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
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)
Logic
All men are mortal. Socrates was mortal. Therefore, all men are Socrates.
Woody Allen in his movie Love and Death cited in: Philip Nicholas Johnson-Laird (2006) How We Reason. p. 142
Theory
Never call yourself a philosopher, nor talk a great deal among the unlearned about theorems, but act conformably to them.
Epictetus, Enchiridion, 46
Hydrogen production from renewable sources is an important step toward reducing carbon dioxide emissions. An EU-funded project seeks to improve the process of extracting hydrogen from wet biomass.
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