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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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16554
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Activities have place, rate, duration, entities, properties, modes, direction, polarity, energy and range [Machamer/Darden/Craver]
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Full Idea:
Activities can be identified spatiotemporally, and individuated by rate, duration, and types of entity and property that engage in them. They also have modes of operation, directionality, polarity, energy requirements and a range.
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From:
Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 3)
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A reaction:
This is their attempt at making 'activity' one of the two central concepts of ontology, along with 'entity'. A helpful analysis. It just seems to be one way of slicing the cake.
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16562
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We understand something by presenting its low-level entities and activities [Machamer/Darden/Craver]
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Full Idea:
The intelligibility of a phenomenon consists in the mechanisms being portrayed in terms of a field's bottom out entities and activities.
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From:
Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 7)
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A reaction:
In other words, we understand complex things by reducing them to things we do understand. It would, though, be illuminating to see a nest of interconnected activities, even if we understood none of them.
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16555
|
Functions are not properties of objects, they are activities contributing to mechanisms [Machamer/Darden/Craver]
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Full Idea:
It is common to speak of functions as properties 'had by' entities, …but they should rather be understood in terms of the activities by virtue of which entities contribute to the workings of a mechanism.
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From:
Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 3)
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A reaction:
I'm certainly quite passionately in favour of cutting down on describing the world almost entirely in terms of entities which have properties. An 'activity', though, is a bit of an elusive concept.
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16528
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Mechanisms are not just push-pull systems [Machamer/Darden/Craver]
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Full Idea:
One should not think of mechanisms as exclusively mechanical (push-pull) systems.
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From:
Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 1)
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A reaction:
The difficulty seems to be that you could broaden the concept of 'mechanism' indefinitely, so that it covered history, mathematics, populations, cultural change, and even mathematics. Where to stop?
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16553
|
Our account of mechanism combines both entities and activities [Machamer/Darden/Craver]
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Full Idea:
We emphasise the activities in mechanisms. This is explicitly dualist. Substantivalists speak of entities with dispositions to act. Process ontologists reify activities and try to reduce entities to processes. We try to capture both intuitions.
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From:
Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 3)
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A reaction:
[A quotation of selected fragments] The problem here seems to be the raising of an 'activity' to a central role in ontology, when it doesn't seem to be primitive, and will typically be analysed in a variety of ways.
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16559
|
Descriptions of explanatory mechanisms have a bottom level, where going further is irrelevant [Machamer/Darden/Craver]
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Full Idea:
Nested hierachical descriptions of mechanisms typically bottom out in lowest level mechanisms. …Bottoming out is relative …the explanation comes to an end, and description of lower-level mechanisms would be irrelevant.
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From:
Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 5.1)
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A reaction:
This seems to me exactly the right story about mechanism, and it is a story I am associating with essentialism. The relevance is ties to understanding. The lower level is either fully understood, or totally baffling.
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16564
|
There are four types of bottom-level activities which will explain phenomena [Machamer/Darden/Craver]
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Full Idea:
There are four bottom-out kinds of activities: geometrico-mechanical, electro-chemical, electro-magnetic and energetic. These are abstract means of production that can be fruitfully applied in particular cases to explain phenomena.
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From:
Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 7)
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A reaction:
I like that. It gives a nice core for a metaphysics for physicalists. I suspect that 'mechanical' can be reduced to something else, and that 'energetic' will disappear in the final story.
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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
|
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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16558
|
Laws of nature have very little application in biology [Machamer/Darden/Craver]
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Full Idea:
The traditional notion of a law of nature has few, if any, applications in neurobiology or molecular biology.
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From:
Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 3.2)
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A reaction:
This is a simple and self-evident fact, and bad news for anyone who want to build their entire ontology around laws of nature. I take such a notion to be fairly empty, except as a convenient heuristic device.
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