner speech, which may appear either in a condensed or expanded form. It has been claimed that this speech reflects the way in which language is involved in conscious thought, fulfilling a number of cognitive functions. We criticize three theories that address this issue: Bermúdez’s view of language as a generator of second-order thoughts, Prinz’s development of Jackendoff’s intermediate-level theory of consciousness, and Carruthers’s theory of inner speech as (...) a rehearsal of action-schemata. We contend they have problems to account for those cases in which inner speech is fragmentary, and for the difference with those instances in which it appears as more sentence-like. In addition, we present verbal overshadowing as a phenomenon that neither of them can easily explain. Finally, we propose an account in which inner speech is fundamentally silent outer speech and argue that it is more explanatory than the alternatives. (shrink)

Saunders Mac Lane has drawn attention many times, particularly in his book Mathematics: Form and Function, to the system of set theory of which the axioms are Extensionality, Null Set, Pairing, Union, Infinity, Power Set, Restricted Separation, Foundation, and Choice, to which system, afforced by the principle, , of Transitive Containment, we shall refer as . His system is naturally related to systems derived from topos-theoretic notions concerning the category of sets, and is, as Mac Lane emphasises, one that is (...) adequate for much of mathematics. In this paper we show that the consistency strength of Mac Lane's system is not increased by adding the axioms of Kripke–Platek set theory and even the Axiom of Constructibility to Mac Lane's axioms; our method requires a close study of Axiom H, which was proposed by Mitchell; we digress to apply these methods to subsystems of Zermelo set theory , and obtain an apparently new proof that is not finitely axiomatisable; we study Friedman's strengthening of , and the Forster–Kaye subsystem of , and use forcing over ill-founded models and forcing to establish independence results concerning and ; we show, again using ill-founded models, that proves the consistency of ; turning to systems that are type-theoretic in spirit or in fact, we show by arguments of Coret and Boffa that proves a weak form of Stratified Collection, and that is a conservative extension of for stratified sentences, from which we deduce that proves a strong stratified version of ; we analyse the known equiconsistency of with the simple theory of types and give Lake's proof that an instance of Mathematical Induction is unprovable in Mac Lane's system; we study a simple set theoretic assertion—namely that there exists an infinite set of infinite sets, no two of which have the same cardinal—and use it to establish the failure of the full schema of Stratified Collection in ; and we determine the point of failure of various other schemata in . The paper closes with some philosophical remarks. (shrink)

There is a long tradition of drawing metaphysical conclusions from investigations into language. This paper concerns one contemporary variation on this theme: the alleged ontological significance of cognitivist truth-theoretic accounts of semantic competence. According to such accounts, human speakers’ linguistic behavior is in part empirically explained by their cognizing a truth-theory. Such a theory consists of a finite number of axioms assigning semantic values to lexical items, a finite number of axioms assigning semantic values to complex expressions on the basis (...) of their structure and the semantic values of their constituents, and a finite number of production schemata. The theory enables the derivation of truth-conditions for each sentence of the language: something of roughly the form ‘S is true iff P’.1 The claim that speakers stand in a cognitive relation to such theories is advanced, not as a conceptual analysis of semantic competence or understanding, but rather as an empirical hypothesis about human speakers in particular, one part of a broader empirical account of our linguistic competence and cognition generally. It therefore must mesh with the rest of our theorizing in these areas and whatever relevant data from neighboring inquiries there may be. The precise nature of the cognitive relation a speaker is supposed to bear to a truththeory is a matter of some dispute. I speak of ‘‘cognizing’’ (following. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Plato and Leibniz against the MaterialistsEmily GrosholzImportant parallels hold between Leibniz’s attitude towards materialism and that of Plato. Both philosophers were interested in and hostile to materialism, and their qualified rejection of materialism became crucial to the systems of their maturity. Leibniz’s attachment to Plato began very early: in a text of 1664 Leibniz quoted the Timaeus, 1 and in another of 1670 he claimed that the Timaeus, along (...) with the Parmenides and the Phaedo, were his favorite dialogues. 2 The influence of the Timaeus is quite apparent in Leibniz’s correspondence with the French Platonist Nicholas Remond (1713–16) and certain essays (particularly “On the Ultimate Origination of Things” [1697] and “Tentamen Anagogicum”), where he appeals to Plato in distinguishing his own position from the materialism of his day, which revived and transformed that of Leucippus and Democritus, Epicurus, and the poet Lucretius.The way in which Leibniz resists and circumvents materialism in these letters and essays has a family resemblance with the way Plato addresses and solves certain metaphysical problems, some of them raised by materialism, in the Timaeus. All the same, the Platonic and Leibnizian strategies also diverge in significant respects. For Plato belongs to the ancient world and Leibniz to the modern world, in which the topic of subjectivity becomes central. Although both philosophers make essential use of abstract mathematical schemata to organize and inform their philosophical positions, Plato tends to give them a constitutive role and Leibniz a regulative role. [End Page 255]What is the point of establishing this analogy, a likeness nuanced by unlikeness, in the metaphysical strategies of Plato and Leibniz? First, it is important to examine philosophical genealogies. In this case the genealogy is attested by Leibniz himself, who feels at once indebted to and impatient with his forebear. Yet it has received much less scholarly recognition than the more obvious link between Aristotle and Leibniz. Second, this kind of examination exhibits the shape and tensile strength of metaphysical systems, as tragedy or fiction exhibits the extent and limits of moral and political systems. I assume that certain metaphysical problems and certain possibilities for metaphysical systems recur through time and that those things that are perennial in philosophy point to what is eternal about it, but I also believe that there is something peculiar about modernity, which imposes a sea-change on philosophy after Descartes. Materialism is a recurrent metaphysical possibility with which contemporary philosophers must still come to terms; the peculiar nature of modern philosophy introduces new ways to address materialism. Surely the study of how Plato and Leibniz took the measure of materialism will be illuminating for philosophers interested in such questions.I. Modern scholars debate over whether Plato knew the writings of Democritus and addressed himself to them. The classical authors were unanimous in the opinion that Plato regarded Democritus as one of his most important opponents. According to an often repeated anecdote, Plato wanted all the writings of Democritus burnt and only gave up this wish when it was clear that the writings were already too widely circulated. 3Commentators have pursued this alleged opposition in various directions. Hammer-Jensen 4 and Natorp 5 have argued that Plato discovered the works of Democritus in the midst of writing the Timaeus and that one can trace their influence in the latter part of the dialogue. Thus they find Plato heavily indebted to Democritus. Taylor, by contrast, rejects the influence of Democritus on Plato altogether. [End Page 256]There is no need to bring in Democritus, and it is perhaps most likely that Plato had never read his works. We cannot prove such a proposition, but we shall at least see that there is not a single sentence in the Timaeus which shows any knowledge of Democritus. Moreover, it is very doubtful whether Plato would have learned anything from Democritus if he had read him. 6However, Taylor’s conviction that Plato would not have been interested in Democritus is based on the assumption, central to his commentary, that the Timaeus must be read as a Pythagorean text, and this in itself is debatable. After all, Plato chose Timaeus the Locrian as the protagonist of... (shrink)

