In _Truth and Objectivity_, Crispin Wright argues that the notion of superassertibility affords the antirealist (with respect to a given range of discourse) a viable alternative to the realist’s more robust notion of truth. Toward this end, he endeavors to prove that a superassertibility predicate can satisfy the traditional equivalence schema: it is true that P iff P. (Wright takes satisfaction of this schema to be a criterion of adequacy for any viable truth predicate.) In this paper, (...) I will argue that, not only does Wright’s attempt to prove that a superassertibility predicate satisfies the equivalence schema fail, an examination of its failure reveals a dilemma for the antirealist who would adopt superassertibility as a model of truth. (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 .

Theoretical equivalence and duality are two closely related notions: but their interconnection has so far not been well understood. In this paper I explicate the contribution of a recent schema for duality to discussions of theoretical equivalence. I argue that duality suggests a construal of theoretical equivalence in the physical sciences. The construal is in terms of the isomorphism of models, as defined by the schema. This construal gives interpretative constraints that should be useful for (...) discussions of theoretical equivalence more generally. I illustrate the construal in various formulations of Maxwell’s electromagnetic theory. (shrink)

A direct equivalence between neural function and neural structure does not provide a fruitful approach to understanding brain functioning. Arbib et al. describe a new and powerful approach to circumvent this problem, which they call schema theory. However, in examples they fall prey to the tradition of finding such equivalences, not doing schema theory justice.

Answering a question formulated by Halbach (2009), I show that a disquotational truth theory, which takes as axioms all positive substitutions of the sentential T-schema, together with all instances of induction in the language with the truth predicate, is conservative over its syntactical base.

The main result of this paper is the equivalence of several definition schemas of bar recursion occurring in the literature on functionals of finite type. We present the theory of functionals of finite type, in [T] denoted byqf-WE-HA ω, which is necessary for giving the equivalence proofs. Moreover we prove two results on this theory that cannot be found in the literature, namely the deduction theorem and a derivation of Spector's rule of extensionality from [S]: ifP→T 1=T 2 (...) and Q[X∶≡T1], then P→Q[X∶≡ T2], from the at first sight weaker rule obtained by omitting “P→”. (shrink)

A form of Kripke's schema turns out to be equivalent to each of the following two statements from metric topology: every open subspace of a separable metric space is separable; every open subset of a separable metric space is a countable union of open balls. Thus Kripke's schema serves as a point of reference for classifying theorems of classical mathematics within Bishop-style constructive reverse mathematics.

We study the fragment of Peano arithmetic formalizing the induction principle for the class of decidable predicates, $I\Delta_1$ . We show that $I\Delta_1$ is independent from the set of all true arithmetical $\Pi_2-sentences$ . Moreover, we establish the connections between this theory and some classes of oracle computable functions with restrictions on the allowed number of queries. We also obtain some conservation and independence results for parameter free and inference rule forms of $\Delta_1-induction$ . An open problem formulated by J. (...) Paris is whether $I\Delta_1$ proves the corresponding least element principle for decidable predicates, $L\Delta_1$ (or, equivalently. the $\Sigma_1-collection$ principle $B\Sigma_1$ ). We reduce this question to a purely computation-theoretic one. (shrink)

Grush's emulator model appears to be consistent with the idea of a body schema, that is, a detailed mental representation of the body, its structure, and movement in relation to the environment. If the emulator is equivalent to a body schema, then the next step will be to specify how the emulator accounts for neuropsychological and developmental phenomena that have long been hypothesized to involve the body schema.

This paper considers the existence of finite equational axiomatisations of behavioural equivalences over a calculus of finite state processes. To express even simple properties such as μxE = μxE[E/x] some notation for substitutions is required. Accordingly, the calculus is embedded in a simply typed lambda calculus, allowing such schemas to be expressed as equations between terms containing first order variables. A notion of first order trace congruence over such terms is introduced and used to show that no finite set of (...) such equations is sound and complete for any reasonable equivalence finer than trace equivalence. The intermediate results are then applied to give two nonaxiomatisability results over calculi of regular expressions. (shrink)

The minimalist view of truth endorsed by Paul Horwich denies that truth has any underlying nature. According to minimalism, the truth predicate ‘exists solely for the sake of a certain logical need’; ‘the function of the truth predicate is to enable the explicit formulation of schematic generalizations’. Horwich proposes that all there really is to truth follows from the equivalence schema: The proposition that p is true iff p, or, using Horwich’s notation, ·pÒ is true ´ p. The (...) (unproblematic) instances of the schema form ‘the minimal theory of truth’. Horwich claims that all the facts involving truth can be explained on the basis of the minimal theory. However, it has been pointed out, e.g. by Gupta (1993), that the minimal theory is too weak to entail any general facts about truth, e.g. the fact that.. (shrink)

