# Tag Info

26

Aristotle's solution was largely accepted until the end of 19th century when Cantor and Dedekind formalized the notion of continuum in terms of set theory. Under their interpretation time is in fact composed of indivisible nows, just like a line is composed of points, and any other magnitude is composed of indivisible elements as well. It does not mean that ...

26

Logic means something different now than what it once did. In classical philosophy one primary branch of philosophy investigated the cosmos, one investigated human life, and a third investigated the forms of reasoning used in the other two: physikē, ethikē, logikē (See Diog. Laert. for variants on this schema.) When an older writer (or a modern classicist) ...

21

Aristotle's syllogistic logic is too weak for serious work. It does not readily express multi-place predicates. You cannot express two-place relations like, "John loves Mary", or three-place relations like, "John is standing between Mary and Joanne", without using some odd-looking additional apparatus for converting n-place predicates ...

20

Because there was a calculus for one-place predicates, Aristotle's syllogistic, roughly equivalent to monadic predicate calculus. Aristotle does discuss "relatives" in Categories, which refer to multi-place relations, or rather to objects entering them. What will later be called oblique syllogisms involving relatives is mentioned in passing in ...

19

We must first distinguish between what is physically possible — what it is possible to actually occur — and what is imaginable, or logically possible under certain premisses. Remarks about the logically possible Initial approaches Logic itself — which I will take to mean classical propositional logic — has very little to say about ...

15

No, Aristotle's logic has not been rendered obsolete or disproved; "modern works still reference/use his logic frequently" (courtesy: V2Blast). See, for example: Łukasiewicz, Jan. 1957. Aristotle's syllogistic from the standpoint of modern formal logic. Oxford: Clarendon Press.&Thomas Greenwood. “The Unity of Logic,” Thomist: A Speculative Quarterly ...

13

Kind of. The obvious As animal sociale is the Latin, especially Scholastic translation of zoon politikon, just as animal rationale is the translation of ζῷον λόγον ἔχον, zōon logon ekhon, he in this sense of course wrote about animal rationale. Texts where he discusses this term, translated accordingly, are e.g. De Partibus Animalium, 686a27ff., as ...

12

The history of ideas and the history of philosophy is a world riddled with boogeymen versions of certain philosophers. Some of the more common historical boogeymen are "Plato", "Aristotle", "scholasticism" / "Medieval philosophy" , "Descartes", "Kant", "Hegel", "Nietzsche", and "Kierkegaard" . You may notice two things about this list: (1) every name is in ...

11

I think Russell is fairly clear in this passage --his gripe is not so much with Aristotle, but with how (in his opinion) Aristotelian thought continued to dominate the fields of science, philosophy, and logic long after it had outlived its usefulness. In particular, he saw the field of logic as having ossified for thousands of years after Aristotle's death....

11

Terminology changed somewhat, and much of what used to be called "logic" as late as early 20th century is now called epistemology, for more details see What are the differences between philosophies presupposing one Logic versus many logics? Posterior Analytics covers mostly that epistemological part of logic. What Aristotle describes is what later was coined ...

10

Shane's answer is great overall on what to read, but reading your title and question body again... you asked what to skip. Skip his Biology in its entirety. There's quite a few texts in there. Mostly interesting only on an anecdotal level (nearly all the primary texts here http://plato.stanford.edu/entries/aristotle-biology/). I'm not saying that it's ...

10

Thomists affirm theism, but God would be a counterexample to your proposition as stated: God is something "that exists" in Himself; He does not "exist by something [else]". Thomists' principle of sufficient reason (PSR) A more accurate statement of Thomists' version of PSR is (Philosophical Axiom 7.1): Everything has sufficient reason of ...

8

Aristotle classified states according to two variables: who holds power? And: in whose interest is it exercised? There are three politically possible answers to the first question (one, some and all:the kingship, aristocracy, and politeia), and two politically possible answers to the second (the holder of power, and everyone). Aristotle treats kingship and ...

8

Most physicists don't accept infinities for a very obvious reason: such infinite physical objects are not quantifiable! That is, we can't measure them or even prove that they are infinite. Through the history of physics, infinities were raised in formulas, and usually in these cases the formulas were thrown away, considered as incomplete, or they kept ...