It has been shown that when participants are asked to make sensibility judgments on sentences that describe a transfer of an object toward or away from their body, they are faster to respond when the response requires a movement in the same direction as the transfer described in the sentence. This phenomenon is known as the action compatibility effect. This study investigates whether the ACE exists for volunteers with Alzheimer's disease, whether the ACE can facilitate language comprehension, and also (...) whether the ACE can still be produced if the order of the two events is inverted, that is, whether overt movement can prime comprehension of transfer sentences. In Study 1, participants with AD, younger, and older adults were tested on an adaptation of the ACE Paradigm. In Study 2, the same paradigm was modified to include an arm movement that participants had to perform prior to sentence exposure on screen. In Study 1, young, older adults, and individuals with AD were faster to respond when the direction of the response movement matched the directionality implied by the sentence. In Study 2, no traditional ACE was found; participants were faster when the direction of the movement immediately preceding the sentence matched the directionality of the sentence. It was found that compatibility effects generated a relative advantage, that transfer schemata are easier to process, and that an ACE-like effect can be the result of mutual priming between language and movement. Results suggested preservation in AD of the neural systems for action engaged during language comprehension, and conditions under which comprehension in AD can be facilitated in real life may be identified. (shrink)

The domain of a quantifier is determined by a variety of factors, which broadly speaking fall into two types. On the one hand, the context of utterance plays a role: if the focus of attention is on a particular collection of kangaroos, for example, then “Q kangaroos” is likely to range over the individuals in that set. On the other hand, the utterance itself will help to establish the quantificational domain, inter alia through presuppositions triggered within the sentence. In (...) this paper, we concentrate our attention on constructions like the following, in which “the square to which... ” is the critical presupposition trigger: Q circles... Q of these circles... Q of these five circles...... have the same colour as the square to which they are connected. Many theories predict that all instances of these schemata will give rise to the presupposition that every circle is connected to a square. We present an analysis which predicts that these sentences should generally be accepted in a context in which not all the circles are connected to a square, with one exception only: if a quantified sentence is of type and Q is non-intersective, then the sentence should be more likely to be rejected. Furthermore, we predict that manipulating the context so as to make the connected circles more or less salient should have an effect on statements with non-intersective quantifiers only. These predictions were tested in a series of experiments. (shrink)

