The University of Warsaw has a splendid modern library with 60,000 m 2 of floor space. It resembles a shopping centre. The long and elegant modern building on ulica Dobra (a typical Varsovian street-name), on the low ground between the old University and the Vistula, was opened in 1998 replacing the previous hopelessly inadequate facilities. It has an imposing sequence of copper-green “great texts” on its front side in Greek, Arabic, Sanskrit, Hebrew, Latin, Polish, music, and mathematics. These are international (...) symbols, posting Warsaw’s claim to international status. But inside, once one has passed the mall-like coffee-shop. (shrink)
Unless you live in the world of theatre or film or politics or sport, you rarely get to meet people whom you can truly describe as “larger than life”. Academia has more than its fair share of boring people: being clever does not mean being interesting. But one academic I met on several occasions before he died was definitely larger than life, and he was Polish. He was Father Józef Maria Bocheński.
alone, in a reclining posture in his drawing-room. He was lean, ghastly, and quite of an earthy appearance. … He was quite different from the plump figure which he used to present … He seemed to be placid and even cheerful … He said he was just approaching to his end … I had a strong curiosity to be satisfied if he persisted in disbelieving a future state even when he had death before his eyes. I was persuaded from what (...) he said, and from his manner of saying it, that he did persist. I asked him if it was not possible that there might be a future state. He answered it was possible that a piece of coal put upon the fire would not burn; and he added that it was a most unreasonable fancy that we should exist for ever … I asked him if the thought of annihilation never gave him any uneasiness. He said not the least; no more than the thought that he had not been, as Lucretius observes. … He said he had no pain, but was wasting away. I left him with impressions which disturbed me for some time. (shrink)
Compulsion and Surprise Two phenomena conspire to convince people that the physical world exists independently of them. One is its recalcitrance, or insusceptibility to control. It resists and constrains our actions. Much as we might wish to do so, we cannot lift heavy boulders, walk through walls, jump rivers, breathe under water, or fly (unaided) over mountains. The other feature, which is connected to the first, is the world’s propensity to surprise us. The sights and sound, pressures and pains of (...) the world force themselves upon us in perception whether we want them to or not, and are often unexpected and surprising. An unusual bird appears in the garden, a stranger calls at the door and reveals he is a long-lost cousin, the post brings an invitation out of the blue, the car won’t start (surprises may be unpleasant as well as pleasant). These two phenomena, recalcitrance and surprise, form a large part of the platonist’s case for the existence of an independent mathematical reality. The recalcitrance of mathematical reality indeed appears to be stronger than that of the physical: the necessity with which mathematical results follow from assumptions is stricter than the physical necessity by which a wall resists attempts to walk through it. This has rarely been put more eloquently than by Jan Łukasiewicz. Speaking in particular of mathematical logic, he wrote.. (shrink)
We define DNA sequence by a bottom-up approach, starting with a real sequence from an actual biological sample. By providing axioms for notions of string, substring and strand, we formally define a DNA sequence, and a DNA molecule as composed of two antiparallel strands. We note that a sequence is a kind of group in which each member stands a certain relation to every other. The spatial aspects of a DNA sequence are also described.
