Is the history of philosophy primarily a contribution to PHILOSOPHY or primarily a contribution to HISTORY? This paper is primarily contribution to history (specifically the history of New Zealand) but although the history of philosophy has been big in New Zealand, most NZ philosophers with a historical bent are primarily interested in the history of philosophy as a contribution to philosophy. My essay focuses on two questions: 1) How did New Zealand philosophy get to be so good? And why, given (...) that is so good (a point I am at pains to establish), has it apparently had so slight a cultural impact within New Zealand itself? Did we get the wrong Anderson – the uninspiring William, who was Professor at Auckland, rather than his talented younger brother John, who had such a huge cultural influence as Professor of Philosophy at Sydney? Perhaps but that can only be part of the story since we managed to attract even bigger stars, (notably Karl Popper) as well as breeding bigger talents of our own (Prior, Baier, Bennett, Mulgan, Hursthouse, Waldron and many more). Do we export our best talent? Sometimes – but the stars that stay and the stars who arrive don’t seem to have much impact in New Zealand itself however brightly they shine in the international philosophical firmament. Is it too esoteric? Perhaps, but esoteric philosophy can still have a cultural impact, witness, Moore, Popper and the younger Anderson. Is it, like many of New Zealand’s cultural products (from romance novels to movies), primarily intended for an international audience? That’s a large part of the answer but only a part. Another part of the answer is that philosophy HAS had a cultural impact but that impact is not readily apparent. For NZ philosophers have been less keen to push their ideological barrows and more keen to produce critical thinkers, and critical thinkers don’t all think alike. The logician George Hughes was apparently a life-changing teacher not because he had a nostrum but because he taught people to think. As one of his students said ‘the only ism you believe in is the syllogism’. On the whole the history of New Zealand Philosphy is a ‘From Log Cabin to White House’ tale, ‘From colonial obscurity through struggle and adversity to philosophical excellence’. But there are shadows in the picture. Some departments have nearly come to grief through bureaucratic and political misadventures, and it is hard to resist the suspicion that there is often an element of hostility to philosophers on the part of both university bureaucrats and fellow-academics. I speculate as to why this is the case (we are too argumentative and don’t confine our argumentative tendencies to the cloister) but conclude with some upbeat reflections. on the future of New Zealand Philosophy. (shrink)

In this paper I focus on a recently discussed phenomenon illustrated by sentences containing predicates of taste: the phenomenon of " perspectival plurality " , whereby sentences containing two or more predicates of taste have readings according to which each predicate pertains to a different perspective. This phenomenon has been shown to be problematic for (at least certain versions of) relativism. My main aim is to further the discussion by showing that the phenomenon extends to other perspectival expressions than predicates (...) of taste and by proposing a general solution to the problem raised by it on behalf of the relativist. The core claim of the solution (" multiple indexing ") is that utterances of sentences containing perspectival expressions should be evaluated with respect to (possibly infinite) sequences of perspective parameters. (shrink)

It is demonstrated that Hamblin's 15 tense theorem does not only hold for temporal logic with linear time but also for branching time. Furthermore three other theorems with finitely many tenses are shown.

In this book, William Brant inquires how violence is reduced. Social causes of violence are exposed. War, sexual domination, leadership, propagandizing and comedy are investigated. Legal systems are explored as reducers and implementers of violence and threats.

We present the logic $${\mathsf {LCB}}$$ LCB which is expressed in a propositional language constantly enriched by new atomic expressions. Our formal framework is the propositional doxastic logic $${\mathsf {KD45}}$$ KD 45 with the belief operator $${\mathcal {B}}$$ B, extended by the $${\mathcal {C}}$$ C operator, to be read it changes that.... We describe the changing beliefs of an agent who uses progressively expanding language. The approach presented here allows us to weaken pragmatic objections to the so-called principle of negative (...) retrospection accepted in $${\mathsf {KD45}}$$ KD 45 and the problem of logical omniscience. In what follows, we present the expanding propositional language used in our formalism, interpreted using an epistemic version of Kripke semantics. Next, we give a syntactic characterization of logic $${\mathsf {LCB}}$$ LCB and prove the soundness and completeness of $${\mathsf {LCB}}$$ LCB in respect to our semantics. Finally, we compare the idea of expanding language with the notion of agent awareness and we relate our formalism to two epistemic temporal logics. (shrink)