In this paper, I distinguish between linguistic and non-linguistic presuppositions. I also propose that we should be interested in conversational presuppositions, which could also be called speaker-meant presuppositions or speaker's presuppositions. I also distinguish between potential and actual presuppositions. I propose that, in some cases, presuppositions can be conversationally implicated and cancellation is possible. I specify what the hard cases are and I try to explain them through ontological considerations. I try to reduce the hard cases through (a) the notion (...) that all actual presuppositions are speaker-meant; (b) the distinction between ontological and linguistic presuppositions; and (c) the uncontroversial notion that even ontological presuppositions are susceptible to semantic under-determination that has to be tackled though pragmatic intrusion. Pragmatic intrusion for presuppositional cases, however, cannot really amount to completing or expanding or in any case computing an explicature in an ordinary sense, as explicatures have to do with truth-conditions and aim to create propositionally complete forms that are truth-evaluable, unlike propositional fragments or schemata that are usually expressed in sentences (; , 2012). They are processes similar to explicatures, but since presuppositions are only pre-conditions for an utterance's being true or false (; Macagno; 2016; ; ), we cannot say that these processes are completely like those of explicatures. Nevertheless, they are pragmatically-motivated, even if hard to cancel. (See on lack of cancellability or on entrenched meanings.) This more or less brings my approach in line with contextualism (even if I accept semantic invariantism, along the lines of or (Invariantism is also shared by , in a form that is compatible with her contextualism.)). (shrink)

How can Deleuzians make his philosophy as accessible as possible to political theorists and democratic publics? This essay provides principles to enter Deleuze's political vision, namely, to research the etymology of words, to discover the image beneath concepts, to diagram schemata using rigid lines, supple lines and lines of flight, and to construct rules that balance experimentation and caution. The essay then employs this method to explicate a fecund sentence about politics in A Thousand Plateaus and presents a (...) case why Deleuze deserves greater visibility in the political theory canon. (shrink)

The general tendency or attitude that Dreier 2004 calls creeping minimalism is ramping up in contemporary analytic philosophy. Those who entertain this attitude will take for granted a framework of deflationary or minimal notions – principally semantical1 and ontological – by means of which to analyse problems in different philosophical fields – e.g. theory of truth, metaethics, philosophy of language, the debate on realism and antirealism, etc. Let us call sweeping minimalist the philosopher affected by creeping minimalism. The framework of (...) minimal notions that the sweeping minimalist takes for granted encompasses, for instance, the concept of truth, reference, proposition, fact, individual, and property. Minimal notions are characterized in terms of general platitudinous principles expressed by schemata like the following (cf.: 26): ‘S’ is true if and only if S; ‘S’ is true if and only if ‘S’ corresponds to the facts; a has the property of being P if and only if a is P. Where ‘S’ and ‘a is P’ stand for sentences satisfying superficial constraints of truth-aptitude (i.e. sentences in declarative form subject to communally acknowledged standards of proper use), and.. (shrink)

El presente artículo ofrece una interpretación original del trabajo de Austin sobre la aserción y los adverbios y deriva de ella una semántica expresivista para las oraciones de acción. En primer lugar, el análisis austiniano de la aserción con su idea de fuerzas asertivas específicas se conecta sistemáticamente con sus observaciones sobre la modificación adverbial para obtener esquemas de aserción para oraciones de acción. En segundo lugar, se interpretan esos esquemas en términos de la expresión de los compromisos inferenciales propios (...) de prácticas argumentativas exculpatorias, justificativas y ejemplarizantes en las que se explota la contrariedad lógica a la par de la contradicción. This paper offers a new interpretation of John Austin's views both on assertion and on adverbs, as result of which an expressivist thesis concerning the semantics for action sentences is advanced. First, Austin's analysis of assertion based on various, specific assertive forces and his remarks on adverbs are systematically connected in order to obtain assertive schemata for action sentences. Finally, those schemata are put to work as the expression of inferential commitments implicit in argumentative practices of different sorts in the deployment of which both logical contrariety and contradiction are exploited. (shrink)

It is, I suppose, a truism that an adequate theory of meaning for a natural language L will associate each sentence of L with its meaning. But the converse does not hold. A theory that associates each sentence with its meaning is not, by virtue of that fact, an adequate theory of meaning. For it is also a truism that a semantic theory should explain the (interesting and explicable) semantic facts. And one cannot decree that the relevant facts (...) are all reportable with instances of schemata like ‘S means that p’ or ‘S, by virtue of its meaning, is true iff p’. Investigation suggests that there is much more for semanticists to explain: natural languages exhibit synonymies, ambiguities, and entailments; for any string of words, there are endlessly many meanings it cannot have; there are semantic generalizations, including crosslinguistic generalizations, that go uncaptured and unexplained by merely associating sentences with their meanings; etc. Initially, one might think these facts are “peripheral” and can thus be ignored if the aim is to explain why sentences mean what they do. But the study of natural language suggests otherwise. (One can’t tell, in advance of investigation, which facts are peripheral to a given domain. It was initially tempting to think that one could ignore falling bodies, and the tides, if the aim was to explain why planets move as they do.). (shrink)

