We argue that no attempt of reducing meaning to a systematic set of rules, according to which the role of linguistic expressions is to be normatively defined, can be abstracted from an irreducibly decisional compound. By comparing Lorenzen ’s project of building an Ortho-language and Brandom ’s inferentialist take on meaning, we distinguish two ways of acknowledging this fact, while claiming that Lorenzen ’s take is more genuinely constructive, insofar as choices be thought of as genuine features of constructions. (...) It brings into a new perspective the relation between dialogical constructivism and Brouwer ’s intuitionism. Finally we bring up a philosophical argument for the claim that interaction rules should be indexed on players and on their choices, when providing deontic bases to semantics. (shrink)

In our previous paper [5], we have studied Kripke-type semantics for propositional logics without the contraction rule. In this paper, we will extend our argument to predicate logics without the structure rules. Similarly to the propositional case, we can not carry out Henkin's construction in the predicate case. Besides, there exists a difficulty that the rules of inference () and () are not always valid in our semantics. So, we have to introduce a notion of normal models.

Glenn Langford; XI—Rules, Moral Rules and the Subjects of Moral Predicates, Proceedings of the Aristotelian Society, Volume 69, Issue 1, 1 June 1969, Pages 187–.

In this paper, a semantics for predicate logics without the contraction rule will be investigated and the completeness theorem will be proved. Moreover, it will be found out that our semantics has a close connection with Beth-type semantics.

The relevance of cognitive penetration has been pointed out concerning three fields within philosophy: philosophy of science, philosophy of mind, and epistemology. This paper argues that this phenomenon is also relevant to the philosophy of language. First, I will defend that there are situations where ethical, social, or cultural rules can affect our taste perceptions. This influence can cause speakers to utter conflicting contents that lead them to disagree and, subsequently, to negotiate the circumstances of application of the taste (...) predicates they have used to describe or express their taste perceptions. Then, to account for the proper dynamics of these cases, I will develop a theoretical framework build upon two elements: the Lewisian idea of the score of a conversation, and Richard’s taxonomy of the different attitudes speakers can have in taste disagreements. In a nutshell, I will argue that speakers can accommodate these conflicting contents as exceptions to the rule that determines the circumstances of application of taste predicates.Keywords: Cognitive penetration, Common ground, Circumstances of application, Accommodation, Exceptions, Score of the conversation, Taste predicates. (shrink)

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem''s modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap''s display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or (...) its converse to be derived. En route from the minimal modal predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules. (shrink)

One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names are predicates (...) in all of their occurrences; they are predicates that are true of their bearers. When a name appears as a bare singular in argument position, it really occupies the predicate position of what in this essay is called a denuded definite description: a definite description with an unpronounced definite article. Sloat provided good evidence for this. The definite article is sometimes pronounced with names in the singular: ‘The Ivan we all love doesn't feel well’. Sloat proposed a disjunctive generalization of when the definite article must be pronounced with a singular name. This essay shows that by slightly revising Sloat's generalization, we arrive at a simple, nondisjunctive, syntactic rule that governs the overt appearance of the definite article with singular names. But Ivan does not necessarily bear the name ‘Ivan’, so one might worry that the sentence “Ivan might not have had ‘Ivan’ as a name” would incorrectly be predicted false. This essay shows that Predicativism does not have this consequence by showing that incomplete definite descriptions in general and incomplete denuded descriptions, such as ‘Øthe Ivan’, in particular are rigid designators. (shrink)

Indexicality is a feature of predicates and predicate components (verbs, adjectives, adverbs and the like) as well as of referring expressions. With classic referring indexicals such as 'I' or 'that' a distinctive rule takes us from token and context to some item present in the content which is the semantic correlate of the token. Predicates and predicate components may function in an analogous fashion. For example 'thus' is an indexical adverb which latches onto some manner of performance present in its (...) context. 'John sang thus', said while indicating someone singing discordantly, claims that John sang discordantly. The phenomenon of predicatival indexicality is widespread in English and is expressed in a variety of idioms. Indexical predication plays important epistemological and psychological roles and the notion may have other interesting philosophical applications. (shrink)

