All the paradoxes arise from the attribution of significance to sentences that are in fact nonsensical(imt172)
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The particular cannot be defined or recognized or known it is something serving the merely grammatical purpose of providing the subject in a subject-predicate sentence as "this is red"(hk311)
(1047a6) Nothing will be either cold or hot or sweet or perceptible at all if people are not perceiving it; indeed, nothing will even have perception if it is not perceiving, i.e. exercising its perception
Everything can be said to be the same at all times and places except in degrees of perfection(LE72)
The organic body level of perfection corresponds to that of the intelligence or mind which occupies the body(LE307)
If there were no connection by way of memory between the different Persona which were made by the same soul, there would not be enough moral identity to say that this was a single person(LE234)
The inner being of the rational soul remains despite the suspending of the exercise of reason(LE234)
Continuity and inner connection of perceptions make someone the same individual including minute presentiment of everything that will happen to it(LE239)
In space there is nothing real which can be simple; points, which are the only simple things in space, are merely limits, not themselves anything that can as parts serve to constitute space. From this follows the impossibility of any explanation in materialist terms of the constitution of the self as a merely thinking subject(k376)
The term ‘principle’ is ambiguous, and commonly signifies any knowledge which can be used as a principle, although in itself, it is no principle. Every universal proposition can serve as major premise in a syllogism, but it is not therefore in itself a principle. The mathematical axioms are instances of universal a priori knowledge and are therefore rightly called principles(k300)
Knowledge from principle is, therefore, that knowledge alone in which I apprehend the particular in the universal through concepts. Thus every syllogism is a mode of deducing knowledge from a principle(k301)
If opinion based on probability is not considered knowledge all history will have to be discounted(LE372)
We need a new kind of logic concerned with degrees of probability(LE466)
The logic of probables involves different inferences from the logic of necessary truths. But the probability of these inferences must be demonstrated through inferences belonging to the logic of necessary propositions(LE484)
The proof of a theorem is a rigorous justification of the veracity of the theorem in such a way that it cannot be disputed by anyone who follows the rules of logic, and who accepts a set of axioms put forth as the basis for the logic system(flt29)
There is a traditional distinction between "proper" names and "class" names, which is explained as consisting in the fact that a proper name applies, essentially, to only one object, whereas a class name applies to all objects of a certain kind(hk87)
It may happen that there is only one instance of a class name, e.g. "satellite of the earth". In such a case, the one member may have a proper name ("the moon"), but the proper name does not have the same meaning as the class name, and has different syntactical functions(hk87b)
Proper names owe their existence in ordinary language to the concept of "substance"(hk87c)
Most of us, nowadays, do not accept "substance" as a useful notion. Are we then to adopt, in philosophy, a language without proper names? Or are we to find a definition of "proper name" which does not depend on "substance"?(hk88)
A proper name is a word designating any continuous portion of space-time which sufficiently interests us; thus they are unnecessary, since any portion of space-time can be described by its co-ordinates. A word must denote something that can be recognized, and space-time regions, apart from qualities, cannot be recognized, since they are all alike(hk89)
The need for proper names is bound up with our way of acquiring knowledge(hk325)
We can speak of any property of x, but not of all properties, because new properties would be thereby generated(lk68)
Every proposition in which a description which describes nothing has a primary occurrence is false(imp179)
The egocentric propositional attitudes, such as those expecting to be in some sort of physical situation, seem to be the most primitive. I(Quine) expect the others presuppose language. Each of the possible worlds suited to the cat examples will have its center or origin in the midst of a cat(or154)
Examples of propositional functions are easy to give: 'x is human' is a propositional function so long as x remains undetermined, it is neither true nor false, but when a value is assigned to x it becomes a true or false proposition. Any mathematical equation is a propositional function(imp156)
Sentences involving such words as 'all,' 'every,' 'a,' 'the, and 'some' require propositional functions for their interpretation. The way in which propositional functions occur can be explained by means of two of the above words, namely, 'all' and 'some'. All the other uses of propositional functions can be reduced to these two(imp158)
For want of the apparatus of propositional functions, many logicians have been driven to the conclusion that there are unreal objects as argued, e.g. by Meinong. In such theories, it seems to Bertrand Russell, there is a failure of that feeling for reality which ought to be preserved even in the most abstract studies(imp169)
When we substitute a description for a name, propositional functions which are always true may become false, if the description describes nothing(imp176)
(203a4) Some, as the pythagoreans and Plato, make the infinite a principle as a substance in its own right, and not as an accident of some other thing. Only the pythagoreans place the infinite among the objects of sense (they do not regard number as separate from these) and assert that what is outside the heaven is infinite. Plato, on the other hand, holds that there is no body outside (the forms are not outside because they are nowhere), yet that the infinite is present not only in the objects of sense but in the forms also. Further the pythagoreans identify the infinite with the even. For this they say, when it is cut off and shut in by the odd, provides things with the element of infinity. An indication of this is what happens with numbers. If the gnomons are placed round the one, and without the one, in the one construction the figure that results is always different, in the other it is always the same. But Plato has two infinities, the Great and the Small