There is a prevalent view against the disquotational and the minimal theories of truth, that the most sensible solution to the Liar—that is, the gappy solution—is not available to them. I would like to argue that, though this solution is unavailable to the two theories, the prevailing argument and the reasoning behind this view are wrong. This paper mainly focuses on Simmons’ “Deflationary Truth and the Liar” (1999), within which the idea that disquotationalism can take the Liar in its stridein (...) terms of the gappy option is thoroughly criticised. Albeit Simmons’ account is about disquotationalism, it is in fact about truth theories with the disquotational feature. For Horwich’s minimal theory of truth to be feasible, it is in need of providing an account of which the primary truth bearers are utterances or sentences. The reasoning behind Simmons’ account and his argument is a widely accepted but in my opinion mistaken reading of deflationary theories, reading the deflationary axiom schemata as emphasising the redundant feature of the true predicate only. By analysing and criticising this reasoning the mistakes of this interpretation of the deflationary theories of truth are revealed. Simmons bases his argument on two premises: taking disquotational theory of truth asdefinitional theory and considering the main feature of the disquotational truth predicate as eliminability. In terms of the notion of parasitic liar, I will argue that Simmons fails to show the plausibility of one crucial premise of his argument—that is, the paradoxical or the pathological feature is missing from the disquotational mirrors of the Liar. I will further show what deflationary feature is misunderstood by those accounts similar to Simmons’. (shrink)

We give a simple proof-theoretic argument showing that Glivenko’s theorem for propositional logic and its version for predicate logic follow as an easy consequence of the deduction theorem, which also proves some Glivenko type theorems relating intermediate predicate logics between intuitionistic and classical logic. We consider two schemata, the double negation shift (DNS) and the one consisting of instances of the principle of excluded middle for sentences (REM). We prove that both schemata combined derive classical logic, while each (...) one of them provides a strictly weaker intermediate logic, and neither of them is derivable from the other. We show that over every intermediate logic there exists a maximal intermediate logic for which Glivenko’s theorem holds. We deduce as well a characterization of DNS, as the weakest (with respect to derivability) scheme that added to REM derives classical logic. (shrink)

We study the arithmetical schema asserting that every eventually decreasing elementary recursive function has a limit. Some other related principles are also formulated. We establish their relationship with restricted parameter-free induction schemata. We also prove that the same principle, formulated as an inference rule, provides an axiomatization of the Σ2-consequences of IΣ1.Using these results we show that ILM is the logic of Π1-conservativity of any reasonable extension of parameter-free Π1-induction schema. This result, however, cannot be much improved: by adapting (...) a theorem of D. Zambella and G. Mints we show that the logic of Π1-conservativity of primitive recursive arithmetic properly extends ILM.In the third part of the paper we give an ordinal classification of -consequences of the standard fragments of Peano arithmetic in terms of reflection principles. This is interesting in view of the general program of ordinal analysis of theories, which in the most standard cases classifies Π-classes of sentences. (shrink)

Dzhaparidze, G., A generalized notion of weak interpretability and the corresponding modal logic, Annals of Pure and Applied Logic 61 113-160. A tree Tr of theories T1,...,Tn is called tolerant, if there are consistent extensions T+1,...,T+n of T1,...,Tn, where each T+i interprets its successors in the tree Tr. We consider a propositional language with the following modal formation rule: if Tr is a tree of formulas, then Tr is a formula, and axiomatically define in this language the decidable logics TLR (...) and TLRω. It is proved that TLR yields exactly the schemata of PA-provable sentences, if Tr is understood as “Tr is tolerant”. In fact, TLR axiomatizes a considerable fragment of provability logic with quantifiers over ∑1-sentences, and many relations that have been studied in the literature can be expressed in terms of tolerance. We introduce and study two more relations between theories: cointerpretability and cotolerance which are, in a sense, dual to interpretability and tolerance. Cointerpretability is a characterization of ∑1-conservativity for essentially reflexive theories in terms of translations. (shrink)

The logical form of a discourse—such as a proposition, a set of propositions, an argument, or an argumentation—is obtained by abstracting from the subject-matter of its content terms or by regarding the content terms as mere place-holders or blanks in a form. In a logically perfect language the logical form of a proposition, a set of propositions, an argument, or an argumentation is determined by the grammatical form of the sentence, the set of sentences, the argument-text, or the argumentation-text (...) expressing it. Two such discourse-texts are said to have the same grammatical form, in this sense, if a uniform one-one substitution of content words transforms the one exactly into the other. The sentence ‘Abe properly respects every agent who respects himself’ may be regarded as having the same grammatical form as the sentence ‘Ben generously assists every patient who assists himself’. (shrink)

Formulas of the propositional modal language with the unary modal operators □, Σ1, 1, Σ2, 2,… are considered as schemata of sentences of arithmetic , where □A is interpreted as “A is PA-provable”, ΣnA as “A is PA-equivalent to a Σn-sentence” and nA as “A is PA-equivalent to a Boolean combination of Σn-sentences”. We give an axiomatization and show decidability of the sets of the modal formulas which are schemata of: PA-provable, true arithmetical sentences.

