This article intends to show that the defense of “understanding” as one of the major goals of science education can be grounded on an anti-reductionist perspective on testimony as a source of knowledge. To do so, we critically revisit the discussion between Harvey Siegel and Alvin Goldman about the goals of science education, especially where it involves arguments based on the epistemology of testimony. Subsequently, we come back to a discussion between Charbel N. El-Hani and Eduardo Mortimer, on the one (...) hand, and Michael Hoffmann, on the other, striving to strengthen the claim that rather than students’ belief change, understanding should have epistemic priority as a goal of science education. Based on these two lines of discussion, we conclude that the reliance on testimony as a source of knowledge is necessary to the development of a more large and comprehensive scientific understanding by science students. (shrink)

‘What is characteristic of every mental activity’, according to Brentano, is ‘the reference to something as an object. In this respect every mental activity seems to be something relational.’ But what sort of a relation, if any, is our cognitive access to the world? This question – which we shall call Brentano’s question – throws a new light on many of the traditional problems of epistemology. The paper defends a view of perceptual acts as real relations of a subject to (...) an object. To make this view coherent, a theory of different types of relations is developed, resting on ideas on formal ontology put forward by Husserl in his Logical Investigations and on the theory of relations sketched in Smith's "Acta cum fundamentis in re". The theory is applied to the notion of a Cambridge change, which proves to have an unforeseen relevance to our understanding of perception. (shrink)

It is often thought that endowing a demonstrative with a Fregean sense leaves no room for maintaining that it is also a rigid designator. In addition, some philosophers claim that indexicals - surely the paradigms of singular reference - pose a serious threat to the Fregean sense/ reference approach as they do not comply with the view that singular terms have Fregean senses. In this paper I argue that neither of these is true.

The standard view of "believes" and other propositional attitude verbs is that such verbs express relations between agents and propositions. A sentence of the form “S believes that p” is true just in case S stands in the belief-relation to the proposition that p; this proposition is the referent of the complement clause "that p." On this view, we would expect the clausal complements of propositional attitude verbs to be freely intersubstitutable with their corresponding proposition descriptions—e.g., "the proposition that p"—as (...) they are in the case of "believes." In many cases, however, intersubstitution of that-clauses and proposition descriptions fails to preserve truth value or even grammaticality. These substitution failures lead some philosophers to reject the standard view of propositional attitude reports. Others conclude that propositional attitude verbs are systematically ambiguous. I reject both these views. On my view, the that-clause complements of propositional attitude verbs denote propositions, but proposition descriptions do not. (shrink)

Based on the notion of a trope, this paper gives a novel analysis of identificational sentences such as 'this is Mary','this is a beautiful woman', 'this looks like Mary', or 'this is the same lump of clay, but not the same statue as that'.

What is logical relevance? Anderson and Belnap say that the “modern classical tradition [,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance.” But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds, less deeply with the containment of classes, and least of all with variable sharing in the Anderson–Belnap manner. Thus modern classical logicians such as Peirce, Frege, Russell, Wittgenstein, and (...) Quine are implicit relevantists on the deepest level. In showing this, I reunite two fields of logic which, strangely from the traditional point of view, have become basically separated from each other: relevance logic and diagram logic. I argue that there are two main concepts of relevance, intensional and extensional. The first is that of the relevantists, who overlook the presence of the second in modern classical logic. The second is the concept of truth-ground containment as following from in Wittgenstein’s Tractatus. I show that this second concept belongs to the diagram tradition of showing that the premisses contain the conclusion by the fact that the conclusion is diagrammed in the very act of diagramming the premisses. I argue that the extensional concept is primary, with at least five usable modern classical filters or constraints and indefinitely many secondary intensional filters or constraints. For the extensional concept is the genus of deductive relevance, and the filters define species. Also following the Tractatus, deductive relevance, or full truth-ground containment, is the limit of inductive relevance, or partial truth-ground containment. Purely extensional inductive or partial relevance has its filters or species too. Thus extensional relevance is more properly a universal concept of relevance or summum genus with modern classical deductive logic, relevantist deductive logic, and inductive logic as its three main domains. (shrink)

