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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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16665
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There are entities, and then positive 'modes', modifying aspects outside the thing's essence [Suárez]
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Full Idea:
Beyond the entities there are certain real 'modes', which are positive, and in their own right act on those entities, giving them something that is outside their whole essence as individuals existing in reality.
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From:
Francisco Suárez (Disputationes metaphysicae [1597], 7.1.17), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 13.3
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A reaction:
Suárez is apparently the first person to formulate a proper account of properties as 'modes' of a thing, rather than as accidents which are separate, or are wholly integrated into a thing. A typical compromise proposal in philosophy. Can modes act?
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16666
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A mode determines the state and character of a quantity, without adding to it [Suárez]
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Full Idea:
The inherence of quantity is called its mode, because it affects that quantity, which serves to ultimately determine the state and character of its existence, but does not add to it any new proper entity, but only modifies the preexisting entity.
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From:
Francisco Suárez (Disputationes metaphysicae [1597], 7.1.17), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 13.3
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A reaction:
He seems to present mode as a very active thing, like someone who gives it a coat of paint, or hammers it into a new shape. I don't see how a 'mode' can have any ontological status at all. To exist, there has to be some way to exist.
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17007
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Forms must rule over faculties and accidents, and are the source of action and unity [Suárez]
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Full Idea:
A form is required that, as it were, rules over all those faculties and accidents, and is the source of all actions and natural motions of such a being, and in which the whole variety of accidents and powers has its root and unity.
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From:
Francisco Suárez (Disputationes metaphysicae [1597], 15.1.7), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.4
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A reaction:
Pasnau emphasises that this is scholastics giving a very physical and causal emphasis to forms, which made them vulnerable to doubts among the new experiment physicists. Pasnau says forms are 'metaphysical', following Leibniz.
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16780
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Partial forms of leaf and fruit are united in the whole form of the tree [Suárez]
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Full Idea:
In a tree the part of the form that is in the leaf is not the same character as the part that is in the fruit., but yet they are partial forms, and apt to be united ….to compose one complete form of the whole.
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From:
Francisco Suárez (Disputationes metaphysicae [1597], 15.10.30), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 26.6
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A reaction:
This is a common scholastic view, the main opponent of which was Aquinas, who says each thing only has one form. Do leaves have different DNA from the bark or the fruit? Presumably not (since I only have one DNA), which supports Aquinas.
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16758
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The best support for substantial forms is the co-ordinated unity of a natural being [Suárez]
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Full Idea:
The most powerful arguments establishing substantial forms are based on the necessity, for the perfect constitution of a natural being, that all the faculties and operations of that being are rooted in one essential principle.
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From:
Francisco Suárez (Disputationes metaphysicae [1597], 15.10.64), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.4
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A reaction:
Note Idea 15756, that this stability not only applies to biological entities (the usual Aristotelian examples), but also to non-living natural kinds. We might say that the drive for survival is someone united around a single entity.
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16742
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We only know essences through non-essential features, esp. those closest to the essence [Suárez]
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Full Idea:
We can almost never set out the essences of things, as they are in things. Instead, we work through their connection to some non-essential feature, and we seem to succeed well enough when we spell it out through the feature closest to the essence.
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From:
Francisco Suárez (Disputationes metaphysicae [1597], 40.4.16), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 23.5
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A reaction:
It is a common view that with geometrical figures we can actually experience the essence itself. So has science broken through, and discerned actual essences of things?
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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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7563
|
The old 'influx' view of causation says it is a flow of accidental properties from A to B [Suárez, by Jolley]
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Full Idea:
The 'influx' model of causation says that causes involve a process of contagion, as it were; when the kettle boils, the gas infects the water inside the kettle with its own 'individual accident' of heat, which literally flows from one to the other.
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From:
report of Francisco Suárez (works [1588]) by Nicholas Jolley - Leibniz Ch.2
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A reaction:
This nicely captures the scholastic target of Hume's sceptical thinking on the subject. However, see Idea 2542, where the idea of influx has had a revival. It is hard to see how the water could change if it didn't 'catch' something from the gas.
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