"A problem that is suitable for argumentative reasoning is one for which there are numerous and good arguments." (Aristotle, "Topics", cca. 350 BC)
"A quantity is infinite if it is such that we can always take a part outside what has been already taken." (Aristotle, "Physics")
"All human actions have one or more of these seven causes: chance, nature, compulsions, habit, reason, passion, desire." (Aristotle)
"But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end." (Aristotle, "Generation of Animals")
"Educating the mind without educating the heart is no education at all." (Aristotle)
"Education and morals will be found almost the whole that goes to make a good man." (Aristotle)
"Education is the best provision for old age." (Aristotle)
"Education is the best provision for old age." (Aristotle)
"For all who argue per impossibile infer by syllogism a false conclusion, and prove the original conclusion hypothetically when something impossible follows from a contradictory assumption, as, for example, that the diagonal [of a square] is incommensurable [with the side] because odd numbers are equal to even if it is assumed to be commensurate. It is inferred by syllogism that odd numbers are equal to even, and proved hypothetically that the diagonal is incommensurate, since a false conclusion follows from the contradictory assumption." (Aristotle, "Laws")
"For generally the infinite has this mode of existence: one thing is always being taken after another, and each thing that is taken is always finite […]." (Aristotle, "Physics")
"For that which is probable is that which generally happens." (Aristotle, "The Art of Rhetoric", 4th century BC)
"For the things we have to learn before we can do, we learn by doing." (Aristotle, "Nicomachean Ethics", Book II, 349 BC)
"[Imagination is] that in virtue of which we say that an image occurs to us and not as we speak of it metaphorically." (Aristotle, "De Anima" III, cca. 350 BC)
"In all disciplines in which there is systematic knowledge of things with principles, causes, or elements, it arises from a grasp of those: we think we have knowledge of a thing when we have found its primary causes and principles, and followed it back to its elements." (Aristotle, "Physics", cca. 350 BC)
"Intuition is the source of scientific knowledge." (Aristotle)
"Metaphysics is universal and is exclusively concerned with primary substance. […] And here we will have the science to study that which is, both in its essence and in the properties which, just as a thing that is, it has. […] That among entities there must be some cause which moves and combines things. […] There must then be a principle of such a kind that its substance is activity." (Aristotle, "Metaphysics", cca. 335-323 BC)
"Of the figures, the first is especially scientific. The mathematical sciences carry out their demonstrations through it – e.g. arithmetic and geometry and optics – and so do almost all those sciences which inquire into the reason why. For deductions giving the reason why are carried out, either in general or for the most part and in most cases, through this figure. For this reason, then, it is especially scientific; for study of the reason why has most importance for knowledge." (Aristotle, "Posterior Analytics", cca. 350 BC)
"Our account does not rob mathematicians of their science, by disproving the actual existence of the infinite in the direction of increase, in the sense of the untraceable. In point of fact they do not need the infinite and do not use it. They postulate any that the finite straight line may be produced as far as they wish." (Aristotle, "Physics")
"For generally the infinite has this mode of existence: one thing is always being taken after another, and each thing that is taken is always finite […]." (Aristotle, "Physics")
"For that which is probable is that which generally happens." (Aristotle, "The Art of Rhetoric", 4th century BC)
"For the things we have to learn before we can do, we learn by doing." (Aristotle, "Nicomachean Ethics", Book II, 349 BC)
"[Imagination is] that in virtue of which we say that an image occurs to us and not as we speak of it metaphorically." (Aristotle, "De Anima" III, cca. 350 BC)
"If 'bounded by a surface' is the definition of body there cannot be an infinite body either intelligible or sensible." ((Aristotle, "De Caelo" ["On the Heavens"], cca. 350 BC)
"In all disciplines in which there is systematic knowledge of things with principles, causes, or elements, it arises from a grasp of those: we think we have knowledge of a thing when we have found its primary causes and principles, and followed it back to its elements." (Aristotle, "Physics", cca. 350 BC)
"In all things which have a plurality of parts, and which are not a total aggregate but a whole of some sort distinct from the parts, there is some cause." (Aristotle, "Metaphysics", cca. 335-323 BC)
"Intuition is the source of scientific knowledge." (Aristotle)
"It is impossible that the existence of something [one thing] should necessitate both the existence and the non-existence of something else [i.e., one (same) other thing]." (Aristotle, "Posterior Analytics", cca. 350 BC)
"It is obvious then, that memory belongs to that part of the soul to which imagination belongs. […] Just as the picture painted on the panel is at once a picture and a portrait, and though one and the same, is both, yet the essence of the two is not the same, and it is possible to think of it both as a picture and as a portrait, so in the same way we must regard the mental picture within us both as an object of contemplation in itself and as a mental picture of something else […]. Insofar as we consider it in relation to something else, e.g. as a likeness, it is also an aid to memory." (Aristotle, "De Memoria et Reminiscentia" [On Memory and Recollection], 4th century BC)
"It is the mark of an educated mind to rest satisfied with the degree of precision which the nature of the subject admits and not to seek exactness where only an approximation is possible." (Aristotle, "Nicomachean Ethics", Book II, 349 BC)