This paper describes the SNePS knowledge-representation and reasoning system. SNePS is an intensional, propositional, semantic-network processing system used for research in AI. We look at how predication is represented in such a system when it is used for cognitive modeling and natural-language understanding and generation. In particular, we discuss issues in the representation of fictional entities and the representation of propositions from fiction, using SNePS. We briefly survey four philosophical ontological theories of fiction and sketch an epistemological theory of fiction (...) using a story operator and rules for allowing propositions to migrate into and out of story spaces. (shrink)

According to a widely held view, people's commitments to laws are dependent on the existence in their community of a conventional practice of complying with certain fundamental laws. This conventionalism has significantly hampered our attempts to explain the normative practice of law. Ronald Dworkin has argued against conventionalism by bringing up the phenomenon of persistent fundamental legal controversies, but neither Dworkin nor his legal positivist respondents have correctly understood the real significance of such controversies. This article argues that such controversies (...) pose a deep challenge to any conception of our legal practice as a genuinely normative, rule-mediated, practice. The article also argues that what is needed to deflect this challenge is a new understanding – different from the widely held conventionalist understanding – of how people's commitments to laws are predicated on their fellows’ like commitments. (shrink)

Let T be a second-order arithmetical theory, Λ a well-order, λ < Λ and X ⊆ ℕ. We use $[\lambda |X]_T^{\rm{\Lambda }}\varphi$ as a formalization of “φ is provable from T and an oracle for the set X, using ω-rules of nesting depth at most λ”.For a set of formulas Γ, define predicative oracle reflection for T over Γ ) to be the schema that asserts that, if X ⊆ ℕ, Λ is a well-order and φ ∈ Γ, then$$\forall (...) \,\lambda < {\rm{\Lambda }}\,.$$In particular, define predicative oracle consistency ) as Pred–O–RFN{0=1}.Our main result is as follows. Let ATR0 be the second-order theory of Arithmetical Transfinite Recursion, ${\rm{RCA}}_0^{\rm{*}}$ be Weakened Recursive Comprehension and ACA be Arithmetical Comprehension with Full Induction. Then,$${\rm{ATR}}_0 \equiv {\rm{RCA}}_0^{\rm{*}} + {\rm{Pred - O - Cons\ }}\left \equiv {\rm{RCA}}_0^{\rm{*}} + \,{\rm{Pred - O - Cons\ }}\left \equiv {\rm{RCA}}_0^{\rm{*}} + \,{\rm{Pred - O - RFN}}\,_{{\bf{\Pi }}_2^1 } \left.$$We may even replace ${\rm{RCA}}_0^{\rm{*}}$ by the weaker ECA0, the second-order analogue of Elementary Arithmetic.Thus we characterize ATR0, a theory often considered to embody Predicative Reductionism, in terms of strong reflection and consistency principles. (shrink)

Along with many other languages, English has a relatively straightforward grammatical distinction between mass-occurrences of nouns and their countoccurrences. As the mass-count distinction, in my view, is best drawn between occurrences of expressions, rather than expressions themselves, it becomes important that there be some rule-governed way of classifying a given noun-occurrence into mass or count. The project of classifying noun-occurrences is the topic of Section II of this paper. Section III, the remainder of the paper, concerns the semantic differences between (...) nouns in their mass-occurrences and those in their count-occurrences. As both the name view and the mixed view are, in my opinion, subject to serious difficulties discussed in Section III.1,I defend a version of the predicate view. Traditionally, nouns in their singular count-occurrences are also analyzed as playing the semantic role of a predicate. How, then, does the predicate view preserve the intuitive difference between nouns in their mass- and those in their count-occurrences? I suggest, in Section III.2, that there are different kinds of predicates: mass-predicates, e.g. ‘is hair’, singular count-predicates, e.g. ‘is a hair’, and plural count-predicates, e.g. ‘are hairs’. Mass-predicates and count-predicates, in my view, are not reducible to each other. The remainder of Section III takes a closer look at the differences and interrelations between these different kinds of predicates. Mass-predicates and count-predicates differ from each other truth-conditionally, and these truth-conditional differences turn out to have interesting implications, in particular concerning the part-whole relation and our practices of counting. But mass- and count-predicates are also related to each other through systematic entailment relations; these entailment relations are examined in Section III.4. (shrink)