The logic of change formulated by K. Świętorzecka, has its motivation coming from the Aristotelian theory of substantial change which is undrstood as a transformation consisting in the disappearing and becoming of individual substances. The transition: becoming/disapearing (and conversely) is expressed in by the primitive operator C, to be read: it changes that …, and it is mapped by the progressively expanding language. We are interested in attributive changes of individual substances. We consider a formalism with two non-normal and not (...) mutually definable operators of possible and necessary change, inspired by Aristotelian distinction of accidental and essential attributes. From we adopt the idea that temporal concepts are defined via change operators, and the idea of an expanding language. In what follows, We axiomatise our new logic and describe its semantics, giving the proof of its completeness. We compare our formalism with selected modal logics. (shrink)

This paper specifies classes of framesmaximally omnitemporally characteristic for Thomas' normal modal logicT 2 + and for each logic in the ascending chain of Segerberg logics investigated by Segerberg and Hughes and Cresswell. It is shown that distinct a,scending chains of generalized Segerberg logics can be constructed from eachT n + logic (n 2). The set containing allT n + and Segerberg logics can be totally- (linearly-) ordered but not well-ordered by the inclusion relation. The order type of this ordered (...) set is *( + 1). Throughout the paper my approach is fundamentally semantical. (shrink)

Spatio-temporal logic is a variant of branching temporal logic where one of the so-called causal relations on spacetime plays the role of a time flow. Allowing only rational numbers as space and time co-ordinates, we prove that a first-order spatio-temporal theory over this flow is recursively enumerable if and only if the dimension of spacetime does not exceed 2. The situation is somewhat different compared to the case of real co-ordinates, because we establish that even dimension 2 does not permit (...) recursive enumerability in this case. The proof of the result on rational spacetime involves a more deeper portion of spacetime geometry than the corresponding, more evident result for the real co-ordinates. (shrink)

We define the paraconsistent supra-logic Pσ by a type-shift from the booleans o of propositional logic Po to the supra-booleans σ of the propositional type logic P obtained as the propositional fragment of the transfinite type theory Q defined by Peter Andrews (North-Holland Studies in Logic 1965) as a classical foundation of mathematics. The supra-logic is in a sense a propositional logic only, but since there is an infinite number of supra-booleans and arithmetical operations are available for this and other (...) types, virtually anything can be specified. The supra-logic is a generalization of Lukasiewicz's three-valued logic, with the intermediate value duplicated many times and ordered such that none of the copies of this value imply other ones, but it differs from Lukasiewicz's many-valued logics as well as from logics based on bilattices. There are several automated theorem provers for classical higher order logic (finite type theory) and it should be possible to modify these to our needs. (shrink)

ABSTRACT We investigate a logic PFD, as introduced in [FA]. In our notation, this logic is enriched with operators P> r(r € [0,1]) where the intended meaning of P> r φ is “the probability of φ (at a given world) is strictly greater than r”. We also adopt the semantics of [FA]: a class of “F-restricted probabilistic kripkean models”. We give a completeness proof that essentially differs from that in [FA]: our “peremptory lemma” (a lemma in PFD rather than about (...) it) facilitates the construction of a canonical model for PFD considerably. We show that this construction can be carried out using only finitary means, and also give a filtration-technique for the intended models. We then define an alternative (in some sense more natural) semantics for the logic, and show some of its properties. Finally, we prove decidability of the logic. (shrink)

Anderson-like ontological proofs, studied in this paper, employ contingent identity, free principles of quantification of the 1st order variables and classical principles of quantification of the 2nd order variables. All these theories are strongly complete wrt. classes of modal structures containing families of world-varying objectual domains of the 1st order and constant conceptual domains of the 2nd order. In such structures, terms of the 1st order receive only rigid extensions, which are elements of the union of all 1st order domains. (...) Terms of the 2nd order receive extensions and intensions. Given a family of preselected world-varying objectual domains of the 2nd order, non-rigid extensions of the 2nd order terms belong always to a preselected domain connected with a given world. Rigid intensions of the 2nd order terms are chosen from among members of a conceptual domain of the 2nd order, which is the set of all functions from the set of worlds to the union of all 2nd order preselected domains such that values of these functions at a given world belong to a preselected domain connected with this world. (shrink)