The dispute between the Fregean and the Neo-Meinongian approach to existence has become entrenched: it seems that nothing but intuitions may be relied upon to decide the issue. And since contemporary analytic philosophers clearly are inclined towards the intuitions that support Frege's approach, it looks as if Fregeanism has won the day. In this paper, however, I try to develop a compromise solution. This compromise consists in abandoning the assumption shared by both Fregeanism and Neo-Meinongianism, namely that the notion of (...) existence adds something to the content of a statement. To the contrary, we should think of existence as a redundant notion. In other words, I will argue that we should be deflationist about existence. Moreover, the kind of deflationism I propose relies on what I call the existence equivalence schema, a schema which follows the blueprint of the well-known truth equivalence schema. From such a perspective, we can say that Fregean philosophers rightly deny the status of a discriminating property to existence; and, conversely, Neo-Meinongians, too, rightly reject the view that existence is captured by quantification or expresses a universal property of objects. Finally, the argument that we should take a deflationist approach to existence builds upon an analysis of natural language (general) existential statements and their intuitive entailment-relations. (shrink)

Availing ourselves of the previously introduced notion of a statementvariable, we can express Aristotle's point even more simply. We can say that, where the letter "P" stands for any statement whatever, the concept of truth is captured by the following schematic statement (we'll call it "Equivalence Schema" or "E" for short) of the necessary and sufficient conditions for a statement's being true: E: It is true that P iff P.2..

There are many variants of deflationism about truth, but one of them, Paul Horwich’s minimalism, stands out because it accepts as axiomatic practical variants of the equivalence schema: 〈p〉 is true if and only if p. The equivalence schema is epistemologically fundamental. In this paper, I call upon empirical studies to show that practical variants of the equivalence schema are widely accepted by non-philosophers. While in the empirical data there is variation in how non-philosophers (...) and philosophers talk about truth and how they judge that a proposition is true, a significant amount of data collected over the years reveal that the ordinary or folk view of truth is compatible with the epistemological fundamentality of alethic minimalism. This, I take it, suggests that people share in the same intuitions that form the bedrock of Horwich’s minimalism. (shrink)

Our main aim in this paper is to contribute towards a better understanding of the epistemology of absence-based inferences. Many absence-based inferences are classified as fallacies. There are exceptions, however. We investigate what features make absence-based inferences epistemically good or reliable. In Section 2 we present Sanford Goldberg’s account of the reliability of absence-based inference, introducing the central notion of epistemic coverage. In Section 3 we approach the idea of epistemic coverage through a comparison of alethic and evidential principles. The (...) Equivalence Schema–a well-known alethic principle–says that it is true that $p$ if and only if $p$ . We take epistemic coverage to underwrite a suitably qualified evidential analogue of the Equivalence Schema: for a high proportion of values of $p$ , subject $S$ has evidence that $p$ due to her reliance on source $S^{*}$ if and only if $p$ . We show how this evidential version of the Equivalence Schema suffices for the reliability of certain absence-based inferences. Section 4 is dedicated to exploring consequences of the Evidential Equivalence Schema. The slogan ‘absence of evidence is evidence of absence’ has received a lot of bad press. More elaborately, what has received a lot of bad press is something like the following idea: absence of evidence sufficiently good to justify belief in $p$ is evidence sufficiently good to justify belief in $\sim p$ . A striking consequence of the Evidential Equivalence Schema is that absence of evidence sufficiently good to justify belief in p is evidence sufficiently good to justify belief in $\sim p$ . We establish this claim in Section 4 and show how this supports the reliability of an additional type of absence-based inference. Section 4 immediately raises the following question: how can we make philosophically good sense of the idea that absence of evidence is evidence of absence? We address this question in Section 5. Section 6 contains some summary remarks. (shrink)

It seems that no philosopher these days wants a theory of truth which can be accused of being metaphysical. But even if we agree that grandiose metaphysics is to be spurned, even if we agree that our theory of truth should be a deflated one, the controversy does not die down. A variety of deflationist options present themselves. Some, with Richard Rorty, take the notion of truth to be so wedded to metaphysics that we are advised to drop it altogether. (...) Others, with Paul Horwich, take the disquotational or equivalence schema—'p' is T if and only if p—to completely capture the content of the predicate 'is true'. And others argue that there is a conception of truth to be had which is non-metaphysical but which goes beyond the triviality expressed by the disquotational schema. (shrink)

The aim of this paper is to connect the current debate on relative truth to the discussions of theories of truth in general, in which the so-called platitudes about truth have recently played a prominent role. Truth-relativists propose adding to the standard truth predicate an argument-place for an extra parameter over and above a possible world and they presume that the predicate that results from this relativization is a truth predicate. Yet this relativization arguably isn't just an innocuous extrapolation of (...) the Lewis-Kaplan line in semantics that naturally conserves the predicate's status as a truth predicate. This status has to be specifically established. I'll discuss arguments to the effect that truth-relativists fail on that score since relative truth doesn't satisfy certain basic platitudes about truth, in particular the Equivalence Schema and the normativity of truth. This suggests that a relativized truth predicate cannot play the role required of a truth predicate. I shall discuss the relativist's defensive strategies in detail, the most promising of which is to claim that it is legitimate to deny the Equivalence Schema by arguing that relativism introduces a revisionary concept of truth and so fundamentally revises semantics. However, I'll point out that solely invoking semantic revision doesn't suffice to justify a denial of the Equivalence Schema and that any further justification of such a denial is ad hoc or question begging. Moreover, I suggest that with respect to the normativity of truth the prospects of truth-relativism are equally dim. (shrink)

