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• 1/8/2013

World

If we regard the two propositions, that the world is infinite in magnitude and that it is finite in magnitude, as contradictory opposites, we are assuming that the world, the complete series of appearances, is a thing in itself that remains even if I suspend the infinite or the finite regress in the series of its appearances. If, however, I reject this assumption, or rather this accompanying transcendental illusion, and deny that the world is a thing in itself, the contradictory opposition of the two assertions is converted into a merely dialectical opposition. Since the world does not exist in itself, independently of the regressive series of my representations, it exists in itself neither as an infinite whole nor as a finite whole. It exists only in the empirical regress of the series of appearances, and is not to be met with as something in itself. If, then, this series is always conditioned, and therefore can never be given as complete, the world is not an unconditioned whole, and does not exist as such a whole, either of infinite or of finite magnitude(k448)
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• 1/18/2013

Word

The word, with the few characteristics which we attach to it, is more properly to be regarded as merely a designation than as a concept of the thing; the so-called definition is nothing more than a determining of the word(k586)
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• 1/8/2013

Will

A will is purely animal, which cannot be determined save through sensuous impulses, that is, pathologically. A will which can be determined independently of sensuous impulses, and therefore through motives which are represented only by reason, is entitled free will and everything which is bound up with this will, whether as ground or as consequence, is entitled practical(k633)
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• 1/8/2013

Whole

We cannot assume that every part of an organized whole is itself again so organized that, in the analysis of the parts to infinity, still other organized parts are always to be met with; in a word, that the whole is organized to infinity(k460)
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• 1/8/2013

Water

(914b10) Water does not enter a tube submerged as the trapped air keeps it out
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• 1/8/2013

Von Neumann

What can exist at all for Zermelo are elements for von Neumann(flpov97)
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• 1/10/2013

Variable

We do not have one implication containing a variable, but rather a variable implication. We have a class of implications, no one of which contains a variable, and we assert that every member of this class is true. This is a first step towards the analysis of the mathematical notion of the variable(pm38)
The variable is perhaps the most distinctively mathematical of all notions. It is certainly also one of the most difficult to understand(pm89)
The variable requires the indefinable notion of any(pm91)
The usual x in algebra does not stand for a particular number, nor for all numbers, nor yet for the class number(pm351)
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• 1/8/2013

Validity

Validity is not a kind of being, but being belongs to valid and invalid propositions alike(pm450)
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• 1/8/2013

Use and Mention

It is rather important to realize this about the two different uses of names or of any other symbols: the one when you are talking about the symbol and the other when you are using it as a symbol, as a means of talking about something else(lk246)
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• 1/18/2013

Universe of Discourse

One might hope that 'always' would mean 'for all values of x'. But 'all values of x', if legitimate, would include as parts 'all propositions' and 'all functions', and such illegitimate totalities. Hence the values of x must be somehow restricted within some legitimate totality. This seems to lead us to the traditional doctrine of a 'universe of discourse' within which x must be supposed to lie(lk71)
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• 1/18/2013

Universal

The lowest species are themselves universals founded on similarity(LE275)
In so far as you conceive the similarities amongst things, you are conceiving something in addition to the things themselves, and that is all that universality is(LE486)
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• 1/8/2013

Unity

Subsistence, reality, unity(not plurality), existence form the basis of the unity of the categories in a possible perception. Reason here represents all of these as conditions, which are themselves unconditioned, of the possibility of a thinking being. Thus the soul knows in itself- 1. The unconditioned unity of relation, i.e. that it itself is not inherent in something else but self-subsistent. 2. The unconditioned unity of quality, that is, that it is not a real whole but simple. 3. The unconditioned unity in the plurality of time, i.e. that it is not numerically different at different times but one and the very same subject. 4. The unconditioned unity of existence in space, i.e. that it is not the consciousness of many things outside it, but the consciousness of the existence of itself only, and of other things merely as its representations(k366)
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• 1/8/2013

Understanding

Experience is itself a species of knowledge which involves understanding; and understanding has rules which I must presuppose as being in me prior to objects being given to me, and therefore as being a priori.(kBxviii)
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• 1/18/2013

Type

Classes and relations cannot be added together to form a new single class, because they are of different logical 'types'(imp53)
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• 1/18/2013

Truth

(1009a6) If all opinions and appearances are true, all statements must be at the same time true and false
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• 1/18/2013

Time

Only on the presupposition of time can we represent to ourselves a number of things as existing at one and the same time or at different times(kA31)
Time is a pure form of sensible intuition(kA32)
Time is the formal a priori condition of all appearances whatsoever(kA34)
We deny to time all claim to absolute reality(kA36)
Time is given a priori(kB46)
Time has only one dimension as space has only three(kB47)
Time is nothing but the intuition of ourselves and of our inner state(kB50)
Time is the formal condition of inner sense to which all our knowledge is subject to(kA99)
If we ascribe succession to time itself, we must think yet another time, in which the sequence would be possible(kA183)
The order, not the lapse, of time is important(kA203)
Time itself cannot be perceived(kB219)
All existence and all change in time have thus to be viewed as simply a mode of the existence of that which remains and persists(kB229)
All appearances of succession in time are one and all only alterations(kB233)
All determination of time presupposes something permanent in perception. This cannot be something in me, since it is only through this permanent that my existence in time can itself be determined(kB276)
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• 1/8/2013

Thought

(429b24) If thinking is a passive affection, then if thought is simple and impassible and has nothing in common with anything else, how can it come to think at all?
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• 1/10/2013

This

Apart from such words as "this" and "that", every name is a description involving some this, and is only a name in virtue of the truth of some proposition(hk94)
"This" might be taken as the only egocentric word not having a nominal definition. The word "this" is, in a sense, a proper name, but it differs from true proper names in the fact that its meaning is continually changing(hk100)
"This" denotes whatever, at the moment when the word is used, occupies the center of attention(hk107)
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• 1/8/2013

Thinking

Thinking is as inseparable from the soul as extension is from body(LO111)
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• 1/8/2013

Thing

To know a thing completely, we must know every possible predicate, and must determine it thereby, either affirmatively or negatively(k489)
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