We only need to think for a moment about surfaces and other interfaces to realise their enormous importance in everydaylife. There are numerous branches of physics, chemistry, biology, and materials science concerned wholly or largely with surfaces, and one sometimes comes across the expression ‘surface science’ Among the natural phenomena connected with surfaces which have aroused scientific interest are surface tension, surface waves, photoelectric emission, reflection, refraction, evaporation, adsorption, adhesion, thin films, detergents, catalysts, cell membranes, skin. All of these phenomena (...) are complex, interesting, and some of them are still far from completely understood. Are surfaces important for philosophy? An epistemologist might well answer affirmatively, thinking of Quine’s "surface irritations" as the basis of our knowledge of the physical world, or Berkeley’s theory of vision, or the view that we perceive a material object in virtue of suitable causal interaction with its surfaces. But at first sight it seems that there is not much of interest for an ontologist. In his work on surfaces, especially in the book of that name, Avrum Stroll has shown to the contrary that there is much ontological interest in surfaces} Every ontologist delights in a newly discovered or hitherto neglected member of the ontological zoo: surfaces are not exactly new, but they have been neglected, and we can be grateful to Stroll for bringing them to greater prominence. (shrink)
Confounding earlier predictions of naysayers and sceptics, by the beginning of the twenty-first century, metaphysics had re-emerged for the first time in decades as a vital, progressive and exciting branch of philosophy. Although the most strident criticisms came from early analytic philosophers such as Carnap, it is analytical metaphysics that has led the way. But rather than trace the stages of the revival of metaphysics, we consider a spread of contemporary themes which have been especially fruitful in expanding the circle (...) of metaphysical discussion from its modest beginnings at the hands of Strawson and Quine in mid-century. The topics are divided into four groups: Expanding the Toolbox; Ontological Speculations; Systematics; and Applications. (shrink)
Before arguing for the nonexistence of God let me say what kind of God I am denying. It is a God as broadly conceived in the Mosaic monotheistic tradition of Judaism, Christianity and Islam, as supreme being. This God has two chief characteristics: supreme power and supreme goodness. As powerful, God is the agency responsible for creating and/or sustaining the world. As good, God is the source and supreme exemplar of positive value or goodness. It follows that as a good (...) creator God takes a parental or caring interest in its creations, especially those like ourselves that also have a sense of good and evil. God is therefore worthy of our reverence, worship, and love. (shrink)
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. (shrink)
The metaphysics of relations (unlike their logic) is still in its infancy. We use the idea of truthmaking to gain purchase on this metaphysics. Assuming a modest supervenience conception of truthmaking, where true relational predications require multiply dependent truthmakers, these are indispensable relations (relational tropes). Though some such relations are required, none are needed for internal relatedness, nor for several other kinds of relational predication. Discerning the metaphysically basic kinds of relations is fraught with uncertainties, but must be tackled if (...) progress is to be made. (shrink)
λ-calculi are of interest to logicians and computer scientists but have largely escaped philosophical commentary, perhaps because they appear narrowly technical or uncontroversial or both. I argue that even within logic λ-expressions need to be understood correctly, as functors signifying functions in intension within a categorical or typed language. λ-expressions are not names but pure viable binders generating functors, and as such they are of use in giving explicit definitions. But λ is applicable outside logic and computer science, anywhere where (...) the notions of complex whole, substitution, abstraction and structure make sense. To illustrate this, two domains are considered. One is somewhat frivolous: the study of flags; the other is very serious: manufacturing engineering. In each case we can employ λ-abstraction to describe substitutions within a structure, and in the latter case there is even a practical need for such a notation. (shrink)
Philosophy in the West divides into three parts: Analytic Philosophy (AP), Continental Philosophy (CP), and History of Philosophy (HP). But all three parts are in a bad way. AP is sceptical about the claim that philosophy can be a science, and hence is uninterested in the real world. CP is never pursued in a properly theoretical way, and its practice is tailor-made for particular political and ethical conclusions. HP is mostly developed on a regionalist basis: what is studied is determined (...) by the nation or culture to which a philosopher belongs, rather than by the objective value of that philosopher’s work. Progress in philosophy can only be attained by avoiding these pitfalls. (shrink)
I consider the idea of a propositional logic of location based on the following semantic framework, derived from ideas of Prior. We have a collection L of locations and a collection S of statements such that a statement may be evaluated for truth at each location. Typically one and the same statement may be true at one location and false at another. Given this semantic framework we may proceed in two ways: introducing names for locations, predicates for the relations among (...) them and an “at” preposition to express the value of statements at locations; or introduce statement operators which do not name locations but whose truth-conditional effect depends on the truth or falsity of embedded statements at various locations. The latter is akin to Prior’s approach to tense logic. In any logic of location there will be some basic operators which we can define. By ringing the changes on the topology of locations, different logical systems may be generated, and the challenge for the logician is then in each case to find operators, axioms and rules yielding a proof theory adequate to the semantics. The generality of the approach is illustrated with familiar and not so familiar examples from modal, tense and place logic, mathematics, and even the logic of games. To the memory of Ted Dawson, who introduced me to philosophy and the writings of Arthur Prior. (shrink)
Using the work of Józef Bocheski as apositive example, this paper sets out the casefor a balanced use of historical knowledge indoing analytic philosophy. Between the twoextremes of relativizing historicism, whichdenies absolute truth, and arrogant scientism,which denies any constructive role for thehistory of ideas in philosophy, lies a viamedia in which historical reflection onconcepts and their history is placed at theservice of the system of cognitive philosophy.Knowledge of the history of philosophy, whilenot a sine qua non, can empower analyticphilosophy to (...) push forward to new and moresatisfactory solutions to old and new problems.Examples are adduced from Bocheski's oeuvreand from the author's own experience. (shrink)
