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actual analysis appearances applied argument Aristotle aspects assertion assume assumption atomic facts belief belongs Bergson called causal laws cause colour common sense consider consists continuity correlation defined desire difficulties doctrine empirical encloses equal event Evolutionism example existence finite Frege Georg Cantor given hasty generalisation Hegel hypothesis imagination impossible induction inferred 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 physics points and instants positions possible premisses present 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 words world of sense Zeno Zeno's
Page 22 - 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.
Page 59 - 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...
Page 53 - 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.
Page 175 - 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.
Page 169 - ... 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.
Page 61 - ... 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...
Page 85 - ... 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?
Page 22 - 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.
Page 49 - 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.
Page 68 - 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'.