„We start, in pure mathematics, from certain rules of inference, by which we can infer that if one proposition is true, then so is some other proposition. These rules of inference constitute the major part of the principles of formal logic.“ (p. 115) #Russell #mathematics #inference #logic
Archiv der Kategorie: Logik
Kant: Erklärung des Unmöglichen
Zitat
„Der Satz des Widerspruchs, der in dem Satz ausgedrückt wird: es ist unmöglich, daß dasselbe zugleich ist und nicht ist, ist der Sache nach nur die Erklärung des Unmöglichen; denn alles, was sich widerspricht, oder was als zugleich seiend und nicht-seiend vorgestellt wird, wird unmöglich genannt.“ (p. 419) #Kant #Widerspruch #unmöglich
Mill: Logic
Zitat
„Logic, then, is the science of the operations of the understanding which are subservient to the estimation of evidence: both the process itself of advancing from known truths to unknown, and all other intellectual operations in so far as auxiliary to this. It includes, therefore, the operation of Naming; for language is an instrument of thought, as well as a means of communicating our thoughts. It includes, also, Definition, and Classification.“ (Intro. §7) #Mill #Logic #Naming #Definition #Classification
Russell: Pure Mathematics
Zitat
„Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true.“ (p 114) #Russell #PureMathematics
Eco: Definition und Syllogismus
Zitat
„Also sind Definition und Syllogismus einerseits zwar radikal verschieden, in gewisser Weise jedoch durchaus miteinander verbunden.“ (p. 290) #Eco #Definition #Syllogismus