The Four-Colour Theorem (4CT) proof, presented to the mathematical community in a pair of papers by Appel and Haken in the late 1970's, provoked a series of philosophical debates. Many conceptual points of these disputes still require some elucidation. After a brief presentation of the main ideas of Appel and Haken’s procedure for the proof and a reconstruction of Thomas Tymoczko’s argument for the novelty of 4CT’s proof, we shall formulate some questions regarding the connections between the points raised by (...) Tymoczko and some Wittgensteinian topics in the philosophy of mathematics such as the importance of the surveyability as a criterion for distinguishing mathematical proofs from empirical experiments. Our aim is to show that the “characteristic Wittgensteinian invention” (Mühlhölzer 2006) – the strong distinction between proofs and experiments – can shed some light in the conceptual confusions surrounding the Four-Colour Theorem. (shrink)

MATERIALISTS claim that in principle mentality could be accounted for entirely by properties of matter. They must, of course, clarify, as far as possible, the precise scope of the concept "properties of matter." According to materialists there exists only one type of "substance" in the universe, namely matter. Sophisticated experimental and theoretical analyses have led contemporary physicists to interpret known material entities as being composed of two classes of elementary particles, namely quarks and leptons and constituents of interaction fields that (...) mediate interactions between some or all of the elementary particles and which comprise photons, gluons, intermediate bosons and gravitons. For instance, protons and neutrons are composed--by hypothesis--of quarks, while electrons are probably the most familiar leptons. Whether any analyzed and postulated elementary particles and constituents of interaction fields are "ultimate" components of matter can never be known. It remains always possible that more basic subcomponents of known components will be discovered. This has happened repeatedly throughout the history of physics. Hence, what physicists understand by the "physical properties" of the basic components of matter must always remain expressed in terms of usually intricate hypothetico-deductive theories which are tentative and fallible. Contemporary relativistic quantum mechanics of elementary particles and of interaction fields provide typical examples of such hypothetico-deductive theories relating to present known basic components of matter. (shrink)

We comment on the previous paper by L. Basano. In particular, we show that its Section 2 is kinematically incorrect (the dynamics of a two-body interaction through tachyon exchange, incidentally, has already been thoroughly expounded in one paper of ours). Its Section 1 is simply a rather subjective introduction. As to its Section 3, containing indeed interesting problems, we again briefly refer to our earlier work. Our conclusions are still in favor of “au revoir to tachyons!,” even if it is (...) known that inside our cosmos tachyons are more likely to have a role in physics (e.g., in elementary particle and black-hole physics) as “exchanged objects” rather than as “asymptotically free” objects. (shrink)

Conventional medical ethics and the law draw a bright line distinguishing the permitted practice of withdrawing life-sustaining treatment from the forbidden practice of active euthanasia by means of a lethal injection. When clinicians justifiably withdraw life-sustaining treatment, they allow patients to die but do not cause, intend, or have moral responsibility for, the patient's death. In contrast, physicians unjustifiably kill patients whenever they intentionally administer a lethal dose of medication. We argue that the differential moral assessment of these two practices (...) is based on a series of moral fictions – motivated false beliefs that erroneously characterize withdrawing life-sustaining treatment in order to bring accepted end-of-life practices in line with the prevailing moral norm that doctors must never kill patients. When these moral fictions are exposed, it becomes apparent that conventional medical ethics relating to end-of-life decisions is radically mistaken. (shrink)

SummaryExtremism in the environment‐versus innateness controversy in the behavioural sciences and in human sociobiology is being examined. Genetic effects can be severely modified or overruled by environmental factors, but may, nevertheless, be important. Dawkins' view that we are survival machines programmed to subserve selfish genes seems untenable and is a root of racialism. It is also argued that morality is compatible with mixed genetic and environmental control of brains via existing biological machinery.