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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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13416
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Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C]
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Full Idea:
The axiomatic conception of mathematics is the only viable one. ...But they are true because they are axioms, in contrast to the view advanced by Frege (to Hilbert) that to be a candidate for axiomhood a statement must be true.
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From:
report of William W. Tait (Intro to 'Provenance of Pure Reason' [2005], p.4) by Charles Parsons - Review of Tait 'Provenance of Pure Reason' §2
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A reaction:
This looks like the classic twentieth century shift in the attitude to axioms. The Greek idea is that they must be self-evident truths, but the Tait-style view is that they are just the first steps in establishing a logical structure. I prefer the Greeks.
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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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5078
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Kant and Mill both try to explain right and wrong, without a divine lawgiver [Taylor,R]
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Full Idea:
Kant and Mill were in total agreement in trying to give content to the distinction between moral right and wrong, without recourse to any divine lawgiver.
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From:
Richard Taylor (Virtue Ethics: an Introduction [2002], Ch.14)
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A reaction:
A nice analysis, in tune with MacIntyre and others, who see such attempts as failures. It is hard, however, to deny the claims of rational principles, or of suffering, in our moral framework. I agree with Taylor's move back to virtue, but it ain't simple.
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5067
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Morality based on 'forbid', 'permit' and 'require' implies someone who does these things [Taylor,R]
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Full Idea:
If morality is based on wrong (meaning 'forbidden'), right ('permitted'), and obligatory ('required'), we are led to ask 'Who is it that thus permits, forbids or requires that certain things be done or not done?'
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From:
Richard Taylor (Virtue Ethics: an Introduction [2002], Ch.2)
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A reaction:
Clear reinforcement for Nietzsche's attack on conventional morals, which Taylor sees as a relic of medieval religious attitudes. Taylor says Kant offered a non-religious version of the same authority. I agree. Back to the Greek pursuit of excellence!
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5079
|
Pleasure can have a location, and be momentary, and come and go - but happiness can't [Taylor,R]
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Full Idea:
Pleasures can be located in a particular part of the body, and can be momentary, and come and go, but this is not the case with happiness.
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From:
Richard Taylor (Virtue Ethics: an Introduction [2002], Ch.16)
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A reaction:
Probably no one ever thought that pleasure and happiness were actually identical - merely that pleasure is the only cause and source of happiness. These are good objections to that hypothesis. Pleasure simply isn't 'the good'.
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5068
|
'Eudaimonia' means 'having a good demon', implying supreme good fortune [Taylor,R]
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Full Idea:
The word 'eudaimonia' means literally 'having a good demon', which is apt, because it suggests some kind of supreme good fortune, of the sort which might be thought of as a bestowal.
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From:
Richard Taylor (Virtue Ethics: an Introduction [2002], Ch.5)
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A reaction:
Beware of etymology. This implies that eudaimonia is almost entirely beyond a person's control, but Aristotle doesn't think that. A combination of education and effort can build on some natural gifts to create a fully successful life.
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5077
|
The modern idea of obligation seems to have lost the idea of an obligation 'to' something [Taylor,R]
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Full Idea:
In modern moral thinking, obligation is something every responsible person is supposed to have, but it is not an obligation to the state, or society, or humanity, or even to God. It is an obligation standing by itself.
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From:
Richard Taylor (Virtue Ethics: an Introduction [2002], Ch.12)
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A reaction:
This nicely pinpoints how some our moral attitudes are relics of religion. Taylor wants a return to virtue, but one could respond by opting for the social contract (with very clear obligations) or Kantian 'contractualism' (answering to rational beings).
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5066
|
If we are made in God's image, pursuit of excellence is replaced by duty to obey God [Taylor,R]
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Full Idea:
Once people are declared to be images of God, just by virtue of minimal humanity, they have, therefore, no greater individual excellence to aspire to, and their purpose became one of obligation, that is, obedience to God's will.
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From:
Richard Taylor (Virtue Ethics: an Introduction [2002], Ch.2)
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A reaction:
An interesting and plausible historical analysis. There is a second motivation for the change, though, in Grotius's desire to develop a more legalistic morality, focusing on actions rather than character. Taylor's point is more interesting, though.
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