Semantic paradoxes like the liar are notorious challenges to truth theories. A paradox can be phrased with minimal resources and minimal assumptions. It is not surprising, then, that the liar is also a challenge to minimalism about truth. Horwich (1990) deals swiftly with the paradox, after discriminating between other strategies for avoiding it without compromising minimalism. He dismisses the denial of classical logic, the denial that the concept of truth can coherently be applied to propositions, and the denial that the (...) liar sentence expresses a proposition, but he endorses the denial that the liar is an acceptable instance of the equivalence schema (E). This paper has two main parts. It first shows that Horwich’s preferred denial is also problematic. As Simmons (1999), Beall and Armour-Garb (2003), and Asay (2015) argued, the solution is ad hoc, faces a possible loss of expressibility, and is ultimately unstable. Finally, the paper explores a different combination of possibilities for minimalism: treating the truth-predicate as context-dependent, rejecting the notion that the liar expresses a proposition, and reinterpreting negation in some contexts as metalinguistic denial. The paper argues that these are preferable options, but signposts possible dangers ahead. (shrink)

It seems that no philosopher these days wants a theory of truth which can be accused of being metaphysical. But even if we agree that grandiose metaphysics is to be spurned, even if we agree that our theory of truth should be a deflated one, the controversy does not die down. A variety of deflationist options present themselves. Some, with Richard Rorty, take the notion of truth to be so wedded to metaphysics that we are advised to drop it altogether. (...) Others, with Paul Horwich, take the disquotational or equivalence schema—'p' is T if and only if p—to completely capture the content of the predicate 'is true'. And others argue that there is a conception of truth to be had which is non-metaphysical but which goes beyond the triviality expressed by the disquotational schema. (shrink)

This article develops a fresh approach to Jørgensen's Dilemma on the basis of Paul Horwich's “minimalist” view that our notion of truth is implicitly defined by the instances of the equivalence schema “The proposition that p is true if and only if p.” The “deflationary” claim that the truth predicate, far from referring to any deep property of propositions, merely plays the logical function of enabling us to take certain attitudes (e.g., acceptance or rejection) towards propositions the content (...) of which we are not completely acquainted with or do not want to state openly is argued to lend powerful support to the claim that normative reasoning is concerned with the “transmission” of truth and falsity in the very sense in which descriptive reasoning is commonly taken to be. This result is all the more valuable since the “minimal” sense in which normative propositions are ascribed the capability of being either true or false involves no questionable ontological commitment to the existence of a “world of norms” as opposed to the familiar world of objects and their properties. (shrink)

This paper outlines an account of numbers based on the numerical equivalence schema, which consists of all sentences of the form ‘#x.Fx=n if and only if ∃nx Fx’, where # is the number-of operator and ∃n is defined in standard Russellian fashion. In the first part of the paper, I point out some analogies between the NES and the T-schema for truth. In light of these analogies, I formulate a minimalist account of numbers, based on the NES, (...) which strongly parallels the minimalist account of truth. One may be tempted to develop the minimalist account in a fictionalist direction, according to which arithmetic is useful but untrue, if taken at face value. In the second part, I argue that this suggestion is not as attractive as it may first appear. The NES suffers from a similar problem to the T-schema: it is deductively weak and does not enable the derivation of any non-trivial generalizations. In the third part of the paper, I explore some strategies to deal with the generalization problem, again drawing inspiration from the literature on truth. In closing this paper, I briefly compare the minimalist to some other accounts of numbers. (shrink)

Künne outlines Bolzano’s attempt to give a definition of the concept of truth and asks whether Frege succeeded in showing that all such endeavours are doomed to failure. Bolzano and Frege are agreed that the schema ‘That p is true if, and only if, p’ captures an important feature of the concept of truth, and in different ways both went beyond this observation: Frege maintained that the two halves of such biconditionals express the same proposition, and Bolzano supplemented the (...) equivalence schema with ‘If it is true that p then it is true because p’. Künne locates this true-because principle in Bolzano’s general theory of grounding and explores whether Frege’s Identity Thesis can be refuted by appealing to it. (shrink)