I want to discuss, in some detail, a short section from Quine’s Philosophy of Logic. It runs from pages 10 to 13 of the second, revised edition of the book and carries the subheading ‘Truth and semantic ascent’.1 In these two and a half pages, Quine presents his well-known account of truth as a device of disquotation, employing what I call Quine’s Ladder. The section merits scrutiny, for it has become the central document for contemporary deflationary views about truth.

In Book Γ of the Metaphysics Aristotle states and attempts to prove what he calls the basic principle of the science of being as being: the law of non‐contradiction. In this paper I defend an interpretation of his proof, inspired by Elizabeth Anscombe's 1961 essay in ‘Three Philosophers’, though some of its features were remarked on by Lukasiewicz in 1910, according to which Aristotle is proving this principle only for substance predicates, and that it is to be understood as the (...) basic principle of metaphysics rather than of logic. It is the principle that every substance has an essential nature, and if it is of the essential nature of x to be F then it cannot be of the essential nature of x to be not‐F since then x's being F and x's being not‐F would be the same. He puts it by saying that in such a case F and not‐F would ‘signify the same’ for x. Since they do not, x cannot be both. (shrink)

In this article I object to Le Poidevin's contention that relative identity is beset with an infinite metaphysical regress. I argue, first, that since Le Poidevin's regress argument presupposes a direct theory of reference, it does not apply to accounts of relative identity which reject this account of reference. I argue, second, that Le Poidevin's regress is not inevitable for one who accepts a direct account of reference, since it does not apply to the formal logic of relative identity which (...) van Inwagen uses to articulate and defend the mysteries of the Trinity and the Incarnation. (shrink)

In his “Space, supervenience and substantivalism”, Le Poidevin proposes a substantivalism in which space is discrete, implying that there are unmediated spatial relations between neighboring primitive points. This proposition is motivated by his concern that relationism suffers from an explanatory lacuna and that substantivalism gives rise to a vicious regress. Le Poidevin implicitly requires that the relationist be committed to the “only x and y ” principle regarding spatial relations. It is not obvious that the relationist is committed to this (...) principle in such a context. An additional motivation for Le Poidevin's argument, that space should be considered to be discrete, is that he believes that substantivalists are committed to a vicious regress. I show that the regress is in fact not of the vicious variety. These two main arguments show that Le Poidevin's suggestion that we drop the density postulate for space is unnecessary. (shrink)

Anselm’s On the Incarnation of the Word is presented as a letter to Pope Urban II for the purpose of exposing and correcting the theological errors of Roscelin of Compiègne, who maintained that since only the Son became incarnate, we must conclude that the Father, the Son and the Holy Spirit are numerically distinct substances. In this paper I argue that Anselm’s rejection of this conclusion involves an account of the Holy Trinity which includes a strongly relativized conception of identity, (...) that is, one which allows an object x and an object y to be the same F, but different Gs. I further contend that Anselm buttresses this account with two non-theological examples of relative identity. Although it may well be the case that advocates of Latin Trinitarianism are generally committed to such an account, since they affirm that the Father is the same substance as the Son but not the same person as the Son, I take Anselm’s defense of this position to be theologically significant, first, because it may well be the first explicit defense of Relative Trinitarianism, and second, because Anselm’s position as a bishop and a Doctor of the Church is an indication of its theological soundness. (shrink)

We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first two kinds of (...) import, the third one being trivial and rule out the squares where at least one relation does not hold. This leads to the following results: (1) three squares are valid when the domain is non-empty; (2) one of them is valid even in the empty domain: the square can thus be saved in arbitrary domains and (3) the aforementioned eight propositions give rise to a cube, which contains two more (non-classical) valid squares and several hexagons. A classical solution to the problem of existential import is thus possible, without resorting to deviant systems and merely relying upon the symbolism of First-order Logic (FOL). Aristotle’s system appears then as a fragment of a broader system which can be developed by using FOL. (shrink)

