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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11897
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A principle of individuation may pinpoint identity and distinctness, now and over time [Mackie,P]
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Full Idea:
One view of a principle of individuation is what is called a 'criterion of identity', determining answers to questions about identity and distinctness at a time and over time - a principle of distinction and persistence.
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From:
Penelope Mackie (How Things Might Have Been [2006], 8.2)
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A reaction:
Since the term 'Prime Minister' might do this job, presumably there could be a de dicto as well as a de re version of individuation. The distinctness consists of chairing cabinet meetings, rather than being of a particular sex.
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11883
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A haecceity is the essential, simple, unanalysable property of being-this-thing [Mackie,P]
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Full Idea:
Socrates can be assigned a haecceity: an essential property of 'being Socrates' which (unlike the property of 'being identical with Socrates') may be regarded as what 'makes' its possessor Socrates in a non-trivial sense, but is simple and unanalysable.
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From:
Penelope Mackie (How Things Might Have Been [2006], 2.2)
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A reaction:
I don't accept that there is any such property as 'being Socrates' (or even 'being identical with Socrates'), except as empty locutions or logical devices. A haecceity seems to be the 'ultimate subject of predication', with no predicates of its own.
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11882
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No other object can possibly have the same individual essence as some object [Mackie,P]
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Full Idea:
Individual essences are essential properties that are unique to them alone. ...If a set of properties is an individual essence of A, then A has the properties essentially, and no other actual or possible object actually or possibly has them.
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From:
Penelope Mackie (How Things Might Have Been [2006], 2.1/2)
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A reaction:
I'm unconvinced about this. Tigers have an essence, but individual tigers have individual essences over and above their tigerish qualities, yet the perfect identity of two tigers still seems to be possible.
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11899
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Why are any sortals essential, and why are only some of them essential? [Mackie,P]
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Full Idea:
Accounts of sortal essentialism do not give a satisfactory explanation of why any sortals should be essential sortals, or a satisfactory account of why some sortals should be essential while others are not.
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From:
Penelope Mackie (How Things Might Have Been [2006], 8.6)
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A reaction:
A theory is not wrong, just because it cannot give a 'satisfactory explanation' of every aspect of the subject. We might, though, ask why the theory isn't doing well in this area.
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11893
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Possibilities for Caesar must be based on some phase of the real Caesar [Mackie,P]
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Full Idea:
I take the 'overlap requirement' for Julius Caesar to be that, when considering how he might have been different, you have to take him as he actually was at some time in his existence, and consider possibilities consistent with that.
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From:
Penelope Mackie (How Things Might Have Been [2006], 6.5)
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A reaction:
This is quite a large claim (larger than Mackie thinks?), as it seems equally applicable to properties, states of affairs and propositions, as well as to individuals. Possibility that has no contact at all with actuality is beyond our comprehension.
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11884
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The theory of 'haecceitism' does not need commitment to individual haecceities [Mackie,P]
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Full Idea:
The theory that things have 'haecceities' must be sharply distinguished from the theory referred to as 'haecceitism', which says there may be differences in transworld identities that do not supervene on qualitative differences.
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From:
Penelope Mackie (How Things Might Have Been [2006], 2.2 n7)
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A reaction:
She says later [p,43 n] that it is possible to be a haecceitist without believing in individual haecceities, if (say) the transworld identities had no basis at all. Note that if 'thisness' is 'haecceity', then 'whatness' is 'quiddity'.
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11905
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Locke's kind essences are explanatory, without being necessary to the kind [Mackie,P]
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Full Idea:
One might speak of 'Lockean real essences' of a natural kind, a set of properties that is basic in the explanation of the other properties of the kind, without commitment to the essence belonging to the kind in all possible worlds.
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From:
Penelope Mackie (How Things Might Have Been [2006], 10.1)
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A reaction:
I think this may be the most promising account. The essence of a tiger explains what tigers are like, but tigers may evolve into domestic pets. Questions of individuation and of explaining seem to be quite separate.
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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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11907
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Maybe the identity of kinds is necessary, but instances being of that kind is not [Mackie,P]
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Full Idea:
One could be an essentialist about natural kinds (of tigers, or water) while holding that every actual instance or sample of a natural kind is only accidentally an instance or a sample of that kind.
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From:
Penelope Mackie (How Things Might Have Been [2006], 10.2)
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A reaction:
You wonder, then, in what the necessity of the kind consists, if it is not rooted in the instances, and presumably it could only result from a stipulative definition, and hence be conventional.
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