8728
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Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]
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Full Idea:
Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths.
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From:
Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2
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A reaction:
Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time!
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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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5845
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Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon]
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Full Idea:
Niceratus said that his father, because he was concerned to make him a good man, made him learn the whole works of Homer, and he could still repeat by heart the entire 'Iliad' and 'Odyssey'.
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From:
Xenophon (Symposium [c.391 BCE], 3.5)
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A reaction:
This clearly shows the status which Homer had in the teaching of morality in the time of Socrates, and it is precisely this acceptance of authority which he was challenging, in his attempts to analyse the true basis of virtue
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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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