Ways and words about infinity have frequently hidden a continuing paradox inspired by Zeno. The basic puzzle is the tortoise's – Mr T's – Extension Challenge, the challenge being how any extension, be it in time or space or both, moving or still, can yet be of an endless number of extensions. We identify a similarity with Mr T's Deduction Challenge, reported by Lewis Carroll, to the claim that a conclusion can be validly reached in finite steps. Rejecting common solutions (...) to both challenges, we use a Wittgensteinian approach for dissolution, noting also that other paradoxes, such as the Surprise Examination and Yablo's, trap us inconsistently into similar endlessnesses. In so doing, we encounter a hopping flea, generate a proportionality paradox and consider the knight's move in chess. (shrink)

Despite the 'progressive' influence of the English Plowden Report and Scottish Primary Memorandum on British primary curricula from the 1960s onwards, secondary education has generally continued to follow a more traditional subject-centred route and post-war educational theorists have not generally been favourably inclined to other than subject-based modes of curriculum planning and organisation. However, in the light of current curriculum reviews on both sides of the Scottish border-callingfor more educationally meaningful curricula-the perennial issue of how school knowledge might best be (...) ordered for the coherent educational experience of pupils seems worth revisiting. To this end, this paper examines some of the influential post-war philosophical arguments against integrated and interdisciplinary approaches to the curricular organisation of knowledge, concluding that they are not as compelling as they might formerly have seemed. (shrink)

The author puts forth an approach to propositional attitude contexts based upon the view that one does not have beliefs of ordinary extensional entitiessimpliciter. Rather, one has beliefs of such entities as presented in various manners. Roughly, these are treated as beliefs of ordered pairs — the first member of which is the ordinary extensional entity and the second member of which is a predicate that it satisfies. Such an approach has no difficulties with problems involving identity, such as of (...) The Morning Star and The Evening Star (section 1). Given the second members of the pairs, the modes of presentation, it is quite natural to allow exportation everywhere. There is no need for essentialism. (One also can have non-essentialistic modal logic if one grants analyticity or the like.) (section 2). Given that the second member of the pair need only be one that is satisfied by the entity that is the first member (and need not be specificative), the method has no difficulties when one is concerned only with discriminations (and not specifications) (section 3). When this method is combined with the Frege-Carnap method of descriptions, fictional entities can be accommodated; Goodman''s unicorn-picture and the like can be brought within a Tarskian semantics; and Geach''s difficulties with intentional identity appear to be handled (section 4). Given the author''s ordered pair construals, there appears to be no additional need for notional construals; i.e., the author''s one unified method appears satisfactory for dealing with both traditionalde re (relational) andde dicto (notional) construals. The Paradox of the Knower and the like do not appear formulatable against the author''s approach. (section 5). The author also argues against the basic principles behind the Church-Langford translation argument (section 6). (shrink)

This paper is a brief discussion of the famous 'Third Man Argument' as it appears in Plato's dialogue Parmenides . I mention, criticise and refine the most influential analytic approach to the argument; show that the actual conclusion of the argument is different from the one attributed to it by the majority of scholars; and elaborate two responses to the argument, both of which shed interesting light on the Theory of Forms.

A material object is constituted by a sum of parts all of which are essential to the sum but some of which seem inessential to the object itself. Such object/sum of parts pairs include my body/its torso and appendages and my desk/its top, drawers, and legs. In these instances, we are dealing with objects and their components. But, fundamentally, we may also speak, as Locke does, of an object and its constitutive matter—a “mass of particles”—or even of that aggregate and (...) the sum of subatomic particles ‘making it up’. The “problem of material constitution” (henceforth, PMC) is generated by assuming inter alia that the members of any such pair are numerically identical, that is, that the constituted and the constituting are one and the same thing. (shrink)

An introduction to composition, persistence, and identity.

