In a series of papers, Sperber provides the following analysis of the phenomenon of ill-understood belief (or 'quasi-belief', as I call it): (i) the quasi-believer has a validating meta-belief, to the effect that a certain representation is true; yet (ii) that representation does not give rise to a plain belief, because it is 'semi-propositional'. In this paper I discuss several aspects of this treatment. In particular, I deny that the representation accepted by the quasi-believer is semantically indeterminate, and I reject (...) Sperber's claim that quasi-belief is a credal attitude distinct from plain belief. (shrink)

My first paper on the Is/Ought issue. The young Arthur Prior endorsed the Autonomy of Ethics, in the form of Hume’s No-Ought-From-Is (NOFI) but the later Prior developed a seemingly devastating counter-argument. I defend Prior's earlier logical thesis (albeit in a modified form) against his later self. However it is important to distinguish between three versions of the Autonomy of Ethics: Ontological, Semantic and Ontological. Ontological Autonomy is the thesis that moral judgments, to be true, must answer to a realm (...) of sui generis non-natural PROPERTIES. Semantic autonomy insists on a realm of sui generis non-natural PREDICATES which do not mean the same as any natural counterparts. Logical Autonomy maintains that moral conclusions cannot be derived from non-moral premises.-moral premises with the aid of logic alone. Logical Autonomy does not entail Semantic Autonomy and Semantic Autonomy does not entail Ontological Autonomy. But, given some plausible assumptions Ontological Autonomy entails Semantic Autonomy and given the conservativeness of logic – the idea that in a valid argument you don’t get out what you haven’t put in – Semantic Autonomy entails Logical Autonomy. So if Logical Autonomy is false – as Prior appears to prove – then Semantic and Ontological Autonomy would appear to be false too! I develop a version of Logical Autonomy (or NOFI) and vindicate it against Prior’s counterexamples, which are also counterexamples to the conservativeness of logic as traditionally conceived. The key concept here is an idea derived in part from Quine - that of INFERENCE-RELATIVE VACUITY. I prove that you cannot derive conclusions in which the moral terms appear non-vacuously from premises from which they are absent. But this is because you cannot derive conclusions in which ANY (non-logical) terms appear non-vacuously from premises from which they are absent Thus NOFI or Logical Autonomy comes out as an instance of the conservativeness of logic. This means that the reverse entailment that I have suggested turns out to be a mistake. The falsehood of Logical Autonomy would not entail either the falsehood Semantic Autonomy or the falsehood of Ontological Autonomy, since Semantic Autonomy only entails Logical Autonomy with the aid of the conservativeness of logic of which Logical Autonomy is simply an instance. Thus NOFI or Logical Autonomy is vindicated, but it turns out to be a less world-shattering thesis than some have supposed. It provides no support for either non-cognitivism or non-naturalism. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

Arthur Prior’s argument for the A-theory of time in “Thank Goodness That’s Over” is perhaps his most famous and well-known non-logical work. Still, I think that this paper is one of his most misunderstood works. Because of this, much of its brilliance has yet to be properly appreciated. In this paper, I suggest that the explanation of this is that it has been treated as though it were following the standard model for a piece of Analytic philosophy. That is, it (...) has been assumed that what Prior was doing was deductively demonstrating the truth of a proposition which can be discussed via any sentences with the same semantic content. Here, I argue that this assumption is wrong on two fronts: Most importantly, the strongest reading of the structure of Prior’s argument is as an abduction rather than as a deduction. Many of the most important lessons of the argument are lost by focusing on the bare propositional content of its premise and conclusion statements. In other words, we can learn as much from the manner in which this argument is presented and expressed as we can from that which is expressed. (shrink)

In his Formal Logic, Arthur N. Prior declared that Jan Łukasiewicz's logical notation is ‘unquestionably the best logical symbolism for most purposes’. Whether he had a substantive, and...

Tarski 1968 makes a move in the course of providing an account of ?definitionally equivalent? classes of algebras with a businesslike lack of fanfare and commentary, the significance of which may accordingly be lost on the casual reader. In ?1 we present this move as a response to a certain difficulty in the received account of what it is to define a function symbol (or ?operation symbol?). This difficulty, which presents itself as a minor technicality needing to be got around (...) especially for the case of symbols for zero-place functions (for ?distinguished elements?), has repercussions?not widely recognised?for the account of functional completeness in sentential logic. A similarly stark comment in Church 1956 reveals an appreciation of this difficulty, though not every subsequent author on the topic has taken the point. We fill out this side of the picture in ?2. The discussion of functional completeness in ?2 is supplemented by some remarks on what is involved in defining a connective, which have been included in an Appendix. The emphasis throughout is on conceptual clarification rather than on proving theorems, and the main body of the paper may be regarded as an elaboration on the remarks just mentioned by Tarski and Church. The Appendix (?3) is intended to be similarly clarificatory, though this time with some corrective intent, of remarks made in and about Makinson 1973. (shrink)

