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)
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. (shrink)
Of those students of Franz Brentano who went on to become professional philosophers, Kazimierz Twardowski (1866-1938) is much less well-known than his older contemporaries Edmund Husserl and Alexius Meinong. Yet in terms of the importance of his contribution to the history of philosophy, he ranks among Brentano’s students behind at most those two, possibly only behind Husserl. The chief contribution of Twardowski to global philosophy came indirectly, through the influence of his theory of truth on his students, and they on (...) their students, and so on. The most important of these grandstudents is one whom Twardowski presumably knew but never taught, and whose adopted name is obtained by deleting four letters from his own: Tarski. (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)
I argue that the assumptions that physically basic things are either mereologically atomic, or that they are continuous and there are no atoms, both face difficult conceptual problems. Both views tend to presuppose a largely unquestioned assumption, that things have parts corresponding to the geometric parts of the regions they occupy. To avoid these problems I propose a third view, that physically simple things occupy a finite volume without themselves having parts. This view is examined enough to tease out some (...) of its consequences and show that it withstands the obvious questions it faces. I conclude by mentioning some precedents for this view in Democritus, Kant, and Whitehead, with close variants in Boscovich, Harré, and Markosian. (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)