This chapter explores the metaphysical views about higher-order logic held by two individuals responsible for introducing it to philosophy: Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970). Frege understood a function at first as the remainder of the content of a proposition when one component was taken out or seen as replaceable by others, and later as a mapping between objects. His logic employed second-order quantifiers ranging over such functions, and he saw a deep division in nature between objects and functions. (...) Russell understood propositional functions as what is obtained when constituents of propositions are replaced by variables, but eventually denied that they were entities in their own right. Both encountered contradictions when supposing there to exist as many objects as functions, and both adopted views about the meaningfulness of higher-order discourse that were difficult to state from within their own strictures. (shrink)

Over the past fifty years the philosophy of language and mind has been dominated by a nondescriptivist approach to content and reference. This book attempts to recast and systematize that approach by offering an indexical model in terms of mental files. According to Recanati, we refer through mental files, the function of which is to store information derived through certain types of contextual relation the subject bears to objects in his or her environment. The reference of a file is determined (...) relationally, not satisfactionally, so a file is not to be equated to the body of (mis-)information it contains. Mental files are the mental equivalent of singular terms, and the reference of linguistic expressions is inherited from that of the files we associate with them. On this approach, mental files, the vehicles of singular thought, do all the work of so-called 'modes of presentation' in Fregean and neo-Russellian theories. (shrink)

Recently, I’ve championed the doctrine that fundamentally different sorts of things exist in fundamentally different ways.1 On this view, what it is for an entity to be can differ across ontological categories.2 Although historically this doctrine was very popular, and several important challenges to this doctrine have been dealt with, I suspect that contemporary metaphysicians will continue to treat this view with suspicion until it is made clearer when one is warranted in positing different modes of existence.3 I address this (...) concern here. The question of when to posit ways of being is closely related to a more general question: when should one think that some philosophically interesting expression is analogous? Accordingly, my strategy here is as follows. First, I briefly explain my interpretation of ontological pluralism, the doctrine that there are ways of being.4 Second, I introduce the notion of an analogous term, and show how, on most ways of implementing ontological pluralism, “existence” is analogous. Third, I discuss two sufficient conditions for when one is warranted in claiming that a philosophically interesting term is analogous. Fourth, I present a series of ontological schemes, each of which satisfies at least one of the sufficient conditions. The upshot is this: if you are attracted to one of these ontologies, you have reason to believe in ways of being. The careful reader will have noted the apparent modesty of my conclusion. Unfortunately, I do not believe that one could ever be rationally required to believe in ways of being. Still, in general a metaphysic is a live option to the extent that it is shown to be rationally permissible to believe. Since the apparent consensus among contemporary analytic metaphysicians is that believing that things can exist in different ways is silly or confused, establishing the rational permissibility of belief in ways of being is a non-trivial task. Let us begin. (shrink)

Frege's theory of indirect contexts and the shift of sense and reference in these contexts has puzzled many. What can the hierarchy of indirect senses, doubly indirect senses, and so on, be? Donald Davidson gave a well-known 'unlearnability' argument against Frege's theory. The present paper argues that the key to Frege's theory lies in the fact that whenever a reference is specified (even though many senses determine a single reference), it is specified in a particular way, so that giving a (...) reference implies giving a sense; and that one must be 'acquainted' with the sense. It is argued that an indirect sense must be 'immediately revelatory' of its reference. General principles for Frege's doctrine of sense and reference are sated, for both direct and indirect quotation, to be understood iteratively. I also discuss Frege's doctrine of tensed and first person statements in the light of my analysis. The views of various other authors are examined. The conclusion is to ascribe to Frege an implicit doctrine of acquaintance similar to that of Russell. (shrink)

