Combining Texts

All the ideas for 'fragments/reports', 'Frege versus Cantor and Dedekind' and 'Seven Types of Atheism'

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

15 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
9978 Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait]
     Full Idea: The tendency to attack forms of expression rather than attempting to appreciate what is actually being said is one of the more unfortunate habits that analytic philosophy inherited from Frege.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], IV)
     A reaction: The key to this, I say, is to acknowledge the existence of propositions (in brains). For example, this belief will make teachers more sympathetic to pupils who are struggling to express an idea, and verbal nit-picking becomes totally irrelevant.
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
9986 The null set was doubted, because numbering seemed to require 'units' [Tait]
     Full Idea: The conception that what can be numbered is some object (including flocks of sheep) relative to a partition - a choice of unit - survived even in the late nineteenth century in the form of the rejection of the null set (and difficulties with unit sets).
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], IX)
     A reaction: This old view can't be entirely wrong! Frege makes the point that if asked to count a pack of cards, you must decide whether to count cards, or suits, or pips. You may not need a 'unit', but you need a concept. 'Units' name concept-extensions nicely!
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
9984 We can have a series with identical members [Tait]
     Full Idea: Why can't we have a series (as opposed to a linearly ordered set) all of whose members are identical, such as (a, a, a...,a)?
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], VII)
     A reaction: The question is whether the items order themselves, which presumably the natural numbers are supposed to do, or whether we impose the order (and length) of the series. What decides how many a's there are? Do we order, or does nature?
18. Thought / E. Abstraction / 2. Abstracta by Selection
9981 Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait]
     Full Idea: If the sense of a proposition about the abstract domain is given in terms of the corresponding proposition about the (relatively) concrete domain, ..and the truth of the former is founded upon the truth of the latter, then this is 'logical abstraction'.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], V)
     A reaction: The 'relatively' in parentheses allows us to apply his idea to levels of abstraction, and not just to the simple jump up from the concrete. I think Tait's proposal is excellent, rather than purloining 'abstraction' for an internal concept within logic.
9982 Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait]
     Full Idea: Although (in Cantor and Dedekind) abstraction does not (as has often been observed) play any role in their proofs, but it does play a role, in that it fixes the grammar, the domain of meaningful propositions, and so determining the objects in the proofs.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], V)
     A reaction: [compressed] This is part of a defence of abstractionism in Cantor and Dedekind (see K.Fine also on the subject). To know the members of a set, or size of a domain, you need to know the process or function which created the set.
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
9985 Abstraction may concern the individuation of the set itself, not its elements [Tait]
     Full Idea: A different reading of abstraction is that it concerns, not the individuating properties of the elements relative to one another, but rather the individuating properties of the set itself, for example the concept of what is its extension.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], VIII)
     A reaction: If the set was 'objects in the room next door', we would not be able to abstract from the objects, but we might get to the idea of things being contain in things, or the concept of an object, or a room. Wrong. That's because they are objects... Hm.
18. Thought / E. Abstraction / 8. Abstractionism Critique
9972 Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait]
     Full Idea: Why should abstraction from two equipollent sets lead to the same set of 'pure units'?
     From: William W. Tait (Frege versus Cantor and Dedekind [1996])
     A reaction: [Tait is criticising Cantor] This expresses rather better than Frege or Dummett the central problem with the abstractionist view of how numbers are derived from matching groups of objects.
9980 If abstraction produces power sets, their identity should imply identity of the originals [Tait]
     Full Idea: If the power |A| is obtained by abstraction from set A, then if A is equipollent to set B, then |A| = |B|. But this does not imply that A = B. So |A| cannot just be A, taken in abstraction, unless that can identify distinct sets, ..or create new objects.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], V)
     A reaction: An elegant piece of argument, which shows rather crucial facts about abstraction. We are then obliged to ask how abstraction can create an object or a set, if the central activity of abstraction is just ignoring certain features.
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
     Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes.
     From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078
     A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book.
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
     Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness.
     From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42
     A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them.
28. God / C. Attitudes to God / 5. Atheism
23061 Free atheism should start by questioning its faith in humanity [Gray]
     Full Idea: A free-thinking atheism would begin by questioning the prevailing faith in humanity. But there is little prospect of contemporary atheists giving up their reverence for this phantom.
     From: John Gray (Seven Types of Atheism [2018], Conc)
     A reaction: He seems to be referring to 'humanism', which I take to be quite different from atheism. I take it as obvious that simple atheism is entirely neutral on the question of whether we should have 'faith' in humanity (which presumably mean optimism).
29. Religion / A. Polytheistic Religion / 4. Dualist Religion
23057 Gnosticism has a supreme creator God, giving way to a possibly hostile Demiurge [Gray]
     Full Idea: Gnostic traditions envisage a supreme God that created the universe and then withdrew into itself, leaving the world to be ruled by a lesser god, or Demiurge, which might be indifferent or hostile to mankind.
     From: John Gray (Seven Types of Atheism [2018], Intro)
     A reaction: It doesn't seem to solve any problems, given that the first God is 'supreme', and is therefore responsible for the introduction and actions of the later Demiurge.
29. Religion / B. Monotheistic Religion / 2. Judaism
23056 Judaism only became monotheistic around 550 BCE [Gray]
     Full Idea: It was only sometime around the sixth century BC, during the period when the Israelites returned to Jerusalem, that the idea that there is only one God emerged in Jewish religion.
     From: John Gray (Seven Types of Atheism [2018], Intro)
     A reaction: There seems to be a parallel move among the Greeks to elevate Zeus to special status.
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
23055 Christians introduced the idea that a religion needs a creed [Gray]
     Full Idea: The notion that religions are creeds - lists of propositions or doctrines that everyone must accept or reject - emerged only with Christianity.
     From: John Gray (Seven Types of Atheism [2018], Intro)
     A reaction: With a creed comes the possibility of heresy. I''m not happy with children being taught to recite something which begins 'I believe…', but which they have never thought about and barely understand.
29. Religion / C. Spiritual Disciplines / 3. Buddhism
23058 Buddhism has no divinity or souls, and the aim is to lose the illusion of a self [Gray]
     Full Idea: Buddhism says nothing of any divine mind and rejects any idea of the soul. The world consists of processes and events. The human sense of self is an illusion; freedom is found in ridding oneself of this illusion.
     From: John Gray (Seven Types of Atheism [2018], Intro)
     A reaction: I'm not clear why shaking off the illusion of a self is a superior state. Freedom to do what? Presumably nothing at all, since there is no self to desire anything.