"Knowledge, then, is a state of capacity to demonstrate, and has the other limiting characteristics which we specify in the Analytics; for it is when one believes in a certain way and the principles are known to him that he has knowledge, since if they are not better known to him than the conclusion, he will have his knowledge only on the basis of some concomitant." (Aristotle," Nicomachean Ethics", cca. 340 BC)
"It is obvious then, that memory belongs to that part of the soul to which imagination belongs. […] Just as the picture painted on the panel is at once a picture and a portrait, and though one and the same, is both, yet the essence of the two is not the same, and it is possible to think of it both as a picture and as a portrait, so in the same way we must regard the mental picture within us both as an object of contemplation in itself and as a mental picture of something else […]. Insofar as we consider it in relation to something else, e.g. as a likeness, it is also an aid to memory." (Aristotle, "De Memoria et Reminiscentia" [On Memory and Recollection], 4th century BC)
"It is the mark of an educated mind to rest satisfied with the degree of precision which the nature of the subject admits and not to seek exactness where only an approximation is possible." (Aristotle, "Nicomachean Ethics", Book II, 349 BC)
"Knowledge, then, is a state of capacity to demonstrate, and has the other limiting characteristics which we specify in the Analytics; for it is when one believes in a certain way and the principles are known to him that he has knowledge, since if they are not better known to him than the conclusion, he will have his knowledge only on the basis of some concomitant." (Aristotle," Nicomachean Ethics", cca. 340 BC)
"Metaphors do somehow make known what they mean by the comparison they involve. Whenever we use them, we transfer meaning according to some similarity. But statements such as the aforesaid do not make anything known. There is no inherent resemblance to justify calling law ‘a measure’ or ‘an image’ , nor is it customary to refer to it as such. If one says that law is literally ‘a measure’ or ‘an
image’, he is either deceiving or being deceived. An image is something fashioned in the likeness of something else, but such is not an inherent characteristic of law. If, on the other hand, the statement is not made in a literal sense, it is evident that it is obscure, and worse than any metaphorical expression." (Aristotle)
"Metaphysics is universal and is exclusively concerned with primary substance. […] And here we will have the science to study that which is, both in its essence and in the properties which, just as a thing that is, it has. […] That among entities there must be some cause which moves and combines things. […] There must then be a principle of such a kind that its substance is activity." (Aristotle, "Metaphysics", cca. 335-323 BC)
"Of the figures, the first is especially scientific. The mathematical sciences carry out their demonstrations through it – e.g. arithmetic and geometry and optics – and so do almost all those sciences which inquire into the reason why. For deductions giving the reason why are carried out, either in general or for the most part and in most cases, through this figure. For this reason, then, it is especially scientific; for study of the reason why has most importance for knowledge." (Aristotle, "Posterior Analytics", cca. 350 BC)
"Our account does not rob mathematicians of their science, by disproving the actual existence of the infinite in the direction of increase, in the sense of the untraceable. In point of fact they do not need the infinite and do not use it. They postulate any that the finite straight line may be produced as far as they wish." (Aristotle, "Physics")
"Sense perception is a prerequisite for memory; the memory of frequently repeated sense perceptions results in experimental proof; experimental proofs provide the materials for a science or an art.” (Aristotle)
"So poetry is something more philosophical and more worthy of serious attention than history, for while poetry is concerned with universal truth, history treats of particular facts [...]" (Aristotle, "Poetics", cca. 350 BC)
"The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree. And since these (e.g. order and definiteness) are obviously causes of many things, evidently these sciences must treat this sort of causative principle also (i.e. the beautiful) as in some sense a cause." (Aristotle, "Metaphysica", cca. 350 BC)
"The infinite is imperfect, unfinished and therefore, unthinkable; it is formless and confused." (Aristotle)
"The intellectual capacity thinks the forms in the phantasmata (mental images) […] And for the following reason, as without having perceptual awareness no one could either learn or understand anything, so when one engages in intellectual activity one must at that time do so by means of a phantasma. For, phantasmata are just as perceptual states (aisthemata) are [in actual external perception] but without matter." (Aristotle, "De Anima" III, cca. 350 BC)
"The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful." (Aristotle, "Metaphysics", cca. 335-323 BC)
"The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree. And since these (e.g. order and definiteness) are obviously causes of many things, evidently these sciences must treat this sort of causative principle also (i.e. the beautiful) as in some sense a cause." (Aristotle, "Metaphysica", cca. 350 BC)
"The infinite is imperfect, unfinished and therefore, unthinkable; it is formless and confused." (Aristotle)
"The intellectual capacity thinks the forms in the phantasmata (mental images) […] And for the following reason, as without having perceptual awareness no one could either learn or understand anything, so when one engages in intellectual activity one must at that time do so by means of a phantasma. For, phantasmata are just as perceptual states (aisthemata) are [in actual external perception] but without matter." (Aristotle, "De Anima" III, cca. 350 BC)