This paper outlines an account of numbers based on the numerical equivalence schema (NES), which consists of all sentences of the form ‘#x.Fx=n if and only if ∃nx Fx’, where # is the number-of operator and ∃n is defined in standard Russellian fashion. In the first part of the paper, I point out some analogies between the NES and the T-schema for truth. In light of these analogies, I formulate a minimalist account of numbers, based on the (...) NES, which strongly parallels the minimalist (deflationary) account of truth. One may be tempted to develop the minimalist account in a fictionalist direction, according to which arithmetic is useful but untrue, if taken at face value. In the second part, I argue that this suggestion is not as attractive as it may first appear. The NES suffers from a similar problem to the T-schema: it is deductively weak and does not enable the derivation of any non-trivial generalizations. In the third part of the paper, I explore some strategies to deal with the generalization problem, again drawing inspiration from the literature on truth. In closing this paper, I briefly compare the minimalist to some other accounts of numbers. (shrink)

Deflationism is usually thought to differ from the correspondence theory over whether truth is a substantial property. However, I argue that this notion of a ‘substantial property’ is tendentious. I further argue that the Equivalence Schema alone is sufficient to lead to idealism when combined with a pragmatist theory of truth. Deflationism thus has more powerful metaphysical implications than is generally thought and itself amounts to a kind of correspondence theory.

A line of argument, presented by David Lewis, to show that the correspondence theory of truth is not a real alternative to deflationism is developed. It is shown that truthmakers, construed as concrete events or states of affairs, are unsatisfactory entities, since we do not know how to individuate them or how to identify their essential qualities. Furthermore, the real work is usually done by supervenience relations, which have little to do with truth. It is argued that the Equivalence (...) Schema is quite sufficient to yield a unitary property of being true, and that this generates a weak, but non-trivial, version of the correspondence theory of truth. (shrink)

According to Wrights minimalism, a notion of truth neutral with respect to realism and antirealism can be built out of the notion of warranted assertibility and a set of a priori platitudes among which the Equivalence Schema has a prominent role. Wright believes that the debate about realism and antirealism will be properly and fruitfully developed if both parties accept the conceptual framework of minimalism. In this paper, I show that this conceptual framework commits the minimalist to the (...) realist thesis that there are mind-independent propositions; with the consequence that minimalism is not neutral to realism and antirealism. I suggest that Wright could avert this conclusion if he rejected the customary interpretation of the Equivalence Schema according to which this Schema applies to propositions. This would however render minimalism unpalatable to philosophers who welcome the traditional reading of the Equivalence Schema and believe that propositions are bearers of truth. (shrink)

Much has been written of late concerning the relative virtues and views of correspondence and deflationary theories of Truth. What is troubling, however, is that it is not always entirely clear exactly what distinguishes different conceptions of truth. Characterizations of the distinction are often vague and sometimes vary from writer to writer. One central thing I want to do here is to diagnose the source of the difficulty in providing a clear characterization of the distinction. In light of this diagnosis, (...) I will argue that there is a simple distinguishing feature of such views. Roughly, the distinction depends on the modal status accorded to the T-sentences by the various conceptions. And finally, I will argue in favor of drawing the distinction in this way by showing that it yields a powerful method of arguing for or against a given conception of truth. (shrink)

Minimalists about truth contend that traditional inflationary theories systematically fail to explain certain facts about truth, and that this failure licenses a ‘reversal of explanatory direction’. Once reversed, they purport that their own minimal theory adequately explains all of the facts involving truth. But minimalists’ main objection to inflationism seems to misfire, and the subsequent reversal of explanatory direction, if it can be made sense of, leaves minimalism in no better explanatory position; and even if the objection were serviceable and (...) the reversal legitimate, minimalists’ adequacy thesis is still implausible. (shrink)

These two books contain a detailed presentation and sustained defense of a philosophical position which Horwich proposes to call “semantic deflationism”. The position consists of an interesting combination of two ideas: truth is metaphysically trivial, and the content of the truth predicate is fully captured by a platitudinous equivalence schema; and the meaning of a word is constituted by the basic regularities of its use.

The objective of the present study was to show that the use of adversative and conclusive connectives to mark off the prototypical schema of argumentative text begins to set in at approximately the age of 10 or 11. Based on Adam's (1992) proposals, we constituted an argumentative text with two blocks of arguments separated by an adversative instruction (the connective but or an equivalent) and followed by a conclusion introduced by a conclusive instruction (the connective thus or an equivalent). (...) Four revising tasks (insertion or substitution with or without five connectives) have been used to asses children's knowledge of the argumentative schema and the use of connectives that punctuate them. The study of good and erroneous locations (concerning the placement of but and thus) showed that there was some regularity in the choices made by the children. The main result of this study shows that argumentative connectives are used differently by children aged 9 and children aged 10 or 11. The argumentative schema is used more consciously by 11-year-olds to guide revising tasks than by 10-year-olds. (shrink)

A notable early result of David Makinson establishes that every monotone modal logic can be extended to LI, LV, or LF, and every antitone logic can be extended to LN, LV, or LF, where LI, LN, LV, and LF are logics axiomatized, respectively, by the schemas □α↔α, □α↔¬α, □α↔⊤, and □α↔⊥. We investigate logics that are both monotone and antitone (hereafter amphitone). There are exactly three: LV, LF, and the minimum amphitone logic AM axiomatized by the schema □α→□β. These (...) logics, along with LI, LN, and a wider class of “extensional” logics, bear close affinities to classical propositional logic. Characterizing those affinities reveals differences among several accounts of equivalence between logics. Some results about amphitone logics do not carry over when logics are construed as consequence or generalized (“multiple-conclusion”) consequence relations on languages that may lack some or all of the nonmodal connectives. We close by discussing these divergences and conditions under which our results do carry over. (shrink)