In this paper the general notion of Bourbaki structures, interpreted in terms of Suppes predicates, will be used to axiomatize a system of meta-rankings in the sense introduced by A. K. Sen. It will be argued that this axiomatization must take place in a Kantian-ruled world in order to provide a link between meta-rankings and individual actions.Dedicated to Prof. Francisco A. Doria on his 50th birthday.

Objective Bayesianism says that the strengths of one’s beliefs ought to be probabilities, calibrated to physical probabilities insofar as one has evidence of them, and otherwise sufficiently equivocal. These norms of belief are often explicated using the maximum entropy principle. In this paper we investigate the extent to which one can provide a unified justification of the objective Bayesian norms in the case in which the background language is a first-order predicate language, with a view to applying the resulting formalism (...) to inductive logic. We show that the maximum entropy principle can be motivated largely in terms of minimising worst-case expected loss. (shrink)

IF "ALL A’S ARE B" AND "ALL A’S ARE C" ARE BOTH EQUALLY WELL SUPPORTED BY OBSERVATIONS SO FAR, YET YIELD CONFLICTING PREDICTIONS, WHICH OUGHT WE TO ADOPT? GOODMAN’S CONFLICT BETWEEN "ALL EMERALDS ARE GREEN" AND "ALL EMERALDS ARE GRUE" IS A SPECIAL CASE OF SUCH CONFLICT, WHICH MAY BE DEALT WITH BY A RULE STATING THAT WE OUGHT NOT TO PROJECT POSITIONAL IN PREFERENCE TO QUALITATIVE PREDICATES. THIS PAPER ATTEMPTS TO ELUCIDATE THE RULES GOVERNING A LARGER CLASS OF (...) SUCH CONFLICTS, IN CASES WHERE ONE PREDICATE B IS "EPISTEMOLOGICALLY PRIOR" TO ANOTHER ONE C. (shrink)

Avicenna is a strong proponent of what some of the later ones call qāʻidat al-wāḥid or ‘rule of the one’ (RO). The gist of RO states: from the one only one directly proceeds. In the secondary literature, discussion of this Avicennian rule is usually limited to a particular application of it i.e., the issue of emanation. As result, it’s not really clear what RO means, nor why Avicenna endorsed it. In this paper, I try and remedy this situation by doing (...) two things – one on the taṣawwur front, the other on the tasdīq. First, explain just what the terms of RO amount to – that is, its subject and predicate. In doing this, I distinguish between a narrow and a broad understanding of RO, and the show that, on the Avicennian view, the scope of RO is broad; it is meant to be a general principle of efficient causality. This is why it is appealed to in various contexts to establish substantial philosophical theses. Second, I consider an argument Avicenna offers for RO in the Mubāḥathāt. In unpacking it, I uncover some of its realist presuppositions, and then further clarify it in light of a critique first raised by Bahmanyār and then later made famous by Fakhr al-Dīn al-Rāzī. I then conclude by seeing whether the Avicennian has the resources within the initial premises of the argument to meet the objection that’s raised. (shrink)

This paper is concerned with the logical structure of arithmetical theories. We survey results concerning logics and admissible rules of constructive arithmetical theories. We prove a new theorem: the admissible propositional rules of Heyting Arithmetic are the same as the admissible propositional rules of Intuitionistic Propositional Logic. We provide some further insights concerning predicate logical admissible rules for arithmetical theories.

