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9978
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Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait]
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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.
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From:
William W. Tait (Frege versus Cantor and Dedekind [1996], IV)
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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.
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9986
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The null set was doubted, because numbering seemed to require 'units' [Tait]
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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).
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From:
William W. Tait (Frege versus Cantor and Dedekind [1996], IX)
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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!
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9984
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We can have a series with identical members [Tait]
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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)?
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From:
William W. Tait (Frege versus Cantor and Dedekind [1996], VII)
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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?
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23266
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The spirit in the soul wants freedom, power and honour [Galen]
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Full Idea:
The spirited part of the soul is desiderative of freedom, victory, power, authority, reputation, and honour.
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From:
Galen (The soul's dependence on the body [c.170], Kiv.2.772)
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A reaction:
This is the concept of 'thumos' [spirit], taken straight from Plato's tripartite account of the soul, in 'Republic'. Note that it includes a desire for freedom (in an age of slavery).
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23220
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The brain contains memory and reason, and is the source of sensation and decision [Galen]
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Full Idea:
The brain is the principal organ of the psychical members. For within the brain is seated memory, reason and intellect, and from the brain is distributed the power, sensation and voluntary motion.
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From:
Galen (The soul's dependence on the body [c.170]), quoted by Matthew Cobb - The Idea of the Brain 1
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A reaction:
[not sure of ref] Interesting that he assigns the whole of mind to the brain, and not just some aspect of it. He had done experiments. Understanding the role of the brain was amazingly slow. Impeded by religion, I guess.
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23265
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The rational part of the soul is the desire for truth, understanding and recollection [Galen]
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Full Idea:
That part of the soul which we call rational is desiderative: …it desires truth, knowledge, learning, understanding, and recollection - in short, all the good things.
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From:
Galen (The soul's dependence on the body [c.170], Kiv.2.772)
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A reaction:
Truth is no surprise, but recollection is. Note the separation of knowledge from understanding. This is a very good characterisation of rationality. For the Greeks it has a moral dimension, of wanting what is good.
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9982
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Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait]
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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.
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From:
William W. Tait (Frege versus Cantor and Dedekind [1996], V)
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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.
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9985
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Abstraction may concern the individuation of the set itself, not its elements [Tait]
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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.
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From:
William W. Tait (Frege versus Cantor and Dedekind [1996], VIII)
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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.
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9980
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If abstraction produces power sets, their identity should imply identity of the originals [Tait]
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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.
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From:
William W. Tait (Frege versus Cantor and Dedekind [1996], V)
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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.
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23268
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We execute irredeemable people, to protect ourselves, as a deterrent, and ending a bad life [Galen]
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Full Idea:
We kill the irredeemably wicked, for three reasons: that they may no longer harm us; as a deterrent to others like them; and because it is actually better from their own point of view to die, when their souls are so damaged they cannot be improved.
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From:
Galen (The soul's dependence on the body [c.170], Kiv.11.816)
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A reaction:
The third one sounds like a dubious rationalisation, given that the prisoner probably disagrees. Nowadays we are not so quick to judge someone as irredeemable. The first one works when they run wild, but not after their capture.
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