I conceptualise the role of dualities in quantum gravity, in terms of their functions for theory construction. I distinguish between two functions of duality in physical practice: namely, discovering and describing ‘equivalent physics’, versus suggesting ‘new physics’. I dub these the ‘theoretical’ versus the ‘heuristic’ functions of dualities. The distinction seems to have gone largely unnoticed in the philosophical literature: and it exists both for dualities, and for the more general relation of theoretical equivalence. The paper develops the heuristic (...) function of dualities: illustrating how they can be used, if one has any luck, to find and formulate new theories. I also point to the different physical commitments about the theories in question that underlie these two functions. I show how a recently developed schema for dualities articulates the differences between the two functions. (shrink)

I conceptualise the role of dualities in quantum gravity, in terms of their functions for theory construction. I distinguish between two functions of duality in physical practice: namely, discovering and describing ‘equivalent physics’, versus suggesting ‘new physics’. I dub these the ‘theoretical’ versus the ‘heuristic’ functions of dualities. The distinction seems to have gone largely unnoticed in the philosophical literature: and it exists both for dualities, and for the more general relation of theoretical equivalence. The paper develops the heuristic (...) function of dualities: illustrating how they can be used, if one has any luck, to find and formulate new theories. I also point to the different physical commitments about the theories in question that underlie these two functions. I show how a recently developed schema for dualities articulates the differences between the two functions. (shrink)

This paper concerns how motor actions are neurally represented and coded. Action planning and motor preparation can be studied using a specific type of representational activity, motor imagery. A close functional equivalence between motor imagery and motor preparation is suggested by the positive effects of imagining movements on motor learning, the similarity between the neural structures involved, and the similar physiological correlates observed in both imaging and preparing. The content of motor representations can be inferred from motor images at (...) a macroscopic level, based on global aspects of the action and the motor rules and constraints which predict the spatial path and kinematics of movements. A more microscopic neural account calls for a representation of object-oriented action. Object attributes are processed in different neural pathways depending on the kind of task the subject is performing. During object-oriented action, a pragmatic representation is activated in which object affordances are transformed into specific motor schemas. Animal as well as human clinical data implicate the posterior parietal and premotor cortical areas in schema instantiation. A mechanism is proposed that is able to encode the desired goal of the action and is applicable to different levels of representational organization. (shrink)

The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema “True(A)↔A”, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in “ordinary” contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) (...) with A within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are “defective”. We can in fact define a hierarchy of “defectiveness” predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (“revenge problems”) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various “levels of defectiveness” can all be made coherent together within a single object language. (shrink)

A well-known result states that, over basic Kalmar elementary arithmetic EA, the induction schema for ∑n formulas is equivalent to the uniform reflection principle for ∑n + 1 formulas . We show that fragments of arithmetic axiomatized by various forms of induction rules admit a precise axiomatization in terms of reflection principles as well. Thus, the closure of EA under the induction rule for ∑n formulas is equivalent to ω times iterated ∑n reflection principle. Moreover, for k < ω, (...) k times iterated ∑n reflection principle over EA precisely corresponds to the extension of EA by k nested applications of ∑n induction rule.The above relationship holds in greater generality than just stated. In fact, we give general formulas characterizing in terms of iterated reflection principles the extension of any given theory by k nested applications of ∑n or Πn induction rules. In particular, the closure of a theory T under just one application of ∑1 induction rule is equivalent to T together with ∑1 reflection principle for each finite Π2 axiomatized subtheory of T.These results have closely parallel ones in the theory of subrecursive function classes. The rules under study correspond, in a canonical way, to natural closure operators on the classes of provably recursive functions. Thus, ∑1 induction rule precisely corresponds to the primitive recursive closure operator, and ∑1 collection rule, introduced below, corresponds to the elementary closure operator. (shrink)