Predicativists hold that proper names have predicate-type semantic values. They face an obvious challenge: in many languages names normally occur as, what appear to be, grammatical arguments. The standard version of predicativism answers this challenge by positing an unpronounced determiner in bare occurrences. I argue that this is a mistake. Predicativists should draw a distinction between two kinds of semantic type—underived semantic type and derived semantic type. The predicativist thesis concerns the underived semantic type of proper names and underdetermines a (...) view about the semantic type of bare occurrences. I’ll argue that predicativists should hold that bare names are derived individual-denoting expressions. I end by considering what this result means for the relationship between predicativism and other metalinguistic theories of names. (shrink)

We provide five semantic preservation properties which apply to the various rules -- primitive, derived and admissible -- of Hilbert-style axiomatizations of relevant logics. These preservation properties are with respect to the Routley-Meyer semantics, and consist of various truth- preservations and validity-preservations from the premises to the conclusions of these rules. We establish some deduction theorems, some persistence theorems and some soundness and completeness theorems, for these preservation properties. We then apply the above ideas, as best we can, (...) to the classical sentential and predicate calculi, to normal and non- normal modal logics, and to many- valued logics. (shrink)

The standard rule of single privative modification replaces privative modifiers by Boolean negation. This rule is valid, for sure, but also simplistic. If an individual a instantiates the privatively modified property (MF) then it is true that a instantiates the property of not being an F, but the rule fails to express the fact that the properties (MF) and F have something in common. We replace Boolean negation by property negation, enabling us to operate on contrary rather than contradictory properties. (...) To this end, we apply our theory of intensional essentialism, which operates on properties (intensions) rather than their extensions. We argue that each property F is necessarily associated with an essence, which is the set of the so-called requisites of F that jointly define F. Privation deprives F of some but not all of its requisites, replacing them by their contradictories. We show that properties formed from iterated privatives, such as being an imaginary fake banknote, give rise to a trifurcation of cases between returning to the original root property or to a property contrary to it or being semantically undecidable for want of further information. In order to determine which of the three forks the bearers of particular instances of multiply modified properties land upon we must examine the requisites, both of unmodified and modified properties. Requisites underpin our presuppositional theory of positive predication. Whereas privation is about being deprived of certain properties, the assignment of requisites to properties makes positive predication possible, which is the predication of properties the bearers must have because they have a certain property formed by means of privation. (shrink)

Since the time, about a century ago, when DeMorgan, Boole and Jevons, inaugurated the study of the logic of numerically definite reasoning, no one has been concerned to establish the validity rules for a very general type of numerically definite inference which is a strong analogue of the classical syllogism. The reader will readily agree that the traditional rules of syllogistic inference cannot even begin to decide whether the following proportionally quantified syllogism is a valid argument: at most (...) 4/7 p are at most 2/3 not-m and at least 3/5 s are precisely 7/8 m, hence, at most 1/3 s are p. Likely reasons, of broad methodological interest, why this readily definable type of formal inference has been neglected will presently be proposed. Among the masters of twentieth century logic, Hilbert and Bernays have, to be sure, meticulously shown how such numerically definite propositions as “at least 7 individuals have the property p” can be expressed in the predicate calculus with the use of the identity relation. They do not, since their concern with such propositions is indirect, proceed to establish a systematic calculus of classes whose “size” or extent is numerically definite. As we shall always notice, traditional logic and even ordinary Boolean algebra prefer to generalize about the laws governing the interrelationship of classes in inference systems without making any hypotheses concerning class “size” or extent except by the classical quantifier “some”, which quantifier admits the measure or extent of a class only in terms of the proposition that a given class contains or does not contain at least one member. Such a restricted admission of the relevance for inference of class size is among the fundamental reasons for the neglect of proportional quantifiers, i.e., quantifiers where numerical value is any rational number r such that 0/100 ≤ r ≤ 100/100. It can, of course, also be pointed out that the traditional syllogism and ordinary Boolean algebra do not i.e. measure, numerically define, the degree of inclusion of one class in another. Inclusion is taken either as total or partial, with no discrimination of the degree of partial inclusion. (shrink)

Gupta’s Rule of Revision theory of truth builds on insights to be found in Martin and Woodruff and Kripke in order to permanently deepen our understanding of truth, of paradox, and of how we work our language while our language is working us. His concept of a predicate deriving its meaning by way of a Rule of Revision ought to impact significantly on the philosophy of language. Still, fortunately, he has left me something to.