(204a33) Thus the view of those who speak after the manner of the pythagoreans is absurd. With the same breath they treat the infinite as substance and divide it into parts
(213b23) The pythagoreans, too, held that void exists and that it enters the world from the infinite air, the world inhaling also the void which distinguishes the natures of things, as if it were what separates and distinguishes the terms of a series. This holds primarily in the numbers; for the void distinguishes their nature
(268a11) The pythagoreans say, the universe and all that is in it is determined by the number three, since beginning and middle and end give the number of the universe, and the number they give is the triad
(293a20) The Italian philosophers known as the Pythagoreans take the view that the center of heaven is fire and the earth is one of the stars, creating night and day by its circular motion about the center. They further construct another earth in opposition to ours to which they give the name counter-earth. In all this they are not seeking for theories and causes to account for the phenomena, but rather forcing the phenomena and trying to accommodate them to certain theories and opinions of their own
(300a15) The same consequences follow from composing the heaven of numbers, as some of the pythagoreans do who make all nature out of numbers. For natural bodies are manifestly endowed with weight and lightness, but an assemblage of units can neither be composed to form a body nor possess weight
(404a17) Some pythagoreans declared the motes in air, others what moved them, to be soul. These motes were referred to because they are seen always in movement, even in a complete calm
(407b22) The pythagoreans held that any soul could be clothed in any body- an absurd view, for each body seems to have a form and shape of its own
(445a16) The theory held by certain of the pythagoreans, that some animals are nourished by odors alone, is unsound. For we see that food must be composite, since the bodies nourished by it are not simple
(985b23) As the number 10 is thought to be perfect and to comprise the whole nature of numbers the Pythagoreans say that the bodies which move through the heavens are ten, but as the visible bodies are only nine, to meet this they invent a tenth- the 'counter-earth'
(987a13) The pythagoreans have said that there are two principles. They thought finitude and infinity were not attributes of certain other things, e.g. of fire or earth or anything else of this kind, but that infinity itself and unity itself were the Substance of the things of which they are predicated. This is why number was the substance of all things. Regarding the question of essence they began to make statements and definitions but treated the matter too simply. They both defined superficially and thought that the first subject of which a given term would be predicable was the substance of the thing, as if one supposed that double and 2 were the same because 2 is the first thing of which double is predicable (to be double and to be 2 are not the same; if they are, one thing will be many- a consequence they actually drew)
(987b11) The pythagoreans say that things exist by imitation of numbers, Plato says they exist by participation (of Forms)
(987b23) Plato agreed with the pythagoreans in saying that the One is substance and not a predicate of something else; and in saying that the numbers are the causes of the substance of other things, but he posits a dyad and constructs the infinite out of great and small, instead of treating the infinite as one. While pythagoreans say that the things themselves are numbers, Plato says that the numbers exist apart from sensible things and that the objects of mathematics exist between forms and sensible things
(989b29) The pythagoreans use stranger principles and elements than the natural philosophers (the reason is that they got the principles from non-sensible things, for the objects of mathematics are of the class of things without movement) They do not tell us at all how there can be movement if limit and unlimited and odd and even are the only things assumed, or how without process and change there can be generation and destruction, or how the bodies that move through the heavens can do what they do. If we granted them that spatial magnitude consists of these elements, or this were proved how would some bodies be light and others have weight? How are we to combine the beliefs that the modifications of number, and number itself are causes of what exists and happens in the heavens both from the beginning and now, and that there is no other number than this number out of which the world is composed?
(1001a10) The pythagoreans thought being and unity were nothing else, but this was their nature, their substance being just Unity and being
(1072b31) Those who suppose, as the Pythagoreans do, that supreme beauty and goodness are not present in the beginning, because the beginnings both of plants and of animals are causes, but beauty and completeness are in the effects of these are wrong in their opinion
(1080b16) The pythagoreans also believe in one kind of number- the mathematical; only they say it is not separate but sensible substances are formed out of it. For they construct the whole universe out of numbers- only not numbers consisting of abstract Units; they suppose the units to have spatial magnitude. But how the first 1 was constructed so as to have magnitude they seem unable to say
(1083b8) That bodies should be composed of numbers, and that this should be mathematical number, is impossible. For it is not true to speak of indivisible magnitudes and units have no magnitude. Arithmetical number consists of abstract units while pythagoreans identify number with real things
(1091a13) The Pythagoreans attribute generation to eternal things for they say that when the one had been constructed, whether out of planes or of surface or of seed or of elements which they cannot express, immediately the nearest part of the unlimited began to be drawn in and limited by the limit
A 'place' must not be taken to be a point, but must be taken to be the extent occupied by a single object of perception(lk114)
If absolute space is admitted, we can of course say that it is difference of place that makes the patches two(lk116)
(182b26) Some think that being and one mean the same; while others solve the argument of Zeno and Parmenides by asserting that being and one are used in a number of ways
Each soul must have received this inner source of the expression of what lies without from a universal cause upon which all of these beings depend and which brings it about that each of them perfectly agrees with and corresponds to the others(LE441)