LetA be a quasi-manual with finite operations. Associate to each E = {e 1 ,..., en} εA the set ΓE of modal formulas: □(e 1 ⋁ ··· ⋁ en), ◊ei → ∼□(e 1 ⋁ ··· ⋁ ei−1 ⋁ ei+1 ⋁ ··· ⋁ en), i=1,..., n. Set Γ A = ώ{ΓE|E εA}. We show that supports ofA are in one-to-one correspondence with certain Kripke models of Γ A where the supports are given by {x ε |A ‖ ◊ x is true}.

The notion of quantum supports introduced by Foulis, Piron, and Randall can be used to construct combinatorial versions of contextualist hidden-variable models for finite quantum logics. The original logic can be uniquely recovered from appropriate such models as a solution of a combinatorial inverse problem. One can thus set up a classical ontology for a finite quantum logics that completely specifies it. Computer studies are used to explore the ideas.

Arguably, there is no substantial, general answer to the question of what makes for the approximate truth of theories. But in one class of cases, the issue seems simply resolved. A wide class of applied dynamical theories can be treated as two-component theories—one component specifying a certain kind of abstract geometrical structure, the other giving empirical application to this structure by claiming that it replicates, subject to arbitrary scaling for units etc., the geometric structure to be found in some real-world (...) dynamical phenomenon. In such a case, a theory is approximately true just if the one geometric structure approximately replicates the other (and if problems remain here, they are problems in geometry, of specifying suitable metric approximation relations, not conceptual problems). This article amplifies and defends this simple approach to approximate truth for dynamical theories. (shrink)

A logic focusing on the analytic a priori and explicitly rejecting the synthetic a priori developed in the early decades of the 20th century, largely through the efforts of the Logical Empiricists. This group was very influenced by Wittgenstein's early work Tractatus Logico-Philosophicus. But Wittgenstein himself, later on, departed from the Tractatus in significant ways that the Logical Empiricists did not follow. Wittgenstein came later to accept the synthetic a priori, and out of this insight comes a non-analytic logic that (...) differs from standard 20th century logic in many distinct ways. This paper details these differences. (shrink)

In this paper I try to answer four basic questions: (1) How the concept of God is to be represented? (2) Are there any logical principles governing it? (3) If so, what kind of logic lies behind them? (4) Can there be a logic of the concept of God? I address them by presenting a formal-logical account to the concept of God. I take it as a methodological desideratum that this should be done within the simplest existing logical formalism. I (...) start with first-order logic (FOL) with identity, and then show that its simplest modal extension (SQML, or the simplest quantified modal logic) is enough for us to formalize a minimally satisfactory theory of the concept of God. I focus exclusively on the monotheistic concept of God. (shrink)

This approach does not define a probability measure by syntactical structures. It reveals a link between modal logic and mathematical probability theory. This is shown (1) by adding an operator (and two further connectives and constants) to a system of lower predicate calculus and (2) regarding the models of that extended system. These models are models of the modal system S₅ (without the Barcan formula), where a usual probability measure is defined on their set of possible worlds. Mathematical probability models (...) can be seen as models of S₅. (shrink)

De re modality is eliminable if there is an effective translation of all wffs into non-de re equivalents. We cannot have logical equivalence unless 'logic' has odd theses, but we can have material equivalence by banning all essences, something the nonde re facts let us do, or by giving everything such humdrum essences as self-identity and banning the more interesting ones. Eliminability cannot be got from weaker assumptions, nor independent ones of even modest generality. The net philosophical import is that, (...) quite apart from the merits of essentialism, de re language has scant utility. (shrink)

In this paper, I present and motivate a modal set theory consistent with the idea that there is only one size of infinity.

In various arguments, Descartes relies on the principles that conceivability implies possibility and that inconceivability implies impossibility. Those principles are in tension with another Cartesian view about the source of modality, i.e. the doctrine of the free creation of eternal truths. In this paper, I develop a ‘two-modality’ interpretation of the doctrine of eternal truths which resolves the tension and I discuss how the resulting modal epistemology can still be relevant for the contemporary discussion.

