11 ideas
17818 | How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau] |
Full Idea: We want to know How many what? You must first partition an aggregate into parts relevant to the question, where no partition is privileged. How the partitioned set is to be numbered is bound up with its unique members, and follows from logic alone. | |
From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'New Problem') | |
A reaction: [Compressed wording of Yourgrau's summary of Frege's 'relativity argument'] Concepts do the partitioning. Yourgau says this fails, because the same argument applies to the sets themselves, as well as to the original aggregates. |
17822 | Nothing is 'intrinsically' numbered [Yourgrau] |
Full Idea: Nothing at all is 'intrinsically' numbered. | |
From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'What the') | |
A reaction: Once you are faced with distinct 'objects' of some sort, they can play the role of 'unit' in counting, so his challenge is that nothing is 'intrinsically' an object, which is the nihilism explored by Unger, Van Inwagen and Merricks. Aristotle disagrees... |
17817 | Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau] |
Full Idea: The Frege-Maddy definition of number (as the 'property' of being-three) explains why the definitions of Von Neumann, Zermelo and others work, by giving the 'principle of collection' that ties together all threes. | |
From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'A Fregean') | |
A reaction: [compressed two or three sentences] I am strongly in favour of the best definition being the one which explains the target, rather than just pinning it down. I take this to be Aristotle's view. |
17815 | We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau] |
Full Idea: Sets could hardly serve as a foundation for number theory if we had to await detailed results in the upper reaches of the edifice before we could make our first move. | |
From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'Two') |
17821 | You can ask all sorts of numerical questions about any one given set [Yourgrau] |
Full Idea: We can address a set with any question at all that admits of a numerical reply. Thus we can ask of {Carter, Reagan} 'How many feet do the members have?'. | |
From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'On Numbering') | |
A reaction: This is his objection to the Fregean idea that once you have fixed the members of a set, you have thereby fixed the unique number that belongs with the set. |
3236 | Equality of opportunity without equality of respect would create a very inhuman society [Williams,B] |
Full Idea: A highly rational, efficient and unmitigated application of the idea of equality of opportunity, while abandoning the idea of equality of respect as vague and nostalgic, would lead to a quite inhuman society. | |
From: Bernard Williams (The Idea of Equality [1962], §3) |
3233 | Equality implies that people are alike in potential as well as in needs [Williams,B] |
Full Idea: Supporters of equality have asserted that people are alike in certain things they could do or achieve, as well as in the things that they need and could suffer. | |
From: Bernard Williams (The Idea of Equality [1962], §2) |
3234 | Equality seems to require that each person be acknowledged as having a significant point of view [Williams,B] |
Full Idea: Equality seems to require that each person is owed an effort at identification; they should not be seen as a surface to which a label can be applied, but one should try to see the world (including the label) from their point of view. | |
From: Bernard Williams (The Idea of Equality [1962], §2) |
3235 | It is a mark of extreme exploitation that the sufferers do not realise their plight [Williams,B] |
Full Idea: It is a mark of extreme exploitation or degradation that those who suffer it do NOT see themselves differently from the way they are seen by the exploiters. | |
From: Bernard Williams (The Idea of Equality [1962], §2) |
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 |
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. |