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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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5952
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Rather than being the whole soul, maybe I am its chief part? [Plutarch]
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Full Idea:
Is each of us not the soul, but the chief part of the soul, by which we think and reason and act, all the other parts of soul as well as of body being mere instruments of its power?
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From:
Plutarch (74: Reply to Colotes [c.85], §1119)
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A reaction:
Socrates is associated with the idea that I am my whole soul (Idea 1650). Plutarch represents an interesting development, which may lead both to the Christian 'soul' and to the Cartesian 'ego'. I think Plutarch is right, but what is the 'soul'?
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5951
|
If atoms have no qualities, they cannot possibly produce a mind [Plutarch]
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Full Idea:
Perception, mind, intelligence and thought cannot so much as be conceived, even with the best will, as arising among void and atoms, things which taken separately have no quality.
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From:
Plutarch (74: Reply to Colotes [c.85], §1112)
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A reaction:
A nice articulation of the intuition of all anti-physicalists. Plutarch would have to rethink his position carefully if he learned of the sheer number of connections in the brain, and of the theory of natural selection. His challenge remains, though.
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5963
|
Some say emotion is a sort of reason, and others say virtue concerns emotion [Plutarch]
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Full Idea:
Some philosophers make the emotions varieties of reason, on the ground that all desire and grief and anger are judgments, while others declare that the virtues have to do with emotions, as when fear is the province of courage.
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From:
Plutarch (68: Generation of the soul in 'Timaeus' [c.85], 1025d)
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A reaction:
The second idea comes from Aristotle, but the second is interesting, and corresponds to the views coming from modern neuroscience, where even the most basic thought seems to involve emotion. What could be the motivation for 'pure' reason?
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9982
|
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
|
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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5948
|
The good life involves social participation, loyalty, temperance and honesty [Plutarch]
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Full Idea:
To live the good life is to live a life of participation in society, of loyalty to friends, of temperance and honest dealing.
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From:
Plutarch (74: Reply to Colotes [c.85], §1108)
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A reaction:
'Participation in society' is the interesting one. This might translate as 'doing your duty', or as 'leading a well-rounded life'. Solitude is wrong if you are indebted to others, and it is unhealthy if you are not. Is solitude really immoral, though?
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5955
|
No one will ever find a city that lacks religious practices [Plutarch]
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Full Idea:
A city without holy places and gods, without any observance of prayers, oaths, oracles, sacrifices for blessings received or rites to avert evils, no traveller has ever seen or will ever see.
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From:
Plutarch (74: Reply to Colotes [c.85], §1125)
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A reaction:
The nearest you might get would be Soviet Moscow, but in 1973 I saw a man there jeering at a woman who was kneeling in the street outside a closed church. Plutarch would be stunned at the decline in religious practices in modern Europe.
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24043
|
Soul must be immortal, since it continually moves, like the heavens [Alcmaeon, by Aristotle]
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Full Idea:
Alcmaeon says that the soul is immortal because it resembles immortal things and that this affection belongs to it because it is always in movement, like divine things, such the moon, the sun, the stars and the whole heaven.
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From:
report of Alcmaeon (fragments/reports [c.490 BCE], DK 24) by Aristotle - De Anima 405a30
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A reaction:
Hm. Fish and rivers seem to be continually moving too. Presumably we are like gods, but then Greek gods seem awfully like humans. I don't know the history of belief in immortality; an interesting topic.
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