The response given to C.G. Hempel’s well-known challenge by Arthur Danto in his Analytical Philosophy of History of 1965 – that deductive-nomological and narrative explanations are logically compatible yet employ incommensurable schemata – is here investigated from a historical perspective. It is shown that the developmental trajectory that emerges from an analysis of Danto’s previous writings – including not only a forgotten paper of 1958 but also his PhD dissertation of 1952 – contains distinctive step-changes with publications of 1953 (...) and 1956 still prior to that of 1958–59 which enabled his subsequent discovery of narrative sentences. It is also argued that Danto’s developmental trajectory runs contrary to that presumed by some prominent commentators. Analytical History of Philosophy was not the midpoint of his ascent from mainstream philosopher of science to high priest of postmodern aesthetics, but represents a reasoned retreat from his early historical idealism. (shrink)

The popular expedient of identifying noncognitivism with the claim that moral judgments are neither true nor false leaves open the question of what kind of thing a moral judgment is—an indeterminacy that has led to decades of confusion as to what the noncognitivist is more precisely committed to. Sometimes noncognitivism is presented as a claim about mental states (“Moral judgments are not beliefs”), sometimes as a claim about meaning (“X is morally good” means no more than “X: hurray!”), sometimes as (...) a claim about speech acts (“Moral judgments are not assertions”). Focus on the last two possibilities. The former calls for a translation schema from a propositional surface grammar to a non-propositional deep structure. Such schemata from the noncognitivist are familiar to students of metaethics. (Cf. A.J. Ayer’s claim that in saying “You acted wrongly in stealing that money” one is “not saying anything more than … ‘You stole that money,’ [but] in a peculiar tone of horror.”) It is less widely realized that the noncognitivist is not obliged to offer any such translation schema, for she might instead plump for the last option, of formulating noncognitivism as a theory not of meaning but of use. Perhaps the moral cognitivist is correct about the meaning of moral sentences (there is a wide range of possibilities here) but wrong about the way people use moral sentences: perhaps people do not assert moral sentences, perhaps the nature of acceptance of a moral claim is not belief. (shrink)

A nonempty sequence T1,...,Tn of theories is tolerant, if there are consistent theories T 1 + ,..., T n + such that for each 1 i n, T i + is an extension of Ti in the same language and, if i n, T i + interprets T i+1 + . We consider a propositional language with the modality , the arity of which is not fixed, and axiomatically define in this language the decidable logics TOL and TOL. It is (...) shown that TOL (resp. TOL) yields exactly the schemata of PA-provable (resp. true) arithmetical sentences, if (A1,..., An) is understood as (a formalization of) PA+A1, ..., PA+An is tolerant. (shrink)