The concepts of categorical diagnosis and conjectural diagnosis are introduced. It is argued that in diagnostic reasoning conjectural diagnosis plays a more important role than categorical diagnosis. Attention is called to the inevitable vagueness of clinical language and to the suitability of epistemic logic and fuzzy logic for diagnostic reasoning.

The paper considers the role of modality in the rational reconstruction of standpoints and arguments. The paper examines in what conditions modal markers can act as argumentative indicators and what kind of cues they provide for the reconstruction of argument. The paper critically re-examines Toulmin’s hypothesis that the meaning of the modals can be analyzed in terms of a field-invariant argumentative force and field-dependent criteria in the light of the Theory of Relative Modality developed within linguistic semantics, showing how this (...) theory can provide a more adequate model for exploiting the modals as indicators. The resulting picture confirms Toulmin’s intuition only in part: on the one hand the modals are always relational in nature and dependent on a contextual conversational background of propositions; on the other hand only epistemic-doxastic modals directly express a speech-act level inferential relation between a set of premises and a standpoint. Other modalities express relations (e.g. causal or final relations) better seen as part of the content of the argument whose argumentative relevance depends on the argumentation scheme employed. Thus non-epistemic modals function as argumentative indicators only indirectly. (shrink)

This paper discusses a new aporia, the aporia of future directed beliefs. This aporia contains three propositions: (1) It is possible that there is someone who is infallible that believes something about the future that is not historically settled, (2) it is necessary that someone is infallible if and only if it is necessary that everything she believes is true, and (3) it is necessary that all our beliefs are historically settled. Every claim in this set is intuitively plausible, and (...) there are interesting arguments for or against each of them. Nevertheless, {(1), (2), (3)} entails a contradiction. Consequently, at least one of the sentences in this set must be false. I consider some possible solutions to the problem and discuss some arguments for and against these solutions. Five solutions, in particular, stand out. Three solutions reject (1), one solution rejects (2), and one solution rejects (3). No solution is without problems, and it is not obvious which one we should choose. Yet, we have to give up at least one sentence in {(1), (2), (3)}. This is the nature of an aporia. (shrink)

In this paper I show that one version of motivational internalism follows from the so-called ideal observer theory. Let us call the version of the ideal observer theory used in this essay (IOT). According to (IOT), it is necessarily the case that it ought to be that A if and only if every ideal observer wants it to be the case that A. We shall call the version of motivational internalism that follows from (IOT) (moral) conditional belief motivational internalism (CBMI). (...) According to (CBMI), it is necessarily the case that, for every x: if x were an ideal observer, it would be the case that x believes that it ought to be that A only if x wants it to be the case that A. Given that it is necessarily true that no ideal observer has any false beliefs, (IOT) entails (CBMI). Or, so I shall argue. (shrink)

The Moral Law is fulfilled iff everything that ought to be the case is the case, and The Good is realised in a possible world w at a time t iff w is deontically accessible from w at t. In this paper, I will introduce a set of temporal modal deontic systems with propositional quantifiers that can be used to prove some interesting theorems about The Moral Law and The Good. First, I will describe a set of systems without any (...) propositional quantifiers. Then, I will show how these systems can be extended by a couple of propositional quantifiers. I will use a kind of TxW semantics to describe the systems semantically and semantic tableaux to describe them syntactically. Every system will include a constant · that stands for The Good. ‘·’ is read as ‘The Good is realised’. All systems that contain the propositional quantifiers will also include a constant '*' that stands for The Moral Law. '*' is read as ‘The Moral Law is fulfilled’. I will prove that all systems (without the propositional quantifiers) are sound and complete with respect to their semantics and that all systems (including the extended systems) are sound with respect to their semantics. It is left as an open question whether or not the extended systems are complete. (shrink)