Abstract Although expressivist theories have been applied to many normative discourses (moral, rationality, knowledge, etc.), the normative discourse of epistemic justification has been somewhat neglected by expressivists. In this paper, I aspire to both remedy this unfortunate situation and introduce a novel version of expressivist theory: Habits-Expressivism. To pave the way for habits-expressivism, I turn to Allan Gibbard's (1990, 2003, 2008) seminal work on expressivism. I first examine Gibbard's (2003, 2008) late plan-reliance expressivism and argue that it faces certain problems (...) when applied to epistemic justification discourse. As a response to these problems, I go on to introduce habits-expressivism and argue that not only does it avoid the identified problems for plan-reliance-expressivism, but it also captures the basic attractions of both plan-reliance expressivism and Gibbard's (1990) early theory of norm-expressivism. (shrink)

Expressivism can make space for normative objectivity by treating normative stances as pro or con attitudes that can be correct or incorrect. And it can answer the logical challenges that bedevil it by treating a simple normative assertion not merely as an expression of a normative stance, but as an expression of the endorsement of a proposition that is true if and only if that normative stance is correct. Although this position has superficial similarities to normative realism, it does full (...) justice to the core expressivist thesis that, at bottom, a normative assertion expresses a normative stance rather than a factual belief. (shrink)

Most interpretations of Aristotle’s Posterior Analytics believe that the term ‘ameson’ is used to describe the principles or foundations of a given system of justification or explanation as epistemically prior to or more fundamental than the other propositions in the system. Epistemic readings (as I shall call them) arguably constitute a majority in the secondary literature. This predominant view has been challenged by Robin Smith (1986) and Michael Ferejohn (1994; 2013), who propose interpretations that should be classified as non-epistemic according (...) to the definition above. My aim in this article is purely negative. I intend to show that these non-epistemic interpretations are liable to serious objections and are in conflict with some important features of Aristotle’s theory of demonstration. (shrink)

The paper has two parts: First, I describe a relatively popular thesis in the philosophy of propositional attitudes, worthy of the name ‘taking tense seriously’; and I distinguish it from a family of views in the metaphysics of time, namely, the A-theories (or what are sometimes called ‘tensed theories of time’). Once the distinction is in focus, a skeptical worry arises. Some A-theorists maintain that the difference between past, present, and future, is to be drawn in terms of what exists: (...) growing-block theorists eschew ontological commitment to future entities; presentists, to future and past entities. Others think of themselves as A-theorists but exclude no past or future things from their ontology. The metaphysical skeptic suspects that their attempt to articulate an ‘eternalist’ version of the A-theory collapses into merely ‘taking tense seriously’– a thesis that does not imply the A-theory. The second half of the paper is the search for a stable eternalist A-theory. It includes discussion of temporary intrinsics, temporal parts, and truth. (shrink)

Peter Geach frequently showed the relevance of some of Frege's insights to contemporary philosophical debates, such as that which Geach called “the Frege Point” – “a proposition may occur in discourse now asserted, now unasserted, and yet be recognizably the same proposition”. Geach argued against a variety of “expressivist” accounts of certain propositions that their proponents could not explain the significance of such propositions in subordinate clauses. The paper extends Geach's argument to show that “the Frege Point” presents a powerful (...) challenge to any attempt, such as those influenced by the later Wittgenstein, to equate meaning with use. (shrink)

A theory of syllogistic reasoning is proposed, derived from the medieval doctrine of 'distribution of terms'. This doctrine may or may not furnish an adequate ground for the logic of the syllogism but does appear to illuminate the psychological processes involved. Syllogistic thinking is shown to have its origins in the approach and avoidance behaviour of pre-verbal organisms and, in verbal (human) organisms, to bridge the gap between the intuitive grasp shown by most of us of the validity of simple (...) logical arguments and the failure of intuition in more complex arguments that require resort to calculation. Some difficulties are considered affecting the use of syllogisms as experimental material. These include failure on the part of the investigator to take account of the fact that a syllogism is always part of a continuing argument in which the topic of the argument is known to all parties and the possibility that subjects may find ways of appearing to solve syllogisms without actually doing so. (shrink)

