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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16648
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Accidents must have formal being, if they are principles of real action, and of mental action and thought [Duns Scotus]
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Full Idea:
Accidents are principles of acting and principles of cognizing substance, and are the per se objects of the senses. But it is ridiculous to say that something is a principle of acting (either real or intentional) and yet does not have any formal being.
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From:
John Duns Scotus (Ordinatio [1302], IV.12.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 10.5
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A reaction:
Pasnau cites this as the key scholastic argument for accidental properties having some independent and real existence (as required for Transubstantiation). Rival views say accidents are just 'modes' of a thing's existence. Aquinas compromised.
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15386
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If only the singular exists, science is impossible, as that relies on true generalities [Duns Scotus, by Panaccio]
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Full Idea:
Scotus argued that if everything is singular, with no objective common feature, science would be impossible, as it proceeds from general concepts. General is the opposite of singular, so it would be inadequate to understand a singular reality.
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From:
report of John Duns Scotus (Ordinatio [1302]) by Claude Panaccio - Medieval Problem of Universals 'John Duns'
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A reaction:
[compressed] It is a fact that if you generalise about 'tigers', you are glossing over the individuality of each singular tiger. That is OK for 'electron', if they really are identical, but our general predicates may be imposing identity on electrons.
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16632
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We distinguish one thing from another by contradiction, because this is, and that is not [Duns Scotus]
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Full Idea:
What is it [that establishes distinctness of things]? It is, to be sure, that which is universally the reason for distinguishing one thing from another: namely, a contradiction…..If this is, and that is not, then they are not the same entity in being.
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From:
John Duns Scotus (Ordinatio [1302], IV.11.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 08.2
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A reaction:
This is a remarkably intellectualist view of such things. John Wycliff, apparently, enquired about how animals were going to manage all this sort of thing. It should appeal to the modern logical approach to metaphysics.
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22127
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Scotus said a substantial principle of individuation [haecceitas] was needed for an essence [Duns Scotus, by Dumont]
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Full Idea:
Rejecting the standard views that essences are individuated by either actual existence, quantity or matter, Scotus said that the principle of individuation is a further substantial difference added to the species - the so-called haecceitas or 'thisness'.
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From:
report of John Duns Scotus (works [1301]) by Stephen D. Dumont - Duns Scotus p.206
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A reaction:
[Scotus seldom referred to 'haecceitas'] I suppose essences have prior existence, but are too generic, so something must fix an essence as pertaining to this particular object. Is the haecceitas part of the essence, or of the particular?
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13094
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The haecceity is the featureless thing which gives ultimate individuality to a substance [Duns Scotus, by Cover/O'Leary-Hawthorne]
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Full Idea:
For Scotus, the haecceity of an individual was a positive non-quidditative entity which, together with a common nature from which it was formally distinct, played the role of the ultimate differentia, thus individuating the substance.
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From:
report of John Duns Scotus (Ordinatio [1302]) by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 6.1.3
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A reaction:
Most thinkers seem to agree (with me) that this is a non-starter, an implausible postulate designed to fill a gap in a metaphysic that hasn't been properly worked out. Leibniz is the hero who faces the problem and works around it.
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16770
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It is absurd that there is no difference between a genuinely unified thing, and a mere aggregate [Duns Scotus]
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Full Idea:
It seems absurd …that there should be no difference between a whole that is one thing per se, and a whole that is one thing by aggregation, like a cloud or a heap.
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From:
John Duns Scotus (Ordinatio [1302], III.2.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 25.5
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A reaction:
Leibniz invented monads because he was driven crazy by the quest for 'true unity' in things. Objective unity may be bogus, but I suspect that imposing plausible unity on things is the only way we can grasp the world.
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16776
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Substance is an intrinsic thing, so parts of substances can't also be intrinsic things [Duns Scotus]
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Full Idea:
Substance ...is an ens per se. No part of a substance is an ens per se when it is part of a substance, because then it would be a particular thing, and one substance would be a particular thing from many things, which does not seem to be true.
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From:
John Duns Scotus (In Praed. [1300], 15.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 26.1
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A reaction:
The tricky bit is 'when it is a part of a substance', meaning a substance must cease to be a substance when it is subsumed into some greater substance. Maybe. Drops of water? Molecules? Bricks? Cells?
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16614
|
Matter and form give true unity; subject and accident is just unity 'per accidens' [Duns Scotus]
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Full Idea:
From matter and form comes one thing per se. This is not so for subject and accident. Matter and form are instrinsic causes of a composite being, but whiteness and a human being are not. Humans can exist without whiteness, so it is one thing per accidens.
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From:
John Duns Scotus (Oxford Commentary on Sentences [1301], II.12.1.14), quoted by Robert Pasnau - Metaphysical Themes 1274-1671
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A reaction:
This isn't much of a theory, but at least it is focusing on an interesting question, and the distinction between genuinely unified, and unified by chance. Compare a loving couple with siblings who hate each other.
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22130
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Scotus defended direct 'intuitive cognition', against the abstractive view [Duns Scotus, by Dumont]
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Full Idea:
Scotus allocated to the intellect a direct, existential awareness of the intelligible object, called 'intuitive cognition', in contrast to abstractive knowledge, which seized the object independently of its presence to the intellect in actual existence.
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From:
report of John Duns Scotus (works [1301]) by Stephen D. Dumont - Duns Scotus p.206
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A reaction:
Presumably if you see a thing, shut your eyes and then know it, that is 'abstractive'. Scotus says open your eyes for proper knowledge.
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22131
|
The will retains its power for opposites, even when it is acting [Duns Scotus, by Dumont]
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Full Idea:
Scotus said the will is a power for opposites, in the sense that even when actually willing one thing, it retains a real, active power to will the opposite. He detaches the idea of freedom from time and variability.
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From:
report of John Duns Scotus (works [1301]) by Stephen D. Dumont - Duns Scotus p.206
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A reaction:
In the sense that we can abandon an action when in the middle of it, this seems to be correct. Not just 'I could have done otherwise', but 'I don't have to be doing this'. This shows that the will has wide power, but not that it is 'free'.
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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
|
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
|
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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