Andrej Ule

In this paper, I would like to point out some problems of the presently reigning functional concept of the logical form of sentences, which presents itself as the final answer to the question of true logical form of sentences and, with this, as the basic scheme of logic. I believe that the present conception of the logical form of sentences is a historical result, which in many ways surpasses all former concepts of logical form in the history of logic, but which seems not the final concept of the logical form. It contains some immanent limitations which are, in my opinion, linked mainly to the ‘functional’ concept of elementary sentences, which is the foundation of all other logical structures of sentences.

We deal with five aspects of the intrinsic connection of logic, ethics, and aesthetics in Wittgenstein's Tractatus: (a) the indication of what Wittgenstein called the "higher" of the world and language; (b) the conveyance of values through an intuition "sub specie aeternitatis"; (c) the discussion of internal properties of volitional totalities; (d) the reference to the metaphysical subject as the subject of volition (the will) (e) the indication of a "happy life". This intrinsic connection supplements the idea of the transcendental unity of logic, ethics, and aesthetics, and goes beyond it.

The Carssirer's conceptions of aprioricity, especially of synthetic a priori principles in exact sciences, is analysed. I consider his 'Marburg's' period, first of all his paper on Kant and modern mathematics. Cassirer defends the thesis on invariance principles as the modern variant of synthetic principles a priori. I analyze his arguments on the existence of apriori principles of science and compare his concept of aprioricity with holistic accounts of theories, 'semantic view of theories' and structural realism.

In the article are presented the main philosophical explanations of the application of mathematics on the real world (Plato, Aristotle, rationalists, empiricists, Kant, Frege, Husserl, Carnap etc.). They indicate some typical triangular structure of relationships where the mathematical structures somehow correspond to the forms of reality, and thus are possible though something third what bound them. The attempts to solve the question of the application of mathematics by the dispensability of mathematics (e.g. Field) do not success because they do not explain the big success of mathematics in science. However they call our attention to the meaning of transpositions of some empirical contents on the level of theirs mathematical representations. That is neither an abstraction nor an idealisation but is the mapping from the empirical into a formal language. The opposite attempts to identify mathematics and the fundamental structure of reality also do not explain the success of mathematics because of the obvious ontological differences between the mathematical and the real objects. I return finally to Plato and show how he denies the reduction of numbers to some sets. We have to distinguish the idea of numbers and the various aspects of it, for example the cardinal and the ordinal numbers. According to this platonic insight only the idea of numbers exists. Its aspects are only some partial reflections of this idea in our mathematical theories and in the application of mathematics.

I analyze Wittgenstein’s criticism of several assumptions that are crucial for a large part of cognitive science. These involve the concepts of computational processes in the brain which cause mental states and processes, the algorithmic processing of information in the brain (neural system), the brain as a machine, psycho physical parallelism, the thinking machine, as well as the confusion of rule following with behavior in accordance with the rule. In my opinion, the theorists of cognitive science have not yet seriously considered Wittgenstein’s criticism so they, quite surprisingly, frequently confuse the question “how does it work?” with “what does it do?” But their most “deleterious” mistake is their confusion of the internal computational (or parallel) processes taking place in the brain (which possibly cause mental states) with socially-based, everyday criteria of recognition and classification of, and knowledge about, the content of mental states.