The model-checking problem for a logic L on a class C of structures asks whether a given L-sentence holds in a given structure in C. In this paper, we give super-exponential lower bounds for fixed-parameter tractable model-checking problems for first-order and monadic second-order logic. We show that unless PTIME=NP, the model-checking problem for monadic second-order logic on finite words is not solvable in time f·p, for any elementary function f and any polynomial p. Here k denotes the size of the (...) input sentence and n the size of the input word. We establish a number of similar lower bounds for the model-checking problem for first-order logic, for example, on the class of all trees. (shrink)

In this paper I want to do the following things. First I want to show that in the part of the Theaetetus where the relationship between knowledge and perception is examined, the concept of knowledge that is in question is very clearly characterized. We are left in no doubt as to what is to count as knowing. Secondly I want to unravel in some detail the case that Socrates puts on Protagoras’ behalf where he draws on what Protagoras actually wrote (...) (151 E-152C); as opposed to what he may have taught secretly to his pupils (152C-160D). Thirdly I wish to argue that if we let the dialogue speak for itself, it is manifest that this case put up on Protagoras’ behalf at 151 E-152C is not overthrown; it is not even shaken. (shrink)

In this paper I want to do the following things. First I want to show that in the part of the Theaetetus where the relationship between knowledge and perception is examined, the concept of knowledge that is in question is very clearly characterized. We are left in no doubt as to what is to count as knowing. Secondly I want to unravel in some detail the case that Socrates puts on Protagoras’ behalf where he draws on what Protagoras actually wrote (...) ; as opposed to what he may have taught secretly to his pupils. Thirdly I wish to argue that if we let the dialogue speak for itself, it is manifest that this case put up on Protagoras’ behalf at 151 E-152C is not overthrown; it is not even shaken.In that part of the dialogue where the question is under examination whether or not knowledge and perception are the same, Socrates uses an idealized concept of knowledge. That is, he restricts the use of the word by setting down what he will consider to be the essential characteristics of knowledge, the sufficient and necessary conditions of its being instantiated. An excellent piece of philosophical procedure. (shrink)

We will show that there is a strong form of emergence in cell biology. Beginning with C.D. Broad's classic discussion of emergence, we distinguish two conditions sufficient for emergence. Emergence in biology must be compatible with the thought that all explanations of systemic properties are mechanistic explanations and with their sufficiency. Explanations of systemic properties are always in terms of the properties of the parts within the system. Nonetheless, systemic properties can still be emergent. If the properties of the components (...) within the system cannot be predicted, even in principle, from the behavior of the system's parts within simpler wholes then there also will be systemic properties which cannot be predicted, even in principle, on basis of the behavior of these parts. We show in an explicit case study drawn from molecular cell physiology that biochemical networks display this kind of emergence, even though they deploy only mechanistic explanations. This illustrates emergence and its place in nature. (shrink)

This is a book about the philosophy of Henri Bergson which shows how relevant Bergson is to much contemporary philosophy. The book takes as its point of departure Bergson's insistence on precision in philosophy. It then discusses a variety of topics including laughter, the nature of time as experienced, how intelligence and language should be construed as a pragmatic product of evolution, and the antinomies of reason represented by magic and religion. This is not just another exposition of Bergson's work. (...) It offers an account of why Bergson commanded such a massive reading public in his own day and why he deserves to be read now. Written in a terse and clear style, this book will prove appealing to teachers and students of philosophy, cognitive science, psychology, religious studies and literature. (shrink)

In an essay on pantheism Schopenhauer observes that his chief objection against it is that it says nothing, that it simply enriches language with a superfluous synonym of the word “world.” It can hardly be denied that by this remark the great pessimist, who was himself an atheist, scored a real point. For if a philosopher starts off with the physical world and proceeds to call it God, he has not added anything to the world except a label, a label (...) which, if we take into account the ordinary significance of the word “God,” might well appear unnecessary and superfluous: one might just as pertinently say that the world is the world as that the world is God. Neither the Jew nor the Christian nor the Moslem understand by “God” the physical world, so that, if someone calls the physical world God, he cannot be taken to mean that the world is God according to the Jewish or Christian or Moslem understanding of God. Does he mean any more than that the physical world is ultimately self-explanatory, that no Cause external to the world, no transcendent Being is requisite or admissible, i.e. that there is no God? If that were all there is in pantheism, the latter would indeed be indistinguishable from atheism, and those who called Spinoza an atheist would be fully justified. (shrink)

This book is a philosophical commentary on Schopenhauer's "Fourfold Root of the Principle of Sufficient Reason," dealing with each of Schopenhauer's principal ...

Towards the close of Book V of theRepublicPlato tells us that the true philosopher has knowledge and that the objects of knowledge are the Forms. By contrast, the ‘lovers of sights and sounds’, he tells us, have no more than belief, the objects of which are physical particulars. He then goes on to present us with some very radical-sounding assertions about the nature of these physical particulars. They are bearers of opposite properties, he says, in so thorough-going a manner that (...) we cannot say of them that they are nor that they are not: they lie somewhere between being and utter non-being.This passage of theRepublic still awaits an agreed interpretation and I want to suggest as a reason for this that it is usually interpreted in isolation. I will argue that it becomes easier to understand when seen against the background of Plato's developing thought. To be more precise, it makes sense when taken as a rejection by Plato of one of his earlier beliefs: namely, a doctrine of essentialism to be found in thePhaedo.The greater part of this paper then will be an attempt to show thatRepublicV is a rejection of thePhaedo'sdoctrine of essences. Its concluding part will try to explain why that doctrine was rejected. (shrink)