Geach's account of the Aristotelian logic of categorical sentences supplemented the views shared by Frege, Russell, Quine and others. I argue that this particular predicate logic approach and Geach's points apply to only one variety of natural language categorical sentences. For example, it takes the universal categorical as a universal conditional “If anything is a man, then it is mortal”. A different natural language form can and should be invoked: “Every man is a mortal.” Employing special restricted quantifiers in a (...) version of predicate logic, we justify a full square of opposition and the rules of quality and quantity that Geach rejected. (shrink)

If ‘F’ is a predicate, then ‘Fer than’ or ‘more F than’ is a corresponding comparative relational predicate. Concerning such comparative relations, John Broome’s Collapsing Principle states that, for any x and y, if it is false that y is Fer than x and not false that x is Fer than y, then it is true that x is Fer than y. Luke Elson has recently put forward two alleged counter-examples to this principle, allegedly showing that it yields contradictions if (...) there are borderline cases. In this paper, I argue that the Collapsing Principle does not rule out borderline cases, but I also argue that it is implausible. (shrink)

Williams (2012) recently proposed the Normative Silence model of Indeterminacy in order to account for a single phenomenon running through all cases of indeterminacy and to reach consensus on the correct epistemic attitude to adopt towards borderline cases of paradigmatically vague predicates. Williams’s Normative Silence model says there is no general normative rule governing God’s and humans’ belief attitudes towards indeterminacies. I claim instead that human rationality and philosophical inquiry require general normative rules leading our belief attitudes towards indeterminacies (...) and that God’s belief attitudes are more difficult to define than Williams assumes. (shrink)

There is a perennial ambiguity in the rule-of-law preposition: it predicates that the law shall rule, but which law? This legal loophole has led to a diverse array of interpretations of the concept. Of these, two appear particularly adverse to what the rule of law should primarily be—the rulership of the law—yet still remain dominant. On the one hand, the rule of law is intended to be the vehicle to deliver above-the-law goods such as human rights or other individual entitlements (...) like property, and to forever shield them against any other force, including the law. On the other hand, the rule of law is believed to be a tool at the rulers’ disposal, who make use of the law but are not bound by it, for either legal or practical reasons. In both cases, a pre-legal setting for society allocates rulership to something but not the law, against the very essence of the ideal: an authoritative legal practice for the sake of regulating the present society. As such, the rule of law has to meet certain requirements of craftsmanship, like conditions in law-making and law-enforcement, and sources, which are to be democratically underpinned. (shrink)

A NewsFusion System is a logic-based system for merging heterogeneous structured news reports. Structured news reports are XML documents, where the textentries are restricted to individual words or simple phrases, such as names and domain-specific terminology, and numbers and units. We assume structured news reports do not require natural language processing. In previous papers, we have presented aspects of a logic-based framework for merging structured news reports based on fusion rules. Fusion rules are a form of scripting language (...) that define how structured news reports should be merged. The antecedent of a fusion rule is a call to investigate the information in the structured news reports and the background knowledge, and the consequent of a fusion rule is a formula specifying an action to be undertaken to form a merged report. It is expected that a set of fusion rules is defined for any given application. In this paper, we present a framework for aggregation predicates that can be used in fusion rules for context-dependent aggregation of structured news reports. We also present a case study that uses aggregation predicates to merge weather reports that have been obtained from a selection of websites. (shrink)

