Combining Texts

All the ideas for 'fragments/reports', 'Introductions to 'Aesthetics and the Phil of Art'' and 'Mathematics and the Metaphysicians'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

9 ideas

5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox

7557	To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell]
	Full Idea: Presumably Zeno appealed to the axiom that the whole has more terms than the parts; so if Achilles were to overtake the tortoise, he would have been in more places than the tortoise, which he can't be; but the conclusion is absurd, so reject the axiom.
	From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.89)
	A reaction: The point is that the axiom is normally acceptable (a statue contains more particles than the arm of the statue), but it breaks down when discussing infinity (Idea 7556). Modern theories of infinity are needed to solve Zeno's Paradoxes.

6. Mathematics / A. Nature of Mathematics / 1. Mathematics

10059	In mathematic we are ignorant of both subject-matter and truth [Russell]
	Full Idea: Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
	From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.76)
	A reaction: A famous remark, though Musgrave is rather disparaging about Russell's underlying reasoning here.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite

7556	A collection is infinite if you can remove some terms without diminishing its number [Russell]
	Full Idea: A collection of terms is infinite if it contains as parts other collections which have as many terms as it has; that is, you can take away some terms of the collection without diminishing its number; there are as many even numbers as numbers all together.
	From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.86)
	A reaction: He cites Dedekind and Cantor as source for these ideas. If it won't obey the rule that subtraction makes it smaller, then it clearly isn't a number, and really it should be banned from all mathematics.

12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence

7554	Self-evidence is often a mere will-o'-the-wisp [Russell]
	Full Idea: Self-evidence is often a mere will-o'-the-wisp, which is sure to lead us astray if we take it as our guide.
	From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.78)
	A reaction: The sort of nice crisp remark you would expect from a good empiricist philosopher. Compare Idea 4948. However Russell qualifies it with the word 'often', and all philosophers eventually realise that you have to start somewhere.

21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics

20327	Modern attention has moved from the intrinsic properties of art to its relational properties [Lamarque/Olson]
	Full Idea: In modern discussions, rather than look for intrinsic properties of objects, including aesthetic or formal properties, attention has turned to extrinsic or relational properties, notably of a social, historical, or 'institutional' nature.
	From: Lamargue,P/Olson,SH (Introductions to 'Aesthetics and the Phil of Art' [2004], Pt 1)
	A reaction: Lots of modern branches of philosophy have made this move, which seems to me like a defeat. We want to know why things have the relations they do. Just mapping the relations is superficial Humeanism.

21. Aesthetics / B. Nature of Art / 1. Defining Art

20326	Early 20th cent attempts at defining art focused on significant form, intuition, expression, unity [Lamarque/Olson]
	Full Idea: In the early twentieth century there were numerous attempts at defining the essence art. Significant form, intuition, the expression of emotion, organic unity, and other notions, were offered to this end.
	From: Lamargue,P/Olson,SH (Introductions to 'Aesthetics and the Phil of Art' [2004], Pt 1)
	A reaction: As far as I can see the whole of aesthetics was demolished in one blow by Marcel Duchamp's urinal. Artists announce: we will tell you what art is; you should just sit and listen. Compare the invention of an anarchic sport.

21. Aesthetics / B. Nature of Art / 7. Ontology of Art

20330	The dualistic view says works of art are either abstract objects (types), or physical objects [Lamarque/Olson]
	Full Idea: The dualistic view of the arts holds that works of art come in two fundamentally different kinds: those that are abstract entities, i.e. types, and those that are physical objects (tokens).
	From: Lamargue,P/Olson,SH (Introductions to 'Aesthetics and the Phil of Art' [2004], Pt 2)
	A reaction: Paintings are the main reason for retaining physical objects. Strawson 1974 argues that paintings are only physical because we cannot yet perfectly reproduce them. I agree. Works of art are types, not tokens.

26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature

1748	Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
	Full Idea: Archelaus was the first person to say that the universe is boundless.
	From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3

27. Natural Reality / G. Biology / 3. Evolution

5989	Archelaus said life began in a primeval slime [Archelaus, by Schofield]
	Full Idea: Archelaus wrote that life on Earth began in a primeval slime.
	From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus
	A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea.