Peter Simons

In continuant causation the initiator is not an event but a continuant. This paper argues that continuant causation cannot be a fundamental nexus in the world, for two reasons. Firstly, continuants are themselves not fundamental. Secondly, what makes it true that an instance of causation occurs at the time it does? In occurrent causation, temporal parts of the causes and effect themselves are candidate truthmakers. Continuants, however, have no temporal parts, so the only plausible candidates for truthmaker on the cause side are occurrents in which the continuant is involved. That leaves unappetizing choices for the defender of fundamental continuant causation. Either the causal instance is not in time, so the truthmaker question does not arise; or the relevant truth has no truthmaker; or continuant causation is derivative after all.

Among biological kinds, the most important are species. But species, however defined, have vague boundaries, both synchronically owing to hybridization and ongoing speciation, and diachronically owing to genetic drift and genealogical continuity despite speciation. It is argued that the solution to the problems of species and their vague boundaries is to adopt a thoroughgoing nominalism in regard to all biological taxa, from species to domains. The base entities are individual organisms: populations of these compose species and higher taxa. This accommodates all the important biological facts while avoiding the legacy problems of pre-evolutionary typological taxonomy, which saw species and other taxa as prior to their members. Species are however not individuals: they are spatiotemporally bounded collections, which are plural particulars.

This paper assesses those features of Lesniewski's Ontology which make it difficult to understand for logicians accustomed to more orthodox systems of logic. It is seen that certain general features of presentation and content can, by selective acceptance or modification, be accommodated with a fairly orthodox viewpoint. The chief difficulty lies in the interpretation of Leśniewski's names, and the constant ‘ϵ’. Four interpretations are suggested in turn: Leśniewski's names as monadic predicates; as class terms; as common nouns; and as empty, singular or plural terms. This last and least orthodox interpretation is argued to be the most suitable, but it is shown how it can be made to live in harmony with either the common noun or the class interpretation.

Although Brentano generally regarded himself as at heart a metaphysician, his work then and subsequently has always been dominated by the Psychology. He is rightly celebrated as the person who reintroduced the Aristotelian-Scholastic notion of intentio back into the study of the mind. Brentano's inspiration was Aristotle's theory of perception in De anima, though his terminology of intentional inexistence was medieval. For the history of the work and its position in his output may I refer to my Introduction to the reprinted English translation. Alongside Aristotle the work shows influences of Descartes, Comte and the British empiricists. The theory of intentionality presented in the Psychology is much less modern and less plausible than almost all recent commentary would have it, and was in any case not where Brentano's main interest lay. Intentionality simply served to demarcate mental phenomena from physical, in Book One, but the main aim was a classification of the mental, outlined in Book Two. Books Three to Five were to have dealt in detail with the three main classes of presentations, judgements and feelings, with the final book considering the metaphysics: mind-body and the immortality of the soul. Brentano's shifting views, recently documented in English with Benito Muller's translation of Descriptive Psychology, a work from the transitional 1890s, made the original plan obsolete. The role of an a priori, philosophical or descriptive psychology, methodologically prior to empirical-experimental genetic psychology, foreshadowed and influenced Husserl's notion of phenomenology, and Brentano's Comtean methodological epoche of desisting from controversial metaphysical statements in favour of an examination of the phenomena likewise presaged Husserl's more ponderous phenomenological reductions. Brentano's other work covers most areas of philosophy, notably ethics, where he upheld a form of a priori intuitionism much admired by G. E. Moore, the philosophy of religion, metaphysics, philosophy of language, deductive and inductive logic, and the history of philosophy. I shall mention just two areas. In his logic lectures from 1866 onwards (a compilation published 1956) Brentano rejected the subject-predicate analysis of simple judgements and proposed instead (for which he apparently secured written assent from Mill) that all judgements are logical compounds of positive and negative existential judgements. For example the universal judgement All men are mortal becomes the negative existential There are no immortal men. On this basis Brentano radically simplified the inference rules of deductive logic. While unlike de Morgan, Frege and others he does not go beyond logic's traditional scope by recognising relations, within its bounds his reformed-term logic is simple, elegant and easily teachable. Some of his ideas in logic influenced the young Husserl. Unfortunately Brentano took against mathematical logic, which he wrongly associated exclusively with Hamilton's confused doctrine of the quantification of the predicate. His inductive logic, which takes up by far the greater part of his logic lectures, remains unresearched to this day.

In his doctoral dissertation Von der mannigfachen Bedeutung des Seienden nach Aristoteles Brentano tried to show that (against criticism of this) one could indeed give a principle defense of Aristotle's table of categories as a coherent system. In later texts Brentano appears sharply critical of Aristotle, mainly in respect to Aristotle's mereology, or theory of part and whole, and to his theory of substance and accident. It is argued that Brentano hadn't observed that Aristotle's belief that there are as many predicative senses of 'be' as there are categories of being is based not on his mereology but on his theory of definition. Overlooking this Brentano was led to far reaching inadequate ontological consequences.

Common nouns enter into modern predicate logic only as parts of predicates, While in lesniewski's 'ontology' they are classified together with proper nouns as 'names'. A system of natural deduction rules is presented which sharply separates proper from common nouns, Within which lesniewski's calculus is contained as a logic solely of common nouns, Together with copula, Identity predicate, Definite article, And quantifiers 'any', 'every', 'some' and 'no'. The fragment developed is closer to the natural syntax of english than either frege's or lesniewski's languages, Enabling these to be seen as complementary rather than competing, As approximations to syntactically more complex languages

Here is a dilemma. By robust common sense, the sun exists. Yet the sun is a vague object, lacking exact identity conditions, and therefore by widely accepted standards of objecthood does not exist. What goes for it goes for almost all other material things. Standard solutions to the problem of vagueness for predicates fall flat for vague objects. This paper attempts a theory which accounts for our common beliefs about vague objects by taking them as well-founded phenomena, founded on collections of more exact objects. The key notions allowing us to assign sensible truth-values to propositions about vague objects are those of truth-value density and expected truth-value. These will be illustrated in use.