Platonism, in its most recent and seemingly most cogent form, has rested on (a) the supposed indispensability of descriptive predicate terms in so-called "improved," or "clarified," or "perspicuous" languages; (b) the distinction between subject and predicate terms based on the asymmetry of the predication relation; and (c) the claimed ontological significance of the different categories of terms implied by (a) and (b). Nominalism, in one of its most pervasive recent forms, has involved the denial of the criterion of ontological commitment (...) embedded in (c) by explicitly or implicitly adopting the criterion expressed in Quine's formula "to be is to be the value of a variable." To avoid the obvious charge that nominalists merely ignore abstract entities by the arbitrary ploy of changing the rules, i.e. denying that ontological commitments are made by the inclusion of primitive predicates in schemata of certain kinds by simply employing a different criterion of commitment, some nominalists have sought to argue for their criterion by pointing to the distinction between singular and general terms and the radically different roles such terms play. The distinction between singular and general terms becomes the premise for an argument that purportedly supports Quine's criterion of ontological commitment. This criterion, in turn, provides the basis for the nomin'alist's use of primitive predicates, as general terms, without ontological commitment to abstract entities. In this paper I shall argue that the nominalist's gambit is inadequate in that the distinction between singular and general terms, as employed by a philosopher like Quine, merely provides a way of stating the nominalist's position and does not provide a reason for holding such a position. To put it another way, if we consider the contemporary nominalist to argue from the distinction between singular and general terms to the cogency of nominalism, since the former provides a ground for Quine's criterion of ontological commitment which, in turn, provides the basis for the latter, then the line of thought is question begging. It is so in that the very way the nominalist draws the distinction presupposes a nominalistic view, since a careful statement of that distinction amounts to a restatement of the nominalistic position. (shrink)

I explore, from a proof-theoretic perspective, the hierarchy of classical and paraconsistent logics introduced by Barrio, Pailos and Szmuc in (Journal o f Philosophical Logic,49, 93-120, 2021). First, I provide sequent rules and axioms for all the logics in the hierarchy, for all inferential levels, and establish soundness and completeness results. Second, I show how to extend those systems with a corresponding hierarchy of validity predicates, each one of which is meant to capture “validity” at a different inferential level. (...) Then, I point out two potential philosophical implications of these results. (i) Since the logics in the hierarchy differ from one another on the rules, I argue that each such logic maintains its own distinct identity (contrary to arguments like the one given by Dicher and Paoli in 2019). (ii) Each validity predicate need not capture “validity” at more than one metainferential level. Hence, there are reasons to deny the thesis (put forward in Barrio, E., Rosenblatt, L. & Tajer, D. (Synthese, 2016)) that the validity predicate introduced in by Beall and Murzi in (Journal o f Philosophy,110(3), 143–165, 2013) has to express facts not only about what follows from what, but also about the metarules, etc. (shrink)

This paper builds on a previous discussion of Stephen Mumford’s rejection of what he takes to be David Best’s argument for a distinction between purposive and aesthetic sports. That discussion concluded that Mumford’s argument misses its target, but closed by introducing a possible alternative argument, not made by Mumford, that might be thought to have the potential to secure Mumford’s conclusion. This paper considers that alternative argument, namely, the thought that the ascription of psychological predicates conceived of in terms of (...) defeasible criteria that constitute logically good evidence could preserve Best’s claim to be making a logical point while allowing a place for intention in relation to aims and purposes in sport. It is argued that the relationship between rules and intention is such that this alternative argument cannot secure Mumford’s conclusion. (shrink)

Disagreements about what is delicious, what is funny, what is morally acceptable can lead to intractable disputes between parties holding opposing views of a given subject. How should we think of such disputes? Do they always amount to genuine disagreements? The answer will depend on how we understand disagreement and how we should think about the meaning and truth of statements in these areas of discourse. I shall consider cases of dispute and disagreement where relativism about truth appears to give (...) the best explanation of the phenomena. I will argue that that we cannot explain the relativist option merely by relativizing truth to an extra parameter, such as a standard of taste, or a sense of humour. Instead, I will focus on cases where the dispute concerns whether either of the two opposing parties is judging in accordance with an existing standard, and I shall suggest that how we should think of these cases bears important affinities with rule-following considerations found in the later Wittgenstein’s work. (shrink)

The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that we (...) suggest an extension to the Curry– Howard interpretation which draws on the idea of labelled deduction, and brings back Frege’s device of variable-abstraction to operate on the labels (i.e., proof-terms) alongside formulas of predicate logic. (shrink)