This is a broad survey of the chronology of the rift between continental and analytic philosophy, starting in 1899. Whereas at that time there was no discernible divide, as the twentieth century progresses we can see a gradual parting of the ways in which philosophy was done, culminating in a period of maximum separation in 1945-68, followed by some convergence. There is one substantial historical thesis proposed, and facts are adduced from the chronology to back it up: that the divide (...) was never absolute, never purely geographical, and above all that it was not inevitable, but was largely the product of accidental historical circumstances, of which the most crucial was the flourishing of totalitarianism in Europe and the disruption caused by two world wars. (shrink)
[Peter Simons] Commonsense ontology contains both continuants and occurrents, but are continuants necessary? I argue that they are neither occurrents nor easily replaceable by them. The worst problem for continuants is the question in virtue of what a given continuant exists at a given time. For such truthmakers we must have recourse to occurrents, those vital to the continuant at that time. Continuants are, like abstract objects, invariants under equivalences over occurrents. But they are not abstract, and their being invariants (...) enables us to infer both their lack of temporal parts and that non-invariant predications about them must be relativized to times. \\\ [Joseph Melia] In this paper I try to eliminate occurrents from our ontology. I argue against Simons' position that occurrents are needed to supply truthmakers for existential claims about continuants. Nevertheless, those who would eliminate occurrents still need some account of our willingness to assert sentences that logically entail their existence. Though it turns out to be impossible to paraphrase away our reference to occurrents, I show that the truthmakers for such sentences are facts that involve only continuants. This is enough to allow us to regard our ordinary talk about occurrents as fictional. Finally, I argue that a proper conception of the underlying temporal facts about continuants can both avoid the problematic tensed theory of time and the problem of temporary intrinsics. (shrink)
This paper brings together two theories that I have propounded separately elsewhere. The first is the view that concrete individuals are constituted completely by tropes, that they are trope bundles. The second and more recently developed theory is that of the two major categories of concrete individuals, continuants and occurrents, the latter are ontologically more basic than the former and that continuants are to be viewed as invariants among occurrents under equivalence relations. The latter theory embodies on its own an (...) account of the nature of identity through time of things that are in time but not extended in time. The question is whether this view is compatible with the trope bundle account of concrete particulars, and, assuming it is (both theories being separately attractive) whether bringing them together entails any modifications (other than complexity) to either theory. After examining likely metaphysical difficulties the tentative conclusion is that the attractiveness of the trope bundle theory persists despite the marriage, but that the mental picture of what tropes and trope bundles are must be overhauled. (shrink)
From the beginning of the nineteenth century to the present day, philosophy in Austria has progressed through four phases. Theparticularities of the first three of these phases have prompted a number of commentators rightly to distinguish a characteristic Austrian, as distinct from German, way of doing philosophy. The main figure of the second phase was Franz Brentano, and his distinctive theory of the four-phase cycle of philosophical development is outlined, and critically compared to other views of the development of philosophy. (...) In Austria itself the caesuras between the phases were marked as much by political as by philosophical events, and the paper shows how philosophy in Austria has been notable in all its phases for the high level and overwhelmingly negative effect of political interference in intellectual life, a doleful saga which continues to this day. (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)
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)
Despite its lack of influence in analytical philosophy, and independently of its content as a process philosophy, Whitehead's system in Process and Reality affords a valuable lesson on how to pursue revisionary systematic metaphysics. This paper argues the case generally for metaphysical revision and system, describes the structure of Whitehead's categorial scheme, endorses his idea of an ultimate which is not an entity, and outlines an alternative, “digital” ultimate or basis composed of several analytical factors. [I]n the absence of a (...) well-defined categoreal scheme of entities, issuing in a satisfactory metaphysical system, every premise in a philosophical argument is under suspicion. (shrink)
Bolzano's theory of collections (Inbegriffe) has usually been taken as a rudimentary set theory. More recently, Frank Krickel has claimed it is a mereology. I find both interpretations wanting. Bolzano's theory is, as I show, extremely broad in scope; it is in fact a general theory of collective entities, including the concrete wholes of mereology, classes-as-many, and many empirical collections. By extending Bolzano's ideas to embrace the three factors of kind, components and mode of combination, one may develop a coherent (...) general account of collections. But it is most difficult to take Bolzano's view to fit modern set theory. So while Krickel's positive thesis is rejected, his negative thesis is confirmed. (shrink)
Gilbert Ryle wrote that "Meaning-theory expanded just when and just in so far as it was released from that 'Fido'-Fido box, the lid of which was never even lifted by Meinong". This paper sets out to relieve Ryle's oversimplification about Meinong and the role of meaning theory in his thought. One step away from canine simplicity about meaning is the recognition of a distinction between sense and reference, such as we find in Frege, Husserl, and the early Russell. In Über (...) Möglichkeit und Wahrscheinlichkeit (1915) Meinong seems to corroborate Ryle when he writes, "Word-meanings are objects", but immediately after this, he qualifies it: "Word-meanings are very often auxiliary objects". The distinction between auxiliary and target objects in Meinong's later work allows us to attribute to him a theory of sense and reference which shows him to have indeed lifted the box-lid. (shrink)
stanislaw lesniewski, Collected Works, Edited by Stanislaw J. Surma, Jan T. Srzednicki and D. I. Barnett, with an annotated bibliography by V. Frederick Rickey. Warsaw:PWN?Polish Scientific Publishers; and Dordrecht, Boston, London: Kluwer. 2 vols., xvi + 794 pp. $274/£163/Dfl. 480.