This paper provides a new argument for a position of Crispin Wright's: given that ethical statements can be embedded within all sorts of sentential operators and are subject to definite standards of warrantedness, they must have truth conditions. Allan Gibbard's normative logic' is the only noncognitivist logic that stands a chance of avoiding Geach's Fregean objection. But what, according to Gibbard, is the point of avoiding inconsistency in one's ethical statements? He must say that it is to ensure that one's (...) ethical statements have a property that has certain features. But the only property that has those features is truth. (shrink)

Both the semantics of fictional discourse and the semantics of indexicality are canonical topics in the philosophy of language, on which there exists well-known significant literature. However, the same cannot be said for the terrain where they overlap. That is, the distinctive issues raised by fictive uses of indexicals and demonstratives have not been extensively studied per se. The aim of the present essay is to shed some light on this terrain, and to advance our understanding of some of these (...) issues. As it happens, accounting for indexicals in fiction requires the use of innovative new tools. In particular, the standard, familiar taxonomy of types / tokens / utterances is not sufficient to account for the complex cognitive significance and truth-conditions, unique to these kinds of case. For instance: it is widely recognized that, with indexicals generally, semantic properties attach to utterances, not to types or to tokens. But in fiction there are no utterances (in the relevant sense). An innovative notion is required, which I call an “indexed token”. This account of indexicals in fiction, based on the notion of an indexed token, is developed within a Perry (2012)-inspired pluri-propositionalist framework. As such, the present essay constitutes an original application of that framework, extending its already impressive reach. (shrink)

ABSTRACT The aim of this paper is to provide a sketch on the way Nāgārjuna deals with the idea of 'relation'. The concept of 'relation' as expressed in the Pāli sources is here theoretically systematized according to three patterns: 1. logical, 2. strictly subordinative existential, 3. non-strictly subordinative existential. After having discussed Nāgārjuna's acceptance and treatment of these three patterns, particular attention is paid to the non-strictly subordinative existential relation. This kind of relation is meant to describe the way the (...) factors of the conditioned co-origination are linked to each other and is exemplified by Nāgārjuna by means of the father-son bond. A possible way to explain the conditioned co-origination doctrine in the light of the father-son example is here suggested by having resource to the 'Cambridge change' theory. Even if in the Pāli Canon the non-strictly subordinative existential pattern is said to apply to all the other factors of the conditioned co-origination, there is no direct evidence that it concerns also the avidyā-saṃskāras link. It will be shown how Nāgārjuna, by applying it to the avidyā-saṃskāras link, seems to introduce a new perspective in the conditioned co-origination theory. RESUMO O objetivo deste artigo é proporcionar um esboço da maneira na qual Nāgārjuna aborda a ideia de 'relação'. O conceito de 'relação' que encontramos nas fontes pāli é aqui sistematizado teoricamente conforme três padrões: 1. lógico, 2. existencial estritamente subordinativo, 3. existencial não estritamente subordinativo. Após ter discutido a recepção e o tratamento nagarjunianos desses três padrões, este estudo dedica atenção especial à relação existencial não estritamente subordinativa. Esse tipo de relação visa descrever a maneira na qual os fatores da cooriginação condicionada estão ligados entre eles, e é tipificada por Nāgārjuna pelo exemplo da ligação pai-filho. Para explicar a doutrina da cooriginação condicionada à luz do exemplo pai-filho, um modo possível aqui sugerido é por meio do recurso à teoria do 'Cambridge change'. Embora no cânone pāli se diga que o modelo de relação existencial não estritamente subordinativa se aplique a todos os outros fatores da cooriginação condicionada, não há nenhuma evidência direta de que ele concerna também à ligação avidyā-saṃskāras. Será mostrado como Nāgārjuna, ao aplicar esse modelo à ligação avidyā-saṃskāras, pareça introduzir uma nova perspectiva na teoria da cooriginação condicionada. (shrink)

