Although the relationship of part to whole is one of the most fundamental there is, this is the first full-length study of this key concept. Showing that mereology, or the formal theory of part and whole, is essential to ontology, Simons surveys and critiques previous theories--especially the standard extensional view--and proposes a new account that encompasses both temporal and modal considerations. Simons's revised theory not only allows him to offer fresh solutions to long-standing problems, but also has far-reaching (...) consequences for our understanding of a host of classical philosophical concepts. (shrink)

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 Le?niewski's names, and the constant ???. Four interpretations are suggested in turn: Le?niewski'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. (shrink)

This book with an introduction by Witold Marciszewski, views the history of philosophy and logic from 1837 to 1939 from the perspective of the cradle of modern exact philosophy - Central Europe. In a series of case studies, it illuminates the developments in this region, most notably in Austria and Poland, examining thinkers such as Bolzano, Brentano, Meinong, Husserl, Twardowski, Lesniewski, and Tarski, as well as the logicians like Frege and Russell with whom they bore a close resemblance. The book (...) challenges established views about the history of philosophy and logic in Europe, and shows the vitality of the Central European tradition. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

SummaryLeśniewski presented his logical systems in a way which conformed to his nominalism, so the question arises whether Leśniewski's logic can be given a natural formal semantics which, unlike current versions, avoids commitment to abstract entities. Building on hints in Wittgenstein's Tractatus, I develop the idea of a way of meaning which is the basis for what I call combinatorial semantics. I then consider whether this commits us to abstract objects or an intensional metalogic.

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. (shrink)

SummaryLeśniewski presented his logical systems in a way which conformed to his nominalism, so the question arises whether Leśniewski's logic can be given a natural formal semantics which, unlike current versions, avoids commitment to abstract entities. Building on hints in Wittgenstein's Tractatus, I develop the idea of a way of meaning which is the basis for what I call combinatorial semantics. I then consider whether this commits us to abstract objects or an intensional metalogic.

Frege's obscure key concept of the unsaturatedness of functions is clarified with the help of the concepts of dependent and independent parts and foundation relations used by Husserl in describing the ontology of complex wholes. Sentential unity in Frege, Husserl and Wittgenstein: all have a similar explanation. As applied to linguistic expressions, the terms 'unsaturated' and 'incomplete' are ambiguous: they may mean the ontological property of Unselbständigkeit, inability to exist alone, or the property of being what categorial grammar calls a (...) functor. Separation of these two senses resolves a dispute between Dummett and Geach on the nature of predicates. (shrink)

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. (shrink)

Frege's obscure key concept of the unsaturatedness of functions is clarified with the help of the concepts of dependent and independent parts and foundation relations used by Husserl in describing the ontology of complex wholes. Sentential unity in Frege, Husserl and Wittgenstein: all have a similar explanation. As applied to linguistic expressions, the terms 'unsaturated' and 'incomplete' are ambiguous: they may mean the ontological property of Unselbständigkeit, inability to exist alone, or the property of being what categorial grammar calls a (...) functor. Separation of these two senses resolves a dispute between Dummett and Geach on the nature of predicates. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

In "meaning and modality" lewy claims the only ground for rejecting disjunctive syllogism as acceptable for entailment is rejection of bivalence. Examining lewis's 'proofs' of the paradoxes of strict implication he suggests the proof of 'if a then (b or not-B)' suppresses a premiss, Restoration of which blocks the paradox, Whereas the proof of 'if (a and not-A) then b' cannot be so blocked. But the paradoxes are dual, So he should have treated them dually by restoring a suppressed disjunct (...) in the consequent of the second. When this is done, The second paradox is blocked and disjunctive syllogism fares no better than the principle lewy discarded. (shrink)

This paper discusses the philosophical background to the paper by lejewski in this issue. lejewski offers an ontologically neutral logic for the first two types (individuals and classes thereof). some peculiarities of the logic used are noted, in particular the distinction between empty individual terms, empty class terms, and non-empty class terms designating the empty class. lejewski ends by denying the truth of the formula meaning "there are classes," but we argue that the way in which truth-conditions for formulae containing (...) class terms are introduced absolves us from taking this as seriously committing us to the existence of classes. the main (inclining but not necessitating) reason for being a platonist lies in the sheer mass of mathematical results for which a non-platonist account has yet to be given. the theory of classes as fictions suggested by our modification of lejewski's view is insufficient to support frege-russell style logicism, but for a non-platonist the upper reaches of cantor's paradise must be regarded as fictitious anyway. (shrink)

(2) All X’s have to be Y’s is to be brought out by glossing the latter as a stronger, nomological generalization involving counterfactural claims, thus: (3) All X’s are Y’s and further if any z that is not an X were an X, then z would be a Y. Professor Rescher points out that while (1) is equivalent to its contrapositive..

ABSTRACT There is more than one way to kill a cat. What are ways? Very little has been written about them in general, but they appear at crucial places in many philosophical discussions. Clarity over the ontology of ways could help in several areas of philosophy. After indicating where ways have been mentioned, I discuss briefly the corresponding linguistic feature, adverbs of manner, before outlining three theories: a Platonistic one making ways a complex kind of function, a Davidsonian one in (...) which ways are (mainly) properties of events, and finally the theory I prefer, a particularist one based on the concept of a higher-order trope. The latter is connected with the theory of truth-makers and avoids ontological commitment to corresponding general objects. (shrink)

ABSTRACT There is more than one way to kill a cat. What are ways? Very little has been written about them in general, but they appear at crucial places in many philosophical discussions. Clarity over the ontology of ways could help in several areas of philosophy. After indicating where ways have been mentioned, I discuss briefly the corresponding linguistic feature, adverbs of manner, before outlining three theories: a Platonistic one making ways a complex kind of function, a Davidsonian one in (...) which ways are properties of events, and finally the theory I prefer, a particularist one based on the concept of a higher-order trope. The latter is connected with the theory of truth-makers and avoids ontological commitment to corresponding general objects. (shrink)