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19

Here is Cantor in his own words (from his influential 1887 letter to Weierstrass): "I begin from the supposition of a linear magnitude ζ which is so small that its product by n , ζ · n, for every finite whole number n however great is smaller than unity, and then prove, from the concept of a linear magnitude and with the help of certain propositions from ...


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

Metaphysics today, as a special sub discipline of philosophy considers a really large number of important topics. For instance, all of the following are live metaphysical questions: The Mind/Body Problem: How is it possible that we have subjective experiences (like the feeling of seeing the colour red, or understanding a poem) given that the other things we ...


12

We do NOT define vacuous statements as true. A vacuously true statement is vacuously true. A "vacuously false" statement is vacuously false; although nobody ever gives this type of statement any thought. Example: Every element of the empty set is a purple flying elephant. We agree that this statement is (i) vacuous; it doesn't really say anything ...


11

Both definitions are outdated. As Husserl put it already back in 1901:"Only if one is ignorant of the modern science of mathematics, particularly of formal mathematics, and measures it by standards of Euclid and Adam Riese, can one remain stuck in the common prejudice that the essence of mathematics lies in number and quantity". In antiquity mathematics was ...


10

You're overthinking it! Just kidding, as a fellow engineer, I have an inkling where you are digging at. Welcome to the fascinating underbelly of mathematics, which is constantly churning and mixing with the philosophy of mathematics. It behaves a bit differently than the upper tiers. Instead of trying to make powerful earth shattering statements about ...


10

The concept of infinitesimal small and infinitely large numbers has been been formalized by the mathematical domain of non-standard analysis. The field of rationals (QQ,+,*) embedds into the ring (Omega_QQ,+,*). Elements of the latter are the equivalence classes of sequences of rational numbers; two sequences are considered equivalent when their ...


8

I agree that to define metaphysics as the study of the "nature of reality" is completely inadequate. It is a shallow definition, misleading, arguably circular. You leave us with a very complicated mission, though, if you expect the answer to this question to be given in pragmatic ("black and white") terms. The first thing that comes to my mind is that the ...


7

To a large extent this was inspired by Yannik's answer; but I hope that I elaborate on points differently enough to not be redundant. As far as I can tell, atheism (or secularism or materialism, considered separately) is a component of an over-arching worldview not the totality of the worldview itself. For example Secular Humanism is a worldview whose ...


7

From a modern point of view mathematics is considered the science of formal structures. Simple examples of such structures are topological spaces, groups, vector spaces, differentiable manifolds. A good overview of all fields of active mathematical research can be read off from the Mathematics Subject Classification, see http://www.ams.org/msc/msc2010.html ...


6

I wouldn't say there are "widely accepted (precise) definitions" for the two terms you mention. I would say there are several different well-known accounts that deal with relationship. The first one I would recommend is from Aristotle's Nicomachean Ethics. For Aristotle, the end goal of life is eudaimonia -- a word that can and has been translated as "...


6

Metaphysics is the title of a collection of lectures by Aristotle. The name is not by Aristotle but due to a later librarian who edited all scriptures of Aristotle. The librarian arranged the scripts in question behind Aristotle's scripts on physics which in Greek means meta ta physica. In his lectures, Aristotle deals with mostly general philosophical ...


5

I found a paragraph in Parfit's On What Matters that gives a definition of "substantive normative claim": There is another way in which some people have come to accept subjective theories about reasons. We can call some normative claim substantive when this claim both (a) states that something has some normative property, and (b) is ...


5

It depends on your point of view. You can define something by opposition, A=-B, but you can define positively A=B or tautologically A=A. Words are defined positively. In politics you have the same issue. Like Paul Sartre says in Critic of the Dialectical Reason the jew has defined himself firstly as opposed to the anti-Semitic.Then he defined himself ...


5

There is a related fallacy of "defining into existence" when implicitly defined entities are illicitly declared existent, versions of the ontological argument are often accused of defining God into existence. Kant clearly expressed the issue in his thesis that "existence is not a predicate". Even for ideal objects in mathematics it must be proved from axioms ...


5

This is a very good question, one that brings metaphysics to life. Unfortunately, I do not have a good answer, though I've tried to think about it. While Cort Ammon and others have given good definitional answers, these are more about the "nature of axiomatic systems," while I suspect what is wanted is more along the lines of, what is a straight line "...


5

The expression being defined is called the definiendum of the definition, and the expression that defines is called the definiens. In your example 'Planet' would be the definiendum. Reference


5

"Neither true nor false” means that the statement has no definite truth valued : it lives in a sort of limbo, a truth value-gap between true and false. “Either true or false” means that the statement has (exactly) one of the two truth values. To say that "Lexical definitions are either true or false" means that a Lexical definition : also known as ...


4

Despite the general consensus, atheism insnt a world view or a life mentality. Its simply the rejection of theism. So an Atheist can be pro live, reject the theory of evolution and be against premarital sex. The same applies to secularism, if you are secular you only want the state and religion to be separated. You still can be a theist and believe in god. ...


4

A lot of this hinges on what one takes to be a 'religion'. The term is not actually all that old in its current usage. (This is one reason why Japanese people imagine that they are not religious - 無宗教 [musyuukyou lit., "non-religious] - because they don't see things they regularly do like 墓参り [hakamairi grave vistations] or お盆 [o-bon holiday in August to ...


4

As you and commenters observe, ontology is viewed slightly differently across disciplines and in philosophy is applied to any metaphysical investigation of the nature of being -- though many philosophers have seen ontology as problems of classification and semantics. In KR, an ontology is used to describe a particular approach to the representation of ...


4

The question asked and the one described are different. You asked if it is possible to define "the supernatural." The answer to that question is, yes. It has been done in many dictionaries, and the word very simply is used to cover all things which have no cause in nature or causality. Within the description you changed the question with the caveat that the ...


4

This sounds like an example of equivocation, which Wikipedia defines as follows the misleading use of a term with more than one meaning or sense (by glossing over which meaning is intended at a particular time). It generally occurs with polysemic words (words with multiple meanings). However, the term equivocation is mainly used for using two senses of ...


4

I've played with such compatablistic definitions of "soul" before. The biggest challenge you face is people just nodding their head and saying, "yeah, sure." "Soul" is just a word. It's four letters. That's it. Nothing more. Period. And therein lies the problem. People assign that four lettered word a meaning. Christians, for instance, assign it a ...


4

The Chinese Word is 哲学 which is the composition of 哲 (wise) and 学 (study) The period it started to develop was during the Spring and Autumn Period which was more or less at the same time of the Greek Philosophy Development I really think that believing Philosophy is just a Greek Phenomenon is really wrong


4

Postmodernism is a grab bag term that applies to many different things that come ... after modernism. It's hard to know what someone means when they say this term as it gets bantered about (usually by people who are opposed to something they call "postmodernism" or by people who thinks it's the best thing ever). One reason it's hard is that what is modernism ...


4

See Aristotle's *Categories. Aristotle analyzes the basic relation of predication, expressed by the word "is" that was later expressed with the ontological dichotomy : substance-accident. In modern terms, he is trying to disentangle the different uses of "is" : "to be equal to", "to belongs to", "to be part of". He classifies four cases by means of two ...


4

I am not familiar with the expression, 'limited free will', but I can see a sense in which it could be used. The so-called libertarian view holds that X is free (has free will) at time t1 if and only if for some event or set of events, E2, there is no event or set of events, E1, that precedes E2 and is causally sufficient for E2. For 'events' we can read '...


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