Peter Geach describes the 'doctrine of distribution' as the view that a term is distributed if it refers to everything that it denotes, and undistributed if it refers to only some of the things that it denotes. He argues that the notion, so explained, is incoherent. He claims that the doctrine of distribution originates from a degenerate use of the notion of ?distributive supposition? in medieval supposition theory sometime in the 16th century. This paper proposes instead that the doctrine of (...) distribution occurs at least as early as the 12th century, and that it originates from a study of Aristotle's notion of a term's being ?taken universally?, and not from the much later theory of distributive supposition. A detailed version of the doctrine found in the Port Royal Logic is articulated, and compared with a slightly different modern version. Finally, Geach's arguments for the incoherence of the doctrine are discussed and rejected. (shrink)

In the present paper I wish to regard constructivelogic as a self-contained system for the treatment ofepistemological issues; the explanations of theconstructivist logical notions are cast in anepistemological mold already from the outset. Thediscussion offered here intends to make explicit thisimplicit epistemic character of constructivism.Particular attention will be given to the intendedinterpretation laid down by Heyting. This interpretation, especially as refined in the type-theoretical work of Per Martin-Löf, puts thesystem on par with the early efforts of Frege andWhitehead-Russell. This quite (...) recent work, however,has proved valuable not only in the philosophy andfoundations of mathematics, but has also foundpractical application in computer science, where thelanguage of constructivism serves as an implementableprogramming language, and within the philosophy oflanguage.\footnote{Nordstr\"{o}m et al. give an overview of the work in computerscience, whereas Ranta provides an impressiveconstructivist alternative to Montague Grammar usingthe richer type structure of Martin-L\"{o}f in placeof the simple classical type theory of Church.} Mypresentation will be carried out through a contrastwith standard metamathematical work.\footnote{Troelstra and van Dalen give an encyclopedictreatment of the metamathematics of constructivism.}In the course of the development I have occasion tooffer some novel considerations on thenature of proof and inference. (shrink)

(2013). Will it be me? Identity, concern and perspective. Canadian Journal of Philosophy: Vol. 43, No. 2, pp. 206-226.

In order to understand Hegel’s form of philosophical reflection in general, we must read his ‘speculative’ sentences about spirit and nature, rationality and reason, the mind and its embodiment as general remarks about conceptual topics in topographical overviews about our ways of talking about ourselves in the world. The resulting attitude to traditional metaphysics gets ambivalent in view of the insight that Aristotle’s prima philosophia is knowledge of human knowledge, developed in meta-scientific reflections on notions like ‘nature’ and ‘essence’, ‘reality’ (...) and ‘truth’, about ‘powers’ and ‘faculties’ – and does not lead by itself to an object-level theory about spiritual things like the soul. We therefore cannot just replace critical metaphysics of the human mind by empirical investigation of human behaviour as empiricist approaches to human cognition in naturalized epistemologies do and neuro-physiological explanations propose. Making transcendental forms and material presuppositions of conceptually informed perception and experience explicit needs some understanding of figurative forms of speech in our logical reflections and leads to other forms of knowledge than empirical observation and theory formation. (shrink)