Hume seems to claim that there does not exist a valid argument that has all non-ethical sentences as premises and an ethical sentence as its conclusion. Starting with Prior, a number of counterexamples to this claim have been proposed. Unfortunately, all of these proposals are controversial. Even the most plausible have a premise that seems like it might be an ethical sentence or a conclusion that seems like it might be non-ethical. Since it is difficult to tell whether any of (...) these counterexamples are genuine, we need a taxonomy that sorts out ethical sentences from non-ethical ones. We need to know the difference between an ‘Is’ and an ‘Ought’. In the first part of the paper, I establish the need for a taxonomy. I consider some of the most influential ‘Is’–‘Ought’ derivations. These include proposals by Prior and Searle. I argue that each proposal has a premise whose status as ethical or non-ethical is difficult to determine. In the second part of the paper, I consider taxonomies proposed by Karmo and Maitzen. I argue against both taxonomies. I end with the claim that we need a taxonomy of ethical sentences and that none of the current proposals are adequate. (shrink)

A. N. Prior’s writings should obviously be studied already for historical reasons. His inventions of modern temporal logic and hybrid logic are clearly important events in the history of logic. But the enduring importance of studying his works also rests on his methodological approach, which remains highly relevant also for systematical reasons. In this paper we argue that Prior’s formulation in the 1950s of a tense-logical paradigm for the study of time should be understood in the light of at least (...) three other principles or perspectives which were manifest already in his studies during the 1940s and further developed in the 1950s: his emphasis on the value of interdisciplinary studies, his reflections on formalisation and his view of the role of symbolic logic in conceptual studies and in the philosophy of science. Our investigation into Prior’s basic tenets and principles makes extensive use of Prior’s Nachlass. It is thereby also exemplified how his correspondence and unpublished papers contain important information for a deeper understanding of Prior’s paradigm for the study of time. (shrink)

Our utterances are typically if not always "situated," in the sense that they are true or false relative to unarticulated parameters of the extra-linguistic context. The problem is to explain how these parameters are determined, given that nothing in the uttered sentences indicates them. It is tempting to claim that they must be determined at the level of thought or intention. However, as many philosophers have observed, thoughts themselves are no less situated than utterances. Unarticulated parameters need not be mentally (...) represented. In this paper, I try to make precise the notion of representation at stake here. In one sense of 'representation', something is represented if it is inferentially relevant. In another, less demanding sense, something is represented if it is relevant to the construction of a context-sensitive, ad hoc concept. Ad hoc concepts act as "proxies" for cognitively more demanding representations. They "imitate" the latter's epistemic and pragmatic roles while being inferentially less sophisticated. Thus, there are two senses in which a thought can be said to be situated: (1) its truth-value is relative to a non-represented contextual parameter, (2) its truth-value is not itself relative, but it involves a context-sensitive, ad hoc concept. (shrink)

In celebrating Arthur Prior we celebrate what he gave to the world. Much of this is measured by what others have made of his ideas after his death. The focus of this paper is a little different. It looks at what Prior himself thought he was accomplishing. In particular it considers Prior’s attitude to the semantic metatheory of the logics that he was interested in. The paper sets out some characteristics of the metalogical study of intensional languages in terms of (...) an indexical theory of truth conditions stated in the language of set theory. In examining Prior’s work using these characteristics, it emerges that Prior had serious reservations about this way of studying modal and tense logics. (shrink)

Two periods in the history of logic and philosophy are characterized notably by vivid interest in self-referential paradoxical sentences in general, and Liar sentences in particular: the later medieval period (roughly from the 12th to the 15th century) and the last 100 years. In this paper, I undertake a comparative taxonomy of these two traditions. I outline and discuss eight main approaches to Liar sentences in the medieval tradition, and compare them to the most influential modern approaches to such sentences. (...) I also emphasize the aspects of each tradition that find no counterpart in the other one. It is expected that such a comparison may point in new directions for future research on the paradoxes; indeed, the present analysis allows me to draw a few conclusions about the general nature of Liar sentences, and to identify aspects that would require further investigation. (shrink)

Perhaps if the future existed, concretely and individually, as something that could be discerned by a better brain, the past would not be so seductive: its demands would he balanced by those of the future. Persons might then straddle the middle stretch of the seesaw when considering this or that object. It might be fun. But the future has no such reality (as the pictured past and the perceived present possess); the future is but a figure of speech, a specter (...) of thought. (shrink)

In this research I will focus on a basis for a formal model based on an alternative kind of logic invented by Hans Götzsche: Occurrence Logic (Occ Log), which is not based on truth values and truth functionality. Also, I have taken into account tense logic developed and elaborated by A. N. Prior. In this article I will provide a conceptual and logical foundation for formal Occurrence Logic based on symbolic logic and will illustrate the most important relations between symbolic (...) logic and Occurrence Logic. There will be a special need to focus on arguments based on symbolic occurrence logic. The interrelationships and dependencies between symbolic logic and Occ Log could be conducive to an approach that can express and analyse ‘the occurrences of the world’s descriptions based on various logical principles at different moments’. Symbolic Occ Log checks the occurrence conditioning and the priority of occurrences by employing occurrence values. I shall conclude that the desired approach could gradually support me in providing a truth-functional independent first-order predicate calculus that could work on semantic analysis of different propositions within world descriptions. (shrink)

In this paper I explore three related topics emerging from Prior's work on the logic of time. First, what is the proper province of logic, if any? Is temporal (modal) logic just logic, on a par with the paradigmatic case of first-order quantification theory or even simple propositional logic? Second, what counts as an interpretation of a formal system? In particular, can formal semantics provide an interpretation? Third, what is the proper role of the meta-theory? In connection with this last (...) question we will see how Prior's attitude towards instants of time may teach us something about the analogous case of possible worlds. (shrink)

Special issue: "Reflecting on the Legacy of C.I. Lewis: Contemporary and Historical Perspectives on Modal Logic".