Since last year, major initiatives have been undertaken by the chair of theoretical philosophy at the University of Tübingen in order to enhance the reception of analytic metaphysics in the European landscape. Here we review the 2013 summer workshop, intended to be the first of an annual series, on “Existence, Truth and Fundamentality”, the invited speakers being Graham Priest (Melbourne), Stephan Leuenberger (Glasgow), Dan López de Sa (Barcelona), Francesco Berto (Aberdeen), Friederike Moltmann (Paris – Pantheon Sorbonne) and Jason Turner (Leeds). (...) The workshop’s scope is fairly large, focusing on three different aspects of contemporary research in metaphysics. However, the underlying idea of organizers Thomas Sattig and Alessandro Torza consisted in exploring their interconnections and even new areas which possibly share the same problem spectrum. Also, they thought of bringing together both young and senior protagonists of the contemporary debate. In this sense, the main thread followed by the speakers consisted in enquiring the ideas of fundamentality, dependence and grounding with respect to ontology (Berto, López de Sa, Turner) and the truthmaking debate (Priest, Moltmann, Leuenberger), thus pretty much in line with some latest tendencies in metaphysics, such as, prima inter paria, the works of Kit Fine. When we say that something is more fundamental than something else, we move into a non-conventional (for the standards of 20 th century philosophy) metodological framework, hardly focusing on the question about what there is, and rather tackling the issue of how fundamentally there is what there is, or how the existence of something is required as a ground for the existence of other things. Here is how Jonathan Schaffer explains the methodological transition in his influential “On What Grounds What” (2009): -/- Among the many assumptions Quine and Carnap share is that metaphysical questions are existence questions, such as whether numbers exist. They only disagree on the further issue of whether such questions are meaningful (at least as the metaphysician might pose them). But why think that metaphysical questions are existence question of this sort? Return to Aristotle’s Metaphysics. There are virtually no existence question posed. The whole discussion is about substances (fundamental units of being). At one point Aristotle pauses to ask if numbers exist, and his answer is a brief and dismissive yes. [. . . ] For Aristotle, the question about numbers is whether they are transcendent substances or grounded in concreta. The question is not whether numbers exist, but how. (Schaffer, 2009, p. 347) -/- The conference opened with Graham Priest’s intriguing and peculiar review of Buddhist cornerstone “The Fundamental Verses of the Middle Way” (Mūlamadhyakamakārikā) by Nāgārjuna (ca. 150-ca. 250 AD), seen as a unrecognized forerunner of multi-valued semantics and dialetheism. Priest shows that Nagarjuna’s thought indeed has valuable analytic grip (contrary to the traditional mystical dismiss of his works altogether) and is even in accord to some formal schemas rejecting both the laws of excluded middle and non-contradiction. Dan López de Sa was interested in the topic of grounding, raising concerns about how to explain the kind of “reality” exemplified by what is not fundamental, but rather derivative on something else. He proposes a conceptual and non-primitive analysis of grounding as linked to fundamentality and derivation, and argues that the view can be advocated along with the acceptance that at least something is not fundamental. Subsequently, he illustrates an impressive range of applications linked to contemporary debates in meta-ontology, truthmaking and philosophy of time. Stephan Leuenberger discussed a semantics for “total logic”, a variant of first order logic which is claimed to have several applications with respect to the issue of excluding negative existentials from the scope of theories accounting for a given ’totality’ of facts. For example, materialism is the claim that everything there is can be traced back to physical facts or to truth implied by those facts. What about the claim that “There are no angels”? According to Leuenberger, ordinary logic falls prey of modal arguments (if it is possible that there are angels, by modus tollens, that it is not metaphysically necessary that everything there is is physical). So, there is space for the introduction of a new operator, the totality operator, claiming of what enters its scope that “that’s the whole truth”. Consequently, total logic’s semantics tackles David Chalmers’ well-known conceivability-based argument in favour of zombie’s (subjects producing behaviour but experiencing no qualia) possible existence. Friederike Moltmann presented a massive array of natural language-based examples on the role played by case-constructions, such as “it is the case that Caesar crossed the Rubicon”, “the case of the stolen statue”, “the case in which it might rain”, and so forth. She suggests that we should take surface phenomena of our language very seriously with regard to the determination of ontological categories and truth-makers. Cases are provided by many natural languages with their own existence predicates (“to occur” and “to present itself ”), and these do not apply to other kind of entities, such as objects and events. Trying to derive a substantive thesis on their nature, she claims that they are filtered entities, a structure taking into account some features of the corresponding objects and events and preserving their relational pattern. Jason Turner discussed meta-ontological concerns against the claim that ontological debates are defective. Analysed the structure of a metaphysical theory and identified two different forms of defectiveness that can occur in ontological questions, the defection from without and the defection from within, the author provided an original solution in order to avoid such difficulties. He argued thus in favor of a logical constancy, a translation principle thanks to it would be possible reconceive an ontological defection. Lastly, Francesco Berto’s talk closed the workshop with a sagacious discussion of meinongian quantification. He substains that Meinongians and Quineans experience no conceptual equivocation. Even if the former claims that “There are things that do not exist”, something that the latter contrasts with the interpretation of existential quantifiers as all-including, they still rely upon the same concept of “existence” and they understand each other when they are outside the ontology room, so that it cannot be that they lack competence. Subsequently, Berto deals with the objection that Meinongians commit analytic falsehood in separating the meaning of “to be” from that of “exists”. The Quinean has no independent evidence for analytic equivalence aside from her emphatic stress on the “is” in “there is”. Meinongians, however, can retort to linguistic considerations and claim that existence predicates display fairly different functions. -/- As for what regards our internal division of the “philosophical labor”, Fabio Ceravolo reviewed Moltmann and Berto’s talks; whereas Mattia Cozzi took care of Priest’s and Leuenberger’s, and Mattia Sorgon of those given by López de Sa and Turner. Conclusively, we would like to thank Thomas Sattig and Alessandro Torza for all of their organizational efforts and the kind welcome they reserved to us. We hope we will have further opportunities to collaborate with Tübingen in supporting similarly innovative and valiant european initiatives. (shrink)

