Prague, Czech Republic

Algebra, Number Theory and Mathematical Logic

Algebra, teorie čísel a matematická logika

Language: Czech Studies in Czech
Subject area: mathematics and statistics
University website: www.cuni.cz
Years of study: 4
Logic
Logic (from the Ancient Greek: λογική, translit. logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference. A valid inference is one where there is a specific relation of logical support between the assumptions of the inference and its conclusion. (In ordinary discourse, inferences may be signified by words like therefore, hence, ergo, and so on.)
Theory
A theory is a contemplative and rational type of abstract or generalizing thinking, or the results of such thinking. Depending on the context, the results might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.
Theory
I firmly believe people have hitherto been a great deal too much taken up about doctrine and far too little about practice. The word doctrine, as used in the Bible, means teaching of duty, not theory. I preached a sermon about this. We are far too anxious to be definite and to have finished, well-polished, sharp-edged systems — forgetting that the more perfect a theory about the infinite, the surer it is to be wrong, the more impossible it is to be right.
George MacDonald, in a letter to his father, quoted in George MacDonald and His Wife (1924) by Greville MacDonald
Theory
How can we possibly test, or improve upon the truth of a theory if it is built in such a manner then any conceivable event can be described, and explained, in terms of its principles? The only way of investigating such all-embracing principles would be to compare them with a different set of equally all embracing principles- but this procedure has been excluded from the very beginning.
Paul Feyerabend, Against Method (1975) pp. 44-45
Theory
It is clear that the arm of criticism cannot replace the criticism of arms. Material force can only be overthrown by material force, but theory itself becomes a material force when it has seized the masses. Theory is capable of seizing the masses when it demonstrates ad hominem, and it demonstrates ad hominem as soon as it becomes radical. To be radical is to grasp things by the root. But for man the root is man himself. What proves beyond doubt the radicalism of German theory, and thus its practical energy, is that it begins from the resolute positive abolition of religion. The criticism of religion ends with the doctrine that man is the supreme being for man. It ends, therefore, with the categorical imperative to overthrow all those conditions in which man is an abased, enslaved, abandoned, contemptible being—conditions which can hardly be better described than in the exclamation of a Frenchman on the occasion of a proposed tax upon dogs: 'Wretched dogs! They want to treat you like men!'
Karl Marx, Contribution to the Critique of Hegel's Philosophy of Right (1843)
Privacy Policy