The formal structure of Frege’s ‘concept script’ has been widely adopted in logic text books since his time, even though its rather elaborate symbols have been abandoned for more convenient ones. But there are major difficulties with its formalisation of pronouns, predicates, and propositions, which infect the whole of the tradition which has followed Frege. It is shown first in this paper that these difficulties are what has led to many of the most notable paradoxes associated with this tradition; the (...) paper then goes on to indicate the lines on which formal logic—and also the lambda calculus and set theory—needs to be restructured, to remove the difficulties. Throughout the study of what have come to be known as first-, second-, and higher-order languages, what has been primarily overlooked is that these languages are abstractions. Many well known paradoxes, we shall see, arose because of the elementary level of simplification which has been involved in the abstract languages studied. Straightforward resolutions of the paradoxes immediately appear merely through attention to languages of greater sophistication, notably natural language, of course. The basic problem has been exclusive attention to a theory in place of what it is a theory of, leading to a focus on mathematical manipulation, which ‘brackets off’ any natural language reading. (shrink)

There will be a few themes. One to get us going: expansion versus contraction. About an object, o, and the region, R, of space(time) in which o is exactly located,1 we may ask: i) must there exist expansions of o: objects in filled superregions2 of R? ii) must there exist contractions of o: objects in filled subregions of..

The prime concern of this paper is with the nature of probability. It is argued that questions concerning the nature of probability are intimately linked to questions about the nature of time. The case study here concerns the single case propensity interpretation of probability. It is argued that while this interpretation of probability has a natural place in the quantum theory, the metaphysical picture of time to be found in relativity theory is incompatible with such a treatment of probability.

The prime purpose of this paper is, first, to restore to discourse-bound occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of occasion sentences and a mathematical foundation for such a logic, thus preparing the ground for more adequate semantic, logical and mathematical foundations of the study of natural language. Some of the insights elaborated in this paper (...) have appeared in the literature over the past thirty years, and a number of new developments have resulted from them. The present paper aims atproviding an integrated conceptual basis for this new development in semantics. In Section 1 it is argued that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantically and thus logically inadequate. Natural language is a system of occasion sentences, eternal sentences being merely boundary cases. The logic hasfewer tasks than is standardly assumed, as it excludes semantic calculi, which depend crucially on information supplied by cognition and context and thus belong to cognitive psychology rather than to logic. For sentences to express a proposition and thus be interpretable and informative, they must first be properly anchored in context. A proposition has a truth value when it is, moreover, properly keyed in the world, i.e. is about a situation in the world. Section 2 deals with the logical properties of natural language. It argues that presuppositional phenomena require trivalence and presents the trivalent logic PPC3, with two kinds of falsity and two negations. It introduces the notion of -space for a sentence A as the basis of logical model theory, and the notion of P A /, functioning as a `private' subuniverse for A/A. The trivalent Kleene calculus is reinterpreted as a logical account of vagueness, rather than of presupposition. PPC3 and the Kleene calculus are refinements of standard bivalent logic and can be combined into one logical system. In Section 3 the adequacy of PPC3 as a truth-functional model of presupposition is considered more closely and given a Boolean foundation. In a noncompositional extended Boolean algebra, three operators are defined: 1a for the conjoined presuppositions of a, ã for the complement of a within 1a, and â for the complement of 1a within Boolean 1. The logical properties of this extended Boolean algebra are axiomatically defined and proved for all possible models. Proofs are provided of the consistency and the completeness of the system. Section 4 is a provisional exploration of the possibility of using the results obtained for a new discourse-dependent account of the logic of modalities in natural language. The overall result is a modified and refined logical and model-theoretic machinery, which takes into account both the discourse-dependency of natural language sentences and the necessity of selecting a key in the world before a truth value can be assigned. (shrink)

Nexuses such as exemplification are the fundamental ties that structure reality as a whole. They are “formal” in the sense of constituting the form, not the matter of reality and they are “transcendental” inasmuch as they transcend the categorial distinctions between the denizens of reality, including that between existents and non-existents. I shall advocate a moderately particularist view about (external) nexuses and argue that it provides not only the best solution to Bradley’s regress, but also an elegant account of symmetrical (...) relations (both formal and material), as well as of temporal and modal change. These advantages are illustrated by the reconstruction of an Aristotelian ontology of exemplification involving substances, kinds and material attributes. (shrink)