"The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful." (Aristotle, "Metaphysics", cca. 335-323 BC)
"The only possible way to conceive universal is by induction, since we come to know abstractions by induction. But unless we have sense experience, we cannot make inductions. Even though sense perception relates to particular things, scientific knowledge concerning such can only be constructed by the successive steps of sense perception, induction, and formulation of universals." (Aristotle, "Posterior Analytics", cca. 350 BC)
"The point is prior to, and in itself more evident than the line. The same may be said of the line relative to the plane surface, and of the plane surface with reference to the solid. It is likewise true of unity in relation to plurality, for which unity is the principle. This also holds in regard to the letter relative to the syllable. [...] The reverse, however, sometimes occurs in the case of our knowledge. Generally the average mind more readily perceives what is posterior, whereas the comprehension of what is prior is reserved to the more profound and learned intellect." (Aristotle, "Topics", cca. 350 BC)
"The whole is more than the sum of its parts." (Aristotle, "Metaphysics", cca. 335-323 BC)
"Those who assert that the mathematical sciences make no affirmation about what is fair or good make a false assertion; for they do speak of these and frame demonstrations of them in the most eminent sense of the word. […] Of what is fair, however, the most important species are order and symmetry, and that which is definite, which the mathematical sciences make manifest in a most eminent degree." (Aristotle, "Metaphysics", cca. 335-323 BC)
"Time and space are divided into the same and equal divisions. Wherefore also, Zeno’s argument, that it is impossible to go through an infinite collection or to touch an infinite collection one by one in a finite time, is fallacious. For there are two senses in which the term ‘infinte’ is applied both to length and to time and in fact to all continuous things: either in regard to divisibility or in regard to number. Now it is not possible to touch things infinite as to number in a finite time, but it is possible to touch things infinite in regard to divisibility; for time itself is also infinite in this sense." (Aristotle)
"What we know is not capable of being otherwise; of things capable of being otherwise we do not know, when they have passed outsideour observation, whether they exist or not. Therefore the object of knowledge is of necessity. Therefore it is eternal; for things that are of necessity in the unqualified sense are all eternal; and things that are eternal are ungenerated and imperishable. " (Aristotle, "Nicomachean Ethics", cca. 340 BC)
"When the consequences of either assumption are the same, we should always assume that things are finite rather than infinite in number, since in things constituted by nature that which is infinite and that which is better ought, if possible, to be present rather than the reverse […]" (Aristotle)
"While those whom devotion to abstract discussions has rendered unobservant of the facts are too ready to dogmatize on the basis of a few observations." (Aristotle, "De Caelo" ["On the Heavens"], cca. 350 BC)
"The same ideas, one must believe, recur in men’s minds not once or twice but again and again." (Aristotle, "De Caelo" ["On the Heavens"], cca. 350 BC)
"The soul never thinks without a picture." (Aristotle)"The whole is more than the sum of its parts." (Aristotle, "Metaphysics", cca. 335-323 BC)
"Those who assert that the mathematical sciences make no affirmation about what is fair or good make a false assertion; for they do speak of these and frame demonstrations of them in the most eminent sense of the word. […] Of what is fair, however, the most important species are order and symmetry, and that which is definite, which the mathematical sciences make manifest in a most eminent degree." (Aristotle, "Metaphysics", cca. 335-323 BC)
"Time and space are divided into the same and equal divisions. Wherefore also, Zeno’s argument, that it is impossible to go through an infinite collection or to touch an infinite collection one by one in a finite time, is fallacious. For there are two senses in which the term ‘infinte’ is applied both to length and to time and in fact to all continuous things: either in regard to divisibility or in regard to number. Now it is not possible to touch things infinite as to number in a finite time, but it is possible to touch things infinite in regard to divisibility; for time itself is also infinite in this sense." (Aristotle)
"What is one is indivisible whatever it may be, e.g. a man is one man, not many. Number on the other hand is a plurality of 'ones' and a certain quantity of them. Hence number must stop at the indivisible: for 'two' and 'three' are merely derivative terms, and so with each of the other numbers." (Aristotle, "Physics", cca. 4th-century BC)
"What we know is not capable of being otherwise; of things capable of being otherwise we do not know, when they have passed outsideour observation, whether they exist or not. Therefore the object of knowledge is of necessity. Therefore it is eternal; for things that are of necessity in the unqualified sense are all eternal; and things that are eternal are ungenerated and imperishable. " (Aristotle, "Nicomachean Ethics", cca. 340 BC)
"When the consequences of either assumption are the same, we should always assume that things are finite rather than infinite in number, since in things constituted by nature that which is infinite and that which is better ought, if possible, to be present rather than the reverse […]" (Aristotle)
"While those whom devotion to abstract discussions has rendered unobservant of the facts are too ready to dogmatize on the basis of a few observations." (Aristotle, "De Caelo" ["On the Heavens"], cca. 350 BC)
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