Initial Assertion Research Articles

Playing Games with Wittgenstein

S TATEN'S ESSAY first offers his own characterization of Wittgenstein, and then attempts to show that my own use of Wittgenstein (in my book The Theory of Literary Criticism) is not consistent with his account; but in so doing he misreads both Wittgenstein's arguments and my own. It is clear enough is at the root of these misreadings: Staten wants to make Wittgenstein seem very much like Derrida.' Whether this does justice to Derrida I leave others to judge; my concern here is with the misrepresentation of Wittgenstein. Staten's initial assertion that Wittgenstein thinks we can all theory and purely describe will surely jolt anyone familiar with the Philosophical Investigations. On its face, that assertion is inconsistent with Wittgenstein's move away from the world of logical atomism and positivism, from Russell's theory of descriptions as well as Ayer's basic experiential propositions, to a quite different one in which language has a more active and varied role than the word description would allow. His notion of language-games, for example, is introduced in part to show that much more is involved in language than describing, and at one point he says quite explicitly that what we call 'descriptions' are instruments for particular uses.2 That is not the utterance of a man who thinks we can banish all theory and purely describe, and a major part of the importance of the Philosophical Investigations lies surely in its being among the most important arguments which attack that belief.

An Introduction to Proving the Correctness of Programs

This paper explains, in an introductory fashion, the method of specifying the correct behavior of a program by the use of input/output assertions and describes one method for showing that the program is correct with respect to those An initial assertion characterizes conditions expected to be true upon entry to the program and a final assertion characterizes conditions expected to be true upon exit from the program. When a program contains no branches, a technique known as symbolic execution can be used to show that the truth of the initial assertion upon entry guarantees the truth of the final assertion upon exit. More generally, for a program with branches one can define a symbolic execution tree. If there is an upper bound on the number of times each loop in such a program may be executed, a proof of correctness can be given by a simple traversal of the (finite) symbolic execution tree. However, for most programs, no fixed bound on the number of times each loop is executed exists and the corresponding symbolic execution trees are infinite. In order to prove the correctness of such programs, a more general assertion structure must be provided. The symbolic execution tree of such programs must be traversed inductively rather than explicitly. This leads naturally to the use of additional assertions which are called inductive assertions.

Strawson's Transcendental Deduction of Other Minds

It is only because the solution is possible that the problem exists. So with all transcendental arguments (p. 30).Although P. F. Strawson mentions transcendental arguments only once in Individuals, there is no doubt as to his commitment to transcendental method. This paper will offer a critique of such a method, as it functions in a single context. Strawson gives a transcendental argument to refute scepticism with regard to other minds. We are all familiar with the gist of this argument. The sceptic holds that one can ascribe states of consciousness only to oneself. This assertion obviously implies that one can ascribe states of consciousness to oneself. But, Strawson argues, “One can ascribe states of consciousness to oneself only if one can ascribe them to others” (p. 96). In other words, the second assertion implies a third, that one can ascribe states of consciousness to others. The third assertion, though implied by the sceptic's initial assertion, contradicts it. Thus scepticism is shown by transcendental argument to imply its own denial. According to Strawson, the very statement of a sceptical position always presupposes concepts sufficient for its solution. “It is only because the solution is possible that the problem exists.”

A Remark on Post Normal Systems

Let N ( T ) be the normal system of Post which corresponds to the Thue system, T , as in Martin Davis, Computability and Unsolvability (McGraw-Hill, New York, 1958), pp. 98-100. It is proved that for any recursively enumerable degree of unsolvability, D , there exists a normal system, N T ( D ) , such that the decision problem for N T ( D ) is of degree D . Define a generalized normal system as a normal system without initial assertion. For such a GN the decision problem is to determine for any enunciations A and B whether or not A and B are equivalent in GN . Thus the generalized system corresponds more naturally to algebraic problems. It is proved that for any recursively enumerable degree of unsolvability, D , there exists a generalized normal system, GN T ( D ) , such that the decision problem for GN T ( D ) , such that the decision problem for GN T ( D ) is of degree D .

Morality and Modern War

There are three distinct standpoints from which it is possible to launch a discussion of the problem of war in this strange and perilous age of ours that has yet to find its name. My initial assertion will be that it is a mistake to adopt any one ot them exclusively and to carry the argument on to its logical conclusion. If this is done, the argument will end in serious difficulties.