Our Knowledge of the External Worldfrom NYU Library, 1914 - 191 pagine |
Dall'interno del libro
Risultati 1-4 di 4
Pagina 196
... mathematical induction . " It frequently happens , when we wish to prove that all finite numbers have some property ... inductive , " I shall call the 196 SCIENTIFIC METHOD IN PHILOSOPHY.
... mathematical induction . " It frequently happens , when we wish to prove that all finite numbers have some property ... inductive , " I shall call the 196 SCIENTIFIC METHOD IN PHILOSOPHY.
Pagina 197
... inductive " numbers as all those that possess all inductive properties ; they will be the same as what are called the " natural " numbers , i.e. the ordinary finite whole numbers . To all such numbers , proofs by mathematical induction ...
... inductive " numbers as all those that possess all inductive properties ; they will be the same as what are called the " natural " numbers , i.e. the ordinary finite whole numbers . To all such numbers , proofs by mathematical induction ...
Pagina 198
... mathematical induction , and the strictly limited scope of this method of proof , the supposed contradictions are seen to contra- dict , not logic , but only our prejudices and mental habits . is The property of being increased by the ...
... mathematical induction , and the strictly limited scope of this method of proof , the supposed contradictions are seen to contra- dict , not logic , but only our prejudices and mental habits . is The property of being increased by the ...
Pagina 244
... Induction , 34 , 222 . mathematical , 195 ff . Inductiveness , 190 , 195 ff . Inference , 44 , 54 . Infinite , vi , 64 , 133 , 149 . historically considered , 155 ff . " true , " 179 , 180 . positive theory of , 185 ff . Infinitesimals ...
... Induction , 34 , 222 . mathematical , 195 ff . Inductiveness , 190 , 195 ff . Inference , 44 , 54 . Infinite , vi , 64 , 133 , 149 . historically considered , 155 ff . " true , " 179 , 180 . positive theory of , 185 ff . Infinitesimals ...
Parole e frasi comuni
actual analysis appearances applied argument Aristotle aspects assume assumption atomic facts belief belongs Bergson called causal laws cause colour common sense consider consists continuity correlation defined desire difficulties doctrine empirical enclosure-series equal event wholly evolutionism example existence finite Frege Georg Cantor given event Hegel hypothesis imagination impossible induction inferred infinite collection infinite divisibility infinite numbers infinite series infinity intuition kind knowledge lecture Leibniz logic mathematical induction mathematical logic means mental merely method motion nature number of points number of terms objects of sense Parmenides perceived perspective space philosophy Plato points and instants positions possible premisses principle private world problem propositions prove Pythagoras question realise reality reason regard relation Rorarius scientific sensation sense-data sensible objects simultaneous Socrates sophisms spatial square supposed symmetrical relation theory thing thought tion touch true truth volitions whole wholly precedes world of sense Zeno Zeno's
Brani popolari
Pagina 14 - By intuition is meant the kind of intellectual sympathy by which one places oneself within an object in order to coincide with what is unique in it and consequently inexpressible.
Pagina 49 - The knowledge that there are no other atomic facts is positive general knowledge; it is the knowledge that "all atomic facts are known to me," or at least "all atomic facts are in this collection" — however the collection may be given. It is easy to see that general propositions, such as "all men are mortal," cannot be known by inference from atomic facts alone. If we could know each individual man, and know that he was mortal, that would not enable us to know that all men are mortal, unless we...
Pagina 43 - The existing world consists of many things with many qualities and relations. A complete description of the existing world would require not only a catalogue of the things, but also a mention of all their qualities and relations.
Pagina 163 - Achilles must first reach the place from which the tortoise started. By that time the tortoise will have got on a little way. Achilles must then traverse that, and still the tortoise will be ahead. He is always coming nearer, but he never makes up to it.
Pagina 157 - ... easier to feel than to state — in which time is an unimportant and superficial characteristic of reality. Past and future must be acknowledged to be as real as the present, and a certain emancipation from slavery to time is essential to philosophic thought.
Pagina 51 - ... respect it is the exact opposite of the logic practised by the classical tradition. In that logic hypotheses which seem prima facie possible are professedly proved impossible, and it is decreed in advance that reality must have a certain special character. In modern logic on the contrary, while the prima facie hypotheses as a rule remain admissible, others, which only logic would have suggested, are added to our stock, and are very often found to be indispensable if a right analysis of the facts...
Pagina 75 - ... arrived by a similar process, since that world contained nothing except himself and his thoughts. We are now in a position to understand and state the problem of our knowledge of the external world, and to remove various misunderstandings which have obscured the meaning of the problem. The problem really is: Can the existence of anything other than our own hard data be inferred from the existence of those data?
Pagina 14 - two profoundly different ways of knowing a thing. The first implies that we move round the object: the second that we enter into it. The first depends on the point of view at which we are placed and on the symbols by which we express ourselves. The second neither depends on a point of view nor relies on any symbol. The first kind of knowledge may be said to stop at the relative; the second, in those cases where it is possible, to attain the absolute.
Pagina 39 - In addition, the relation of equality must be symmetric and transitive. By symmetry is meant that if the relation holds between a and b, it also holds between b and a; symbolically, if a = b, then b = a. By transitivity is meant that if a = b and b. = c, then a = c. This level of measurement is so primitive that it is not always recognized as measurement, but it is a necessary condition for all higher levels of measurement.
Pagina 58 - There is not any superfine brand of knowledge, obtainable by the philosopher, which can give us a standpoint from which to criticize the whole of the knowledge of daily life. The most that can be done is to examine and purify our common knowledge by an internal scrutiny, assuming the canons by which it has been obtained'.