Kurt Gödel’s Incompleteness theorem is well known in Mathematics/Logic/Philosophy circles. Gödel was able to find a way for any given P (UTM), (read as, “P of UTM” for “Program of Universal Truth Machine”), actually to write down a complicated polynomial that has a solution iff (=if and only if), G is true, where G stands for a Gödel-sentence. So, if G’s truth is a necessary condition for the truth of a given polynomial, then P (UTM) has to answer first (...) that G is true in order to secure the truth of the said polynomial. But, interestingly, P (UTM) could never answer that G was true. This necessarily implies that there is at least one truth a P (UTM), however large it may be, cannot speak out. Daya Krishna and Karl Potter’s controversy regarding the construal of India’s Philosophies dates back to the time of Potter’s publication of “Presuppositions of India’s Philosophies” (1963, Englewood Cliffs Prentice-Hall Inc.) In attacking many of India’s philosophies, Daya Krishna appears to have unwittingly touched a crucial point: how can there be the knowledge of a ‘non-cognitive’ mokṣa? [‘mokṣa’ is the final state of existence of an individual away from Social Contract]—See this author’s Indian Social Contract and its Dissolution (2008) mokṣa does not permit the knowledge of one’s own self in the ordinary way with threefold distinction, i.e., subject–knowledge-object or knower–knowledge–known. But what is important is to demonstrate whether such ‘knowledge’ of non-cognitive mokṣa state can be logically shown, in a language, to be possible to attain, and that there is no contradiction involved in such demonstration, because, no one can possibly express the ‘experience-itself’ in language. Hence, if such ‘knowledge’ can be shown to be logically not impossible in language, then, not only Daya Krishna’s arguments against ‘non-cognitive mokṣa’ get refuted but also it would show the possibility of achieving ‘completeness’ in its truest sense, as opposed to Gödel’s ‘Incompleteness’. In such circumstances, man would himself become a Universal Truth Machine. This is because the final state of mokṣa is construed as the state of complete knowledge in Advaita. This possibility of ‘completeness’ is set in this paper in the backdrop of Śrī Śaṅkarācārya’s Advaitic (Non-dualistic) claim involved in the mahāvākyas (extra-ordinary propositions). (Mahāvākyas that Śaṅkara refers to are basically taken from different Upaniṣads. For example, “Aham Brahmāsmi” is from Bṛhadāraṇyaka Upanisad, and “Tattvamasi” is from Chāndogya Upaniṣad. Śrī Śaṅkarācārya has written extensively. His main works include his Commentary on Brahma-Sūtras, on major Upaniṣads, and on ŚrīmadBhagavadGītā, called Bhāṣyas of them, respectively. Almost all these works are available in English translation published by Advaita Ashrama, 5 Dehi Entally Road, Calcutta, 700014.) On the other hand, the ‘Incompleteness’ of Gödel is due to the intervening G-sentence, which has an adverse self-referential element. Gödel’s incompleteness theorem in its mathematical form with an elaborate introduction by R.W. Braithwaite can be found in Meltzer (Kurt Gödel: on formally undecidable propositions of principia mathematica and related systems. Oliver & Boyd, Edinburgh, 1962). The present author believes first that semantic content cannot be substituted by any amount of arithmoquining, (Arithmoquining or arithmatization means, as Braithwaite says,—“Gödel’s novel metamathematical method is that of attaching numbers to the signs, to the series of signs (formulae) and to the series of series of signs (“proof-schemata”) which occur in his formal system…Gödel invented what might be called co-ordinate metamathematics…”) Meltzer (1962 p. 7). In Antone (2006) it is said “The problem is that he (Gödel) tries to replace an abstract version of the number (which can exist) with the concept of a real number version of that abstract notion. We can state the abstraction of what the number needs to be, [the arithmoquining of a number cannot be a proof-pair and an arithmoquine] but that is a concept that cannot be turned into a specific number, because by definition no such number can exist.”.), especially so where first-hand personal experience is called for. Therefore, what ultimately rules is the semanticity as in a first-hand experience. Similar points are voiced, albeit implicitly, in Antone (Who understands Gödel’s incompleteness theorem, 2006). (“…it is so important to understand that Gödel’s theorem only is true with respect to formal systems—which is the exact opposite of the analogous UTM (Antone (2006) webpage 2. And galatomic says in the same discussion chain that “saying” that it ((is)) only true for formal systems is more significant… We only know the world through “formal” categories of understanding… If the world as it is in itself has no incompleteness problem, which I am sure is true, it does not mean much, because that is not the world of time and space that we experience. So it is more significant that formal systems are incomplete than the inexperiencable ‘World in Itself’ has no such problem.—galatomic”) Antone (2006) webpage 2. Nevertheless galatomic certainly, but unwittingly succeeds in highlighting the possibility of experiencing the ‘completeness’ Second, even if any formal system including the system of Advaita of Śaṅkara is to be subsumed or interpreted under Gödel’s theorem, or Tarski’s semantic unprovability theses, the ultimate appeal would lie to the point of human involvement in realizing completeness since any formal system is ‘Incomplete’ always by its very nature as ‘objectual’, and fails to comprehend the ‘subject’ within its fold. (shrink)

We aim at developing a systematic method of separating omniscience principles by constructing Kripke models for intuitionistic predicate logic $\mathbf {IQC}$ and first-order arithmetic $\mathbf {HA}$ from a Kripke model for intuitionistic propositional logic $\mathbf {IPC}$. To this end, we introduce the notion of an extended frame, and show that each IPC-Kripke model generates an extended frame. By using the extended frame generated by an IPC-Kripke model, we give a separation theorem of a schema from a set of schemata (...) in $\mathbf {IQC}$ and a separation theorem of a sentence from a set of schemata in $\mathbf {HA}$. We see several examples which give us separations among omniscience principles. (shrink)

In Knowledge and Belief Jaakko Hintikka presents a fairly detailed system of epistemic logic and tries to show its philosophical importance by bringing it to bear upon such problems as what goes wrong in saying “It’s raining, but I don’t believe it.” In setting up the system, Hintikka presents a way of symbolizing certain locutions containing expressions like ‘knows that’, ‘know who’, and ‘believes that’; he introduces certain notions which are analogous to the standard logical concepts consistency, validity, entailment, and (...) logical equivalence; and he sets up certain criteria which determine when these analogues of consistency, validity, etc. apply to epistemic and doxastic sentences and schemata-i.e., to sentences and schemata which contain, in their symbolic renditions, one or more of the so-called epistemic operators: ‘K’, ‘B’, ‘P’, and ‘C’. The analogue of logical consistency which Hintikka introduces is called “defensibility.” Intuitively, a sentence is defensible provided that it is true in at least one of the “most knowledgeable of possible worlds” -i.e., provided it is true in at least one of the possible worlds which have the feature that each inhabitant which is capable of knowing and/or believing things knows all the logical consequences of every proposition it knows and believes all the logical consequences of every proposition it believes. The remaining notions are defined by reference to defensibility in just the way validity, entailment, and logical equivalence are often defined by reference to consistency. Thus self-sustenance, the epistemic analogue of validity, is defined thus. (shrink)