We gather the following miscellaneous results in proof theory from the attic.1. 1. A provably well-founded elementary ordering admits an elementary order preserving map.2. 2. A simple proof of an elementary bound for cut elimination in propositional calculus and its applications to separation problem in relativized bounded arithmetic below S21.3. 3. Equivalents for Bar Induction, e.g., reflection schema for ω logic.4. 4. Direct computations in an equational calculus PRE and a decidability problem for provable inequations in PRE.5. 5. Intuitionistic (...) fixed point theories which are conservative extensions of HA.6. 6. Proof theoretic strengths of classical fixed points theories.7. 7. An equivalence between transfinite induction rule and iterated reflection schema over IΣn.8. 8. Derivation lengths of finite rewrite rules reducing under lexicographic path orders and multiply recursive functions.Each section can be read separately in principle. (shrink)

The starting point of this paper concerns the apparent difference between what we might call absolute truth and truth in a model, following Donald Davidson. The notion of absolute truth is the one familiar from Tarski’s T-schema: ‘Snow is white’ is true if and only if snow is white. Instead of being a property of sentences as absolute truth appears to be, truth in a model, that is relative truth, is evaluated in terms of the relation between sentences and (...) models. I wish to examine the apparent dual nature of logical truth (without dwelling on Davidson), and suggest that we are dealing with a distinction between a metaphysical and a linguistic interpretation of truth. I take my cue from John Etchemendy, who suggests that absolute truth could be considered as being equivalent to truth in the ‘right model’, i.e., the model that corresponds with the world. However, the notion of ‘model’ is not entirely appropriate here as it is closely associated with relative truth. Instead, I propose that the metaphysical interpretation of truth may be illustrated in modal terms, by metaphysical modality in particular. One of the tasks that I will undertake in this paper is to develop this modal interpretation, partly building on my previous work on the metaphysical interpretation of the law of non-contradiction (Tahko 2009). After an explication of the metaphysical interpretation of logical truth, a brief study of how this interpretation connects with some recent important themes in philosophical logic follows. In particular, I discuss logical pluralism and propose an understanding of pluralism from the point of view of the metaphysical interpretation. (shrink)

In his previous work, the author has introduced the axiom schema of inductive dichotomy, a weak variant of the axiom schema of inductive definition, and used this schema for elementary ) positive operators to separate open and clopen determinacies for those games in which two players make choices from infinitely many alternatives in various circumstances. Among the studies on variants of inductive definitions for bounded ) positive operators, the present article investigates inductive dichotomy for these operators, and (...) applies it to constructive investigations of variants of determinacy statements for those games in which the players make choices from only finitely many alternatives. As a result, three formulations of open determinacy, that are all classically equivalent with each other, are equivalent to three different semi-classical principles, namely Markov’s Principle, Lesser Limited Principle of Omniscience and Limited Principle of Omniscience, over a suitable constructive base theory that proves clopen determinacy. Open and clopen determinacies for these games are thus separated. Some basic results on variants of inductive definitions for \ positive operators will also be given. (shrink)

Alston begins his exposition of the realist conception of truth in chapter 1 with a roughly Aristotelian formulation: “A statement is true if and only if what the statement says to be the case actually is the case”. This condition has the drawback that it defines truth via illocutionary acts; yet, as Alston argues, propositions are the most basic truth-bearers. Alston therefore turns to the universalized T-schema for a condition that characterizes the truth of propositions without mentioning illocutionary acts: (...) “ The proposition that p is true iff p”, where “” is a substitutional rather than objectual quantifier over propositions. Later Alston avers that this account of truth is equivalent to another that is overtly realist in characterizing truth in terms of facts, a minimalist correspondence theory: “ The proposition that p is true iff it is a fact that p”. (shrink)

Many approaches to the semantics of generic sentences posit an unpronounced quantifier gen. However, while overt quantifiers are conservative, gen does not seem to be. A quantifier Q is conservative iff instances of the following schemas are equivalent: Q As are F and Q As are As that are F. All ravens are black is obviously equivalent to All ravens are ravens that are black, yet ravens are black is not equivalent to ravens are ravens that are black. This may (...) cast doubt on theviability of quantificational analyses of generics. This paper proposes a theory of why such “conservativity” generics are problematic that is compatible with the conservativity of gen and also accounts for perennially troublesome examples such as books are paperbacks and bees are workers. (shrink)