What primitive concepts does formal ontology require? Forsaking as too indirect the linguistic way of discerning the categories of being, this paper considers what primitives might be required for representing things in themselves (noumena) and representations of them in a thoroughly crafted large autonomous multi-purpose database. Leaving logical concepts and material ontology aside, the resulting 32 categories in 13 families range from the obvious (identity/difference, existence/non-existence) through the fairly obvious (part/whole, one/many, sequential order) and the surprisingly familiar (illocutionary modes, mass/count, (...) indexical/descriptive) to the controversial (moment/fundament, transparent/opaque) and the arcane (modes of class delimitation, taxonomic rank, aspects of designators). Any such list is speculative and tentative, but the test of this one will be in its implementation, a new departure for philosophical category theories. (shrink)
Suppose you hold the following opinions in the philosophy of logic. First-order predicate logic is expressively inadequate to regiment concepts of mathematic and natural language; logicism is plausible and attractive; set theory as an adjunct to logic is unnatural and ontologically extravagant; humanly usable languages are finite in lexicon and syntax; it is worth striving for a Tarskian semantics for mathematics; there are no Platonic abstract objects. Then you are probably already in cognitive distress. One way to decease your unhappiness, (...) short for embracing Platonism, is to accept higher-order logic and look, as did Arthur Prior, for a plausible way to neutralize the ontological commitment to abstract entities that this acceptance appears to entail. (shrink)
By considering a wide and expressly classified range of examples from natural and logical languages, the attempt is made to isolate from other concomitants the features of existential sentences which make them existential. One such concomitant is the imputation of singularity. There are many ways to say something exists, and their relationships are charted. It is denied that there is anything in reality called existence, or any special existential facts.
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)
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)
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 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)
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)
The brief article of 1910 which is translated here is, as the prefatory note explains, significant for understanding both the way in which ?ukasiewicz came to many-valued logic and the influences under which he stood at the time.
The philosophies of late Brentano and early Wittgenstein can be brought closer in two ways. One way discovers a surprising amount of part-whole theory in the Tractatus if we see states of affairs (not wholly wilfully) as thinglike rather than factlike. This throws up a modal analogue to Chisholm's entia successiva in the form of situations. The other way sees all propositions as truth-functions of existential propositions, supporting Brentano's view that existentials are primary, and incidentally yielding a reistic semantics for (...) the Tractatus. I draw a quick moral, that we should beware of excessive simplicity in metaphysics, and apply it to Chisholm's views on part and whole. (shrink)
A realist theory of truth for a class of sentence holds that there are entities in virtue of which these sentences are true or false. We call such entities ‘truthmakers’ and contend that those for a wide range of sentences about the real world are moments (dependent particulars). Since moments are unfamiliar we provide a definition and a brief philosophical history, anchoring them in our ontology by showing that they are objects of perception. The core of our theory is the (...) account of truthmaking for atomic sentences, in which we expose a pervasive ‘dogma of logical form’, which says that atomic sentences cannot have more than one truthmaker. The authors uphold the mutual independence of logical and ontological complexity. The theory is compared with that of Wittgenstein’s Tractatus, and the authors outline formal principles of truthmaking taking account of both kinds of complexity and suggesting how to overcome Wittgenstein’s problem of negation. (shrink)
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)
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)