For his contribution to the general series of Harper Essays in Philosophy, Hilary Putnam selects only one of several philosophical problems in the interrelated fields of logic and/or mathematics that have interested him, viz. the nominalism-realism issue: Are the "abstract entities" spoken of in these sciences, such as classes, number, functions from various kinds of things to real numbers, things that "really exist" or not? He is concerned to present a detailed argument for his own "qualified realism" rather than a (...) survey of current opinions. He argues persuasively that while a nominalist would like to eliminate all talk of logical classes such as S, M and P in favor of such circumlocutions as "The following schema turns out to be true no matter what words or phrases of the appropriate kind one may substitute for the letters S, M and P," etc., such descriptions avoid references to classes only by replacing them with equally nonphysical entities such as "all possible words, strings of letters, formalized languages," etc., and that the notion of truth or validity itself cannot be applied to physical objects or material inscriptions, but to what sentences mean or say, and the things they say are not physical. He rejects Quine's distinction that first order statements or arguments such as "All crows are black; all back things absorb light, therefore," etc., are logical truths, whereas "For all classes S, M and P, if all S is M and all M is P, then all S is P," are mathematical. This runs counter, he says, to the whole logical tradition. The natural intention of the logician in setting down first-order schemata is to assert implicitly their validity and that itself is a second-order assertion. All logic, therefore, including quantification theory, involves references to classes. This also highlights the difficulty of distinguishing between logic and mathematics in terms of first and second order logic, for if only the former is stipulated to be the proper domain of logic, then we must accept the awkward consequence that validity and implication turn out to be notions that belong to mathematics rather than logic. Since the nominalistic position presents the same problems for mathematics as for logic, Putnam sees no point in trying to draw any sharp distinction between the two, which explains his initial broad interpretation of logic as including all of pure mathematics and also the title of the book. To avoid some of the classical objections to a realistic interpretation of sets, he points up the distinction between a predicative and impredicative conception of set. Whereas the latter speaks of all sets of individuals as a well-defined totality, the former defines "set" only for a particular language N or a hierarchic series of languages, N, N', N", etc. in which it is still nonsensical to speak of "all sets" without qualification, though one can speak of "all" up to any given level in the series. While some form of set theory is necessary for all the sciences, both formal and physical, one can get along with predicative set theory. Putnam's basic argument for realism then comes down to this. Quantification over mathematical entities such as things, real numbers and functions is indispensable for logic, mathematics and the physical sciences and this commits one to accept the existence of such entities. In the final stages of the argument he examines and rejects the alternative options to realism, namely that realistic locutions about such entities represent logically deviant forms of speech, or that mathematical truths are "true by pure convention" or that such "entities" are useful fictions. In the closing paragraphs he indicates two other philosophical problems in logic that merit extensive discussion, namely the problem of equivalent constructions which is relevant to the question of whether mathematics needs "foundations" and the problem of whether we may not have to revise logical principles as we have geometrical ones on the grounds that in some sense logic may have empirical foundations.--A. B. W. (shrink)

The notion of schema has been given a major role by Recanati within his conception of primary pragmatic processes, conceived as a type of associative process. I intend to show that Recanati’s considerations on schemata may challenge the relevance theorist’s argument against associative explanations in pragmatics, and support an argument in favor of associative (versus inferential) explanations. More generally, associative relations can be shown to be schematic, that is, they have enough structure to license inferential effects without any appeal (...) to genuine inferential processes. Associative processes are thus able to explain a number of pragmatic and linguistic phenomena which have instead been thought to require specialized inferential processes. (shrink)

This new book integrates material drawn from a variety of sources – feminist theory, cultural and literary analysis, sociology and art history – in an original discussion of women′s relationship to modern and post–modern culture. The essays in the book challenge the continuing separation of sociological from textual analysis in cultural (and feminist) theory and enquiry. They address critically the question of women′s writing, exploring the idea that women may begin to define their own lives and construct their identities in (...) a patriarchal culture through the very process of writing. They also present a cogent defence of a feminist cultural politics, including a politics of the body. (shrink)

Kant posits the schema as a hybrid bridging the generality of pure concepts and the particularity of sensible intuitions. However, I argue that countenancing such schemata leads to a third-man regress. Siding with those who think that the mid-way posit of the Critique of Pure Reason's schematism section is untenable, my diagnosis is that Kant's transcendental inquiry goes awry because it attempts to analyse a form/matter union that is primitive. I therefore sketch a nonrepresentational stance aimed at respecting this (...) primitivity. (shrink)