In this paper, I will develop a new theory of the nature of happiness, or “perfect happiness.” I will examine what perfect happiness is and what it is not and I will try to answer some fundamental questions about this property. According to the theory, which I shall call “the fulfillment theory,” perfect happiness is perfect fulfillment. The analysis of happiness in this paper is a development of the old idea that happiness is getting what you want and can be (...) classified as a kind of desire-satisfaction theory. According to the fulfillment theory of happiness, it is necessarily the case that an individual x is perfectly happy if and only if all x’s wants are fulfilled. The interpretation of this basic definition is important, since the consequences of the particular version defended in this essay are radically different from the consequences of many other popular theories of happiness. The fulfillment theory is also quite different from most other desire-satisfaction theories of happiness. We will see that it has many interesting consequences and that it can be defended against some potentially serious counterarguments. The upshot is that the analysis of (perfect) happiness developed in the present paper is quite attractive. (shrink)

In this paper, I will develop a set of boulesic-doxastic tableau systems and prove that they are sound and complete. Boulesic-doxastic logic consists of two main parts: a boulesic part and a doxastic part. By ‘boulesic logic’ I mean ‘the logic of the will’, and by ‘doxastic logic’ I mean ‘the logic of belief’. The first part deals with ‘boulesic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of boulesic expression: ‘individual x wants it to be (...) the case that’ and ‘individual x accepts that it is the case that’. The second part deals with ‘doxastic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of doxastic expression: ‘individual x believes that’ and ‘it is imaginable to individual x that’. Boulesic-doxastic logic investigates how these concepts are related to each other. Boulesic logic is a new kind of logic. Doxastic logic has been around for a while, but the approach to this branch of logic in this paper is new. Each system is combined with modal logic with two kinds of modal operators for historical and absolute necessity and predicate logic with necessary identity and ‘possibilist’ quantifiers. I use a kind of possible world semantics to describe the systems semantically. I also sketch out how our basic language can be extended with propositional quantifiers. All the systems developed in this paper are new. (shrink)

In this paper, I develop a new set of doxastic logical systems and I show how they can be used to solve several well-known problems in doxastic logic, for example the so-called problem of logical omniscience. According to this puzzle, the notions of knowledge and belief that are used in ordinary epistemic and doxastic symbolic systems are too idealised. Hence, those systems cannot be used to model ordinary human or human-like agents' beliefs. At best, they can describe idealised individuals. The (...) systems in this paper can be used to symbolise not only the doxastic states of perfectly rational individuals, but also the beliefs of finite humans. Proof-theoretically, I will use a tableau technique. Every system is combined with predicate logic with necessary identity and ‘possibilist’ quantifiers and modal logic with two kinds of modal operators for relative and absolute necessity. The semantics is a possible world semantics. Finally, I prove that every tableau system in the paper is sound and complete with respect to its semantics. (shrink)

One way to obtain a comprehensive semantics for various systems of modal logic is to use a general notion of non-normal world. In the present article, a general notion of modal system is considered together with a semantic framework provided by such a general notion of non-normal world. Methodologically, the main purpose of this paper is to provide a logical framework for the study of various modalities, notably prepositional attitudes. Some specific systems are studied together with semantics using non-normal worlds (...) of different kinds. (shrink)

The principal aim of this essay is to discuss some logical features of the so-called Classical model of cognitive architecture as it is advocated by J. Fodor and Z. Pylyshyn in their much discussed article 'Connectionism and Cognitive Architecture: A Critical Analysis'. It is pointed out that their structural assumptions have consequences of a logical kind which call into question the view that the Classical architecture (in their sense) can be employed to model human cognition. It seems that the consequences (...) have escaped Fodor and Pylyshyn's notice, or else they have failed to appreciate them, since some of their claims evidently conflict with them. It is also investigated whether the human mind can be characterized as being logical in some weaker sense of logic. Furthermore, it is argued that J. H. Fetzer's view that it is a semiotic system is more realistic than the Classical model, but the distinction he suggests between human cognition and other kinds may be problematic. (shrink)

The work of Hugh MacColl (1837–1909) suffered the same fate after his death as before it:despite being vaguely alluded to and in part even commended, on the whole it has remained an unknown quantity. Even worse, those of his ideas which have played a decisive role in the history of logic have been credited to his successors; this is especially the case with the definition of strict implication and the first formal development of formal modal logic. This paper takes an (...) initial step towards a rectification of this unfortunate misrepresentation, presenting a bibliography of MacColl’s most significant publications with particular regard to their reception. (shrink)