This paper shows a role of the contraction rule in decision problems for the logics weaker than the intuitionistic logic that are obtained by deleting some or all of structural rules. It is well-known that for such a predicate logic L, if L does not have the contraction rule then it is decidable. In this paper, it will be shown first that the predicate logic FLec with the contraction and exchange rules, but without the weakening rule, is undecidable (...) while the propositional fragment of FLec is decidable. On the other hand, it will be remarked that logics without the contraction rule are still decidable, if our language contains function symbols. (shrink)

This paper reflects on the idea of ‘visualization’ of legal rules as part of an account of rule following in action. Presenting an alternative to Van Schooten’s (Jurisprudence and communication. Deborah Charles, Liverpool, 2012) account of interpretation, I first distinguish between two modes of interpretation: rehearsing and discursive. I argue that the former is the more basic one, relating to our respecting sources, rather than noticing signs, in action. In other (Wittgensteinian) words, we have to understand how we take (...) guidance from rules. This account can profit from an analysis of what ‘seeing’ amounts to. Taking my cue from Merleau-Ponty, I point to the intertwinement between agent and world in seeing, in rule-following, and eventually in legal rule-following. The proof of the pudding is an alternative account of the time-honoured paradigm of legal interpretation: Hart’s ‘no vehicles in the park’. I show how this example is predicated on detecting ‘depth-clues’ in a rule, which allow an agent to correlate his vantage point to a vanishing point of a rule. The example illustrates a key-feature of rule following: reflexivity. I cannot follow a rule unless I project myself into its picture. (shrink)

A theory of higher-order vagueness for partially-defined, context-sensitive predicates like is blue is offered. According to the theory, the predicate is determinately blue means roughly is an object o such that the claim that o is blue is a necessary consequence of the rules of the language plus the underlying non-linguistic facts in the world. Because the question of which rules count as rules of the language is itself vague, the predicate is determinately blue is both vague (...) and partial in a sense analogous (though not completely identical) to the sense in which is blue is vague and partial. However, higher-order vagueness stops there. Although the anti-extension of is determinately blue differs from that of is blue, further iterations of determinately have no semantic effect. The paper closes with a discussion of the need to posit sharp and precise lines dividing the range of potential application of a vague predicate into semantically distinct categories. It is argued that this is less of a problem for the present theory than for many others, because the categories into which the range is divided by the present theory -- like the category of counting as blue because the rules of the language offer speakers no discretion, as opposed to the category of counting as blue because speakers have invoked an absolute minimum of discretion in adjusting the contextually sensitive boundaries of the predicate -- are not those that the linguistic competence of ordinary speakers equips them to make highly accurate and reliable judgments about. (shrink)

According to Gupta and Belnap, the “extensional behavior” of ‘true’ matches that of a circularly defined predicate. Besides promising to explain semantic paradoxicality, their general theory of circular predicates significantly liberalizes the framework of truth-conditional semantics. The authors’ discussions of the rationale behind that liberalization invoke two distinct senses in which a circular predicate’s semantic behavior is explained by a “revision rule” carrying hypothetical information about its extension. Neither attempted explanation succeeds. Their theory may however be modified to employ a (...) relativized notion of extension. The resulting contextualist semantics for ‘true’ construes circularity as a pragmatic phenomenon. (shrink)

The intention here is that of giving a formal underpinning to the idea of 'meaning-is-use' which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett-Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i. e. the so-called reduction rules. For that (...) we suggest an extension to the Curry-Howard interpretation which draws on the idea of labelled deduction, and brings back Frege's device of variable-abstraction to operate on the labels (i. e., proof-terms) alongside formulas of predicate logic. (shrink)

We introduce a Gentzen-style sequent calculus axiomatization for Basic Predicate Calculus. Our new axiomatization is an improvement of the previous axiomatizations, in the sense that it has the subformula property. In this system the cut rule is eliminated.