In this essay, we defend the design of the Salk polio vaccine trial and try to put some limits on the role schemata should play in designing clinical research studies. Our presentation is structured as a response to de Freitas and Pietrobon who identified the CONSORT statement as a schema that would have, had it existed at the time, ruled out the design of the Salk polio vaccine trial of 1954 in favor of a completely randomized controlled clinical trial. (...) We argue that large-scale public health interventions often require evidence beyond simple efficacy, the limit of what an RCT can provide, and that the design actually adopted for the Salk trial represented a reasonable—albeit imperfect—compromise. This is of more than historical interest in that many contemporary studies are of the scale and scope to require a more pragmatic, rather than explanatory, approach to study design. (shrink)

This article critically studies coronavirus pandemic news in the press. The article attempts to study the way the news of COVID-19 is used for political and ideological purposes. In order to achieve the aim, two newspapers namely, The New York Times from the United States of America and Global Times from China are selected. Van Dijk’s news schemata framework is used for the analysis of the reports selected from the two newspapers. Van Dijk’s news schemata is crucial for (...) the analysis of any news story whether such a news story is taken from a news channel or a newspaper and whether broadcasted or printed. Based on data analysis, the article found out that the news of COVID-19 has been politicized and used for ideological interests. The article recommends that pandemics should not be politicized, instead we should work together to save our lives and live peacefully. (shrink)

:This essay investigates the relationships among scripts, schemata, and social norms. The authors examine how social norms are triggered by particular schemata and are grounded in scripts. Just as schemata are embedded in a network, so too are social norms, and they can be primed through spreading activation. Moreover, the expectations that allow a social norm’s existence are inherently grounded in particular scripts and schemata. Using interventions that have targeted gender norms, open defecation, female genital cutting, (...) and other collective issues as examples, the authors argue that ignoring the cognitive underpinnings of a social norm can hamper the effectiveness of behavioral interventions. (shrink)

This article deals with frames and schemata in news reporting. It distinguishes frames and schemata in newsroom discourse and news reports. On the individual cognitive level, a frame is defined as a set of schemata for different aspects of reality. They emerge in newsroom discourse and in exchange with other discourses, i. e., they are not idiosyncratic but shared among those working in a newsroom. It is supposed that news report structures correspond to these newsroom frames and (...) schemata. The article discusses these considerations in regard to related explanations of news production, especially attitudinal approaches such as news bias. While the latter assume that journalists prefer information consistent with their own attitudes or that news reporting is ‘synchronized’ with editorial tendencies, the framing approach proposes that information in routine news reports correspond to newsroom frames. In this study I will use xenophobia as an example to identify newsroom frames in a qualitative frame analysis. In the second part of the study, quantitative analysis of news framing examines whether news report information correlates with newsroom frames. Finally, I will present empirical evidence that shows that newsroom frames play a role in news reporting. (shrink)

The schema, or theoretical framework, holism, is concerned with the essence of society as a whole. Though undermined by Popper, it cannot be refuted ? nor proved. The extreme alternative is individualism. Several forms, due to Freud, Wittgenstein, and phenomenology, make presuppositions that require the individualist interpretation of society to be reopened at a new point. Popper's ? or Weber's ? is the sturdiest; its units being individual actions plus their unintended by?products. The Weber?Popper schema can provide a framework for (...) many satisfactory societal explanations. But individualism misses the holistic possibility of dynamic societal forces; the individualist fails to produce any dynamic laws. A dynamic bipolar schema could put both schemata to work without prescribing which would predominate. Empirical investigation would determine the more fruitful for a given problem. This schema would be ?justified? by fostering a satisfactory empirical social theory. The present investigation also reveals where the real controversies about schemata lie. (shrink)

Some twenty different background approaches, or schemata, permeate the social sciences. Most of their exponents regard their choice as excluding the rest. This paper is concerned to show that all such conflict is merely disputatious since virtually all the schemata require one another. Taking the individual's need to act as starting-point, certain restrictions limiting his freedom of action are identified as factors of the overt societal situation. These, however, fail to explain all aspects of his powerlessness, to account (...) for which he then seeks such deeper constraints as unseen powers or human conspiracies. Social scientists for their part develop theories or interpretations of the societal situation. The paper turns to the first of three groups of interpretations, concentrating on one constituent of the group, functionalism, which is a mirror-image of another constituent, 'conflict theory'. The complementarity of these two is claimed to apply to virtually all the schemata considered. (The second and third groups are deferred to the sequel.) The Appendix deals with the way in which explanatory factors can be combined. Having removed the unreal contentions associated with various schemata, the way is clear to treatment of the one substantive issue among them - to do with holism - in the sequel. (shrink)