A bounded monotone sequence of reals without a limit is called a Specker sequence. In Russian constructive analysis, Church's Thesis permits the existence of a Specker sequence. In intuitionistic mathematics, Brouwer's Continuity Principle implies it is false that every bounded monotone sequence of real numbers has a limit. We claim that the existence of Specker sequences crucially depends on the properties of intuitionistic decidable sets. We propose a schema about intuitionistic decidability that asserts “there exists an intuitionistic enumerable set (...) that is not intuitionistic decidable” and show that the existence of a Specker sequence is equivalent to ED. We show that ED is consistent with some certain well known axioms of intuitionistic analysis as Weak Continuity Principle, bar induction, and Kripke Schema. Thus, the assumption of the existence of a Specker sequence is conceivable in intuitionistic analysis. We will also introduce the notion of double Specker sequence and study the existence of them. (shrink)

The uniform reflection principle for the theory of uniform T-sentences is added to PA. The resulting system is justified on the basis of a disquotationalist theory of truth where the provability predicate is conceived as a special kind of analyticity. The system is equivalent to the system ACA of arithmetical comprehension. If the truth predicate is also allowed to occur in the sentences that are inserted in the T-sentences, yet not in the scope of negation, the system with the reflection (...) schema for these T-sentences assumes the strength of the Kripke-Feferman theory KF, and thus of ramified analysis up to go. (shrink)

We consider the problem of finding and classifying representations in algebraic logic. This is approached by letting two players build a representation using a game. Homogeneous and universal representations are characterized according to the outcome of certain games. The Lyndon conditions defining representable relation algebras (for the finite case) and a similar schema for cylindric algebras are derived. Finite relation algebras with homogeneous representations are characterized by first order formulas. Equivalence games are defined, and are used to establish (...) whether an algebra is ω-categorical. We have a simple proof that the perfect extension of a representable relation algebra is completely representable. An important open problem from algebraic logic is addressed by devising another two-player game, and using it to derive equational axiomatisations for the classes of all representable relation algebras and representable cylindric algebras. Other instances of this approach are looked at, and include the step by step method. (shrink)

We define classes Φnof formulae of first-order arithmetic with the following properties:(i) Everyφϵ Φnis classically equivalent to a Πn-formula (n≠ 1, Φ1:= Σ1).(ii)(iii)IΠnandiΦn(i.e., Heyting arithmetic with induction schema restricted to Φn-formulae) prove the same Π2-formulae.We further generalize a result by Visser and Wehmeier. namely that prenex induction within intuitionistic arithmetic is rather weak: After closing Φnboth under existential and universal quantification (we call these classes Θn) the corresponding theoriesiΘnstill prove the same Π2-formulae. In a second part we consideriΔ0plus collection-principles. (...) We show that both the provably recursive functions and the provably total functions ofare polynomially bounded. Furthermore we show that the contrapositive of the collection-schema gives rise to instances of the law of excluded middle and hence. (shrink)

We consider countable so‐called rich subsemigroups of ; each such semigroup T gives a variety CPEAT that is axiomatizable by a finite schema of equations taken in a countable subsignature of that of ω‐dimensional cylindric‐polyadic algebras with equality where substitutions are restricted to maps in T. It is shown that for any such T, if and only if is representable as a concrete set algebra of ω‐ary relations. The operations in the signature are set‐theoretically interpreted like in polyadic equality (...) set algebras, but such operations are relativized to a union of cartesian spaces that are not necessarily disjoint. This is a form of guarding semantics. We show that CPEAT is canonical and atom‐canonical. Imposing an extra condition on T, we prove that atomic algebras in CPEAT are completely representable and that CPEAT has the super amalgamation property. If T is rich and finitely represented, it is shown that CPEAT is term definitionally equivalent to a finitely axiomatizable Sahlqvist variety. Such semigroups exist. This can be regarded as a solution to the central finitizability problem in algebraic logic for first order logic with equality if we do not insist on full fledged commutativity of quantifiers. The finite dimensional case is approached from the view point of guarded and clique guarded (relativized) semantics of fragments of first order logic using finitely many variables. Both positive and negative results are presented. (shrink)

This paper gives an analysis of the adverbial quantifiers exemplified in “I regretted it every time I had dinner with him.” Sentences of this kind display what I call a ‘matching effect’; they are true if every event in the denotation oftime I had dinner with him can be matched with an event regretting that dinner event. They are thus truth-conditionally equivalent to sentences of the form “There are at least as many As as Bs.” The difficulties of giving a (...) compositional interpretation to sentences of this form have been discussed in, e.g., Boolos 1981. I first show that the matching effect is semantic and not pragmatic. I then give an analysis of these sentences in a neo-Davidsonian framework, interpreting the adverbials as quantifiers over events. Syntactically they are analyzed as objects of a null preposition. This allows a simple compositional semantic interpretation in which the null preposition is interpreted exactly as other prepositions are by Davidson (1967), namely as denoting a function from the event argument of the matrix verb to the prepositional object. The matching effect then follows automatically. I extend the analysis to account for other sentences which directly instantiate the schema “For every A there is a B” and its equivalents, and show how the matching effect follows in general from the functional nature of thematic roles and prepositions. (shrink)