In recent years combinations of tense and modality have moved intothe focus of logical research. From a philosophical point of view, logical systems combining tense and modality are of interest because these logics have a wide field of application in original philosophical issues, for example in the theory of causation, of action, etc. But until now only methods yielding completeness results for propositional languages have been developed. In view of philosophical applications, analogous results with respect to languages of predicate logic (...) are desirable, and in this paper I present two such results. The main developments in this area can be split into two directions, differing in the question whether the ordering of time is world-independent or not. Semantically, this difference appears in the discussion whether T x W-frames or Kamp-frames (resp. Ockham-frames) provide a suitable semantics for combinations of tense and modality. Here, two calculi are presented, the first adequate with respect to Kamp-semantics, the second to T x Wsemantics. (Both calculi contain an appropriate version of Gabbay's irreflexivity rule.) Furthermore, the proposed constructions of canonical frames simplify some of those which have hitherto been discussed. (shrink)

The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that we (...) suggest an extension to the Curry– Howard interpretation which draws on the idea of labelled deduction, and brings back Frege’s device of variable-abstraction to operate on the labels (i.e., proof-terms) alongside formulas of predicate logic. (shrink)

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)

Abstract:Bipolar or related disorders (BoRD) present unique practical and existential problems for people who live with them. All agents experience changes in the things they care about over time. However people living with BoRD face drastic shifts in what seems valuable to them, which upset their longitudinal values (if, indeed, any stable longitudinal values are available in the first place). Navigating these evaluative high seas presents agents living with BoRD with a distinctive existential question, not shared by those on calmer (...) waters. I draw out two contrasting ways in which someone living with BoRD might seek to support their self-determination in these circumstances, by crafting appropriate self care and support regimes. The first strategy involves managing one’s affective episodes so that they do not interrupt one’s plans and long-term agency over time. The second involves a regimen that allows one the greatest degree of freedom in adapting to changes in one’s experiences of value. What distinguishes these sorts of self-determination is the scope at which they are predicated. Although both sorts of self-determination allow an individual to rule themselves, they alter the overall shape of one’s autonomy in quite different ways. (shrink)

According to the eligibility theory of meaning, often attributed to David Lewis, the referent of a predicate is the property that best balances the twin constraints of charity and eligibility, where eligibility is a function of metaphysical naturalness. This sort of metasemantics, which is motivated by its ability to resolve problems of indeterminacy and secure shared reference between disputing parties, can be somewhat friendly towards revisionary theories, since highly natural properties can act as “reference magnets,” securing our reference despite some (...) mismatch with usage. In this paper, I apply these considerations to normative ethics and argue that the theory of rule utilitarianism achieves a high balance of charity and eligibility. I proceed by comparing rule utilitarianism to two of its well-known rivals, act utilitarianism and Rossian pluralism. I show how the former achieves a high degree of eligibility but only at a significant cost of charity, while the latter does the opposite, fitting very nicely with our considered judgments but at the price of very low eligibility. Rule utilitarianism, on the other hand, strikes a good balance between these extremes; it assigns to our core moral term a relatively natural property without doing too much damage to our moral convictions. Thus, rule utilitarianism should be regarded as a promising moral theory by any philosopher who takes seriously considerations of eligibility and naturalness. (shrink)

Certain instances of contraction are provable in Zardini’s system $\mathbf {IK}^\omega $ which causes triviality once a truth predicate and suitable fixed points are available.

Is the Dionysian God, or an experience of the Dionysian God, absolutely ineffable? Does the Dionysian corpus assert or perform such ineffability? This paper will argue that the answer to each of these questions is no. The Dionysian God is known hyper-nous as the hyper-ousia cause of all. And the Dionysian corpus unambiguously refers to, asserts of, and metaphorizes about this God just so. In arguing these points, this paper will call upon both the speech act theory of John Searle (...) and the metaphor theory of George Lakoff and Mark Johnson. More particularly, it will look to Searle’s rules of reference and predication and conditions of illocutionary acts, as well as Lakoff and Johnson’s schematization of metaphor gestalt and entailment to show how Dionysian expressions of inexpressibility are rule-governed and the Dionysian God is thereby effable. (shrink)