Frege uses Greek letters in two different ways in his Begriffsschrift. One way is the familiar use of bound variables, in conjunction with variable-binding operators, to mark and close argument-places. The other, which is quite unfamiliar, employs letters to mark places for operators to reach into, without thereby closing these places. Frege thereby invents a powerful and compact notation for functional operations which can be recommended even today. His regrettable double use of Greek letters obscured his invention, and this, together with the fact that in the Grundgesetze he no longer has need of function-valued functions, explains why the device was overlooked and has not passed into general use

Frege's theory of real numbers has undeservedly received almost no attention, in part because what we have is only a fragment. Yet his theory is interesting for the light it throws on logicism, and it is quite different from standard modern approaches. Frege polemicizes vigorously against his contemporaries, sketches the main features of his own radical alternative, and begins the formal development. This paper summarizes and expounds what he has to say, and goes on to reconstruct the most important steps which he is likely to have subsequently taken. The various difficulties facing his theory in this reconstruction are outlined, and some surprising consequences drawn about the nature of his logicism

LeSniewski’s systems of Ontology and Mereology, considered from a purely formal point of view, possessstriking algebraic parallels, ascan be seen in their respective relations to Boolean algebra. But there are alsoimportant divergences, above all that general Mereology is silent, where Ontology is not, on the existenceof ‘atoms’ (individuals). By employing plural terms, LeSniewski sought to accommodate talk of (distributive)classes, without according these an autonomous ontological status. His logic also – like predicate logic– has no place for mass predication in its raw state. It is argued that reference both to pluralities and tomasses is ineliminable, and that one must therefore separate the grammatical distinction singular/pluralfrom the ontological distinction individual/class/mass. A kind of language, modelled on kiniewski’s, issuggested which enables these distinctions to be held apart and at the same time, building on the work ofRichard Sharvy, allows us to express the most important relationships between individuals, classes andmasses.

For most of the history of metaphysics, the subject has been dominated by the concept of substance. There is an everyday commonsense notion of substance which is perfectly harmless and which I shall defend against attempts to remove it or revise it away. But I deny that substance has to be construed as a primitive even in everyday terms. Borrowing Strawson’s distinction between descriptive and revisionary metaphysics, I press the legitimate claims of revisionary metaphysics and argue that there is no place for a fundamental concept of substance within it, although aspects of the concept are likely to find their place therein.

This paper presents a tree method for testing the validity of inferences, including syllogisms, in a simple term logic. The method is given in the form of an algorithm and is shown to be sound and complete with respect to the obvious denotational semantics. The primitive logical constants of the system, which is indebted to the logical works of Jevons, Brentano and Lewis Carroll, are term negation, polyadic term conjunction, and functors affirming and denying existence, and use is also made of a metalinguistic concept of formal synonymy. It is indicated briefly how the method may be extended to other systems.

Where there is mind there is representational opacity, and vice versa. Opacity arises because where there is representation there may be misrepresentation, and the status of the misrepresenting sign or state of the misrepresenting sign‐user can only be characterized via the terms used for a correctly represented object. Opacity is not a blight for naturalism, but must be recognized and exploited if naturalism is to adequately embrace the mental. Opacity is illustrated for language, for the mental itself, for depiction and other non‐linguistic representation. Alethic modality, a candidate counterexample to the thesis (opacity without mind is defused consequences for our conception of non‐human intelligence are outlined

During the realist revival in the early years of this century, philosophers of various persuasions were concerned to investigate the ontology of truth. That is, whether or not they viewed truth as a correspondence, they were interested in the extent to which one needed to assume the existence of entities serving some role in accounting for the truth of sentences. Certain of these entities, such as the Sätze an sich of Bolzano, the Gedanken of Frege, or the propositions of Russell and Moore, were conceived as the bearers of the properties of truth and falsehood. Some thinkers however, such as Russell, Wittgenstein in the Tractatus, and Husserl in the Logische Untersuchungen, argued that instead of, or in addition to, truth-bearers, one must assume the existence of certain entities in virtue of which sentences and/or propositions are true. Various names were used for these entities, notably 'fact', 'Sachverhalt', and 'state of affairs'. (1) In order not to prejudge the suitability of these words we shall initially employ a more neutral terminology, calling any entities which are candidates for this role truth-makers.

I argue, along lines first explored by Wittgenstein in the Tractatus and elaborated by Peter Geach, (1) that the logical notion of negation may be illuminated by exploiting the notion of a toggle; (2) that the toggle nature of negation may best be appreciated by studying the logical notion of duality; (3) that apparent obstacles to the application of duality due to semantic opacity in intentional contexts may be overcome, and (4) that the result illuminates the connection between duality and the semantics for relevant logics. © 2011 Elsevier B.V., All rights reserved.

Modal logic like many others sustains a hexagon of opposition, with the two “additional” vertices expressing contingency and non-contingency. We first illustrate hexagons of opposition generally by treating them as cut-down entailment lattices with order distinctions among multiple arguments suppressed. We then approach the modal case by treating it heuristically as a particular case of the hexagon for quantified propositions. Historically, possibility and contingency were sometimes confused: we show using the notion of duality that contingency, as negation-symmetric, is logically less interesting than possibility