8

The context is human action and its "rationality": [ 1113b.1 ] The activities in which the virtues are exercised deal with means. Therefore virtue also depends on ourselves. And so also does vice. [...] if it is in our power to do and to refrain from doing right and wrong, and if, as we saw, being good or bad is doing right or wrong, it ...

7

I am a mathematician that found this page by accident, so I can't help you with the Zeno's paradox part (I think that was solved by calculus hundreds of years ago). But I would like to clarify some misconceptions. The thermal time hypothesis is not directly related to loop quantum gravity. It is instead a mathematical result from the theory of von Neumann ...

7

1 is not a number because 1 happens to be the (a?) unit. And a number, by definition, is a multitude of units. So clearly then, the two are distinct. See Metaphysics 1052b35, Posterior Analytics 72a22, and Topics 108b30. To see why, for example, 2 is a number whereas 1 is a unit, see Metaphysics 1039a15.

7

Regarding specifically Russell's attitude towards Aristotle's logic, I have come to wonder if in the course of a justified complaint about an enormous time span of intellectual stagnation, Russell maybe missed an opportunity to recognize a few excellent aspects of Aristotle's logic, which, after dismissing them, took much effort to be rediscovered by Russell ...

7

Strictly speaking there are no absolute necessities in physics. But strictly speaking there are no absolute necessities in mathematics and logic either. Mathematical theories have axioms, necessity of conclusions is relative to them, and to logic used. The law of excluded middle is rejected by intuitionists, the law of non-contradiction by dialetheists (see ...

7

There are several notions of intuitionistic continuum, the closest ones to Aristotle's are Brouwer's "fluid continuum", and especially late Weyl’s version of it since On the New Foundational Crisis of Mathematics (1921). We have to keep in mind, however, that Brouwer and Weyl received their view through a major intermediary, Kant. Although Aristotle’s and ...

7

Aristotle, 'In the case of objects which involve no matter, what thinks and what is thought are identical' ('De Anima', III, 430a, 3-4). (J.A. Smith tr., Oxford.)

7

The paper General Theory of Natural Equivalences by Eilenberg and Mac Lane (1945), where the terminology is first introduced, mentions neither Aristotle, nor Kant, nor even Carnap, who was still alive. The motivation given was: "In a metamathematical sense our theory provides general concepts applicable to all branches of mathematics, and so ...

7

I'd make two points. The first is that you can't do everything at once, so you should recognise that acquiring a competence in philosophy will be a slow process. A single text or a set of guides will at best give you a picture of the field. They will tell you what philosophy is, or how it is understood on sites such as this, or in a particular tradition, but ...

7

That's not quite right for the parsing. What you're seeing is BOOK Chapter and Bekker notation. Your example: Met. I.3 983b6–18 = Metaphysics Book I Chapter 3 Bekker page 983 column b lines 6-18. So 6-18 is not the paragraph numbers but rather the line numbers in the Bekker edition. This is the standard scholarly way to cite Aristotle. You can also ...

7

Aristotle, Aristotle's Categories and De Interpretatione, Published by Clarendon Press, Oxford, 1963. Translated with notes by J.L.Ackrill. Ackrill was a fine scholar and I still find this book reliable. Jonathan Barnes is a principal expert on Aristotle and the relevant part of his Aristotle: A Very Short Introduction, ISBN 10: 0192854089 / ISBN 13: ...

7

Given that you have about a month and a half to prepare, in which you estimate you can read two or three books, I would not recommend starting with Aristotle to understand Being and Time. Instead, I might focus on the skills necessary to grasp Cartesian Meditations and also to understand the sort of problems Being and Time is dealing with. Neither of these ...

7

The efficient cause is not numerically identical with the effect because the "things" involved into the "production process" are different individials : the father of John generates John but he is a different individual : the father is not numerically identical with the son. But the father, in order to produce a man must be himself a man, i.e. he must ...

7

An n-ary relation gives rise to parameterized unary predicates if one fixes n-1 arguments. Wilfrid Hodges argues that this is what logicians did before the nineteenth century. (There may be other works of his that better explain this.) More concretely, they would re-write the relevant statements by using natural language reasoning so that all relations are ...

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