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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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5515
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Imaginary cases are good for revealing our beliefs, rather than the truth [Parfit]
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Full Idea:
I believe it is worth considering imaginary cases (such as Teletransportation), as we can use them to discover, not what the truth is, but what we believe.
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From:
Derek Parfit (The Unimportance of Identity [1995], p.293)
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A reaction:
The trouble is that we might say that IF I were suddenly turned into a pig, then I would come to believe in dualism, but that will not and cannot happen, because dualism is false. It seems essential to accept the natural possibility of the case.
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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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5516
|
Reduction can be by identity, or constitution, or elimination [Parfit, by PG]
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Full Idea:
We can distinguish Identifying Reductionism (as in 'persons are bodies'), or Constitutive Reductionism (as in 'persons are distinct, but consist of thoughts etc.'), or Eliminative Reductionism (as in 'there are no persons, only thoughts etc.').
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From:
report of Derek Parfit (The Unimportance of Identity [1995], p.295) by PG - Db (ideas)
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A reaction:
Constitutive Reductionism seems the most common one, as in 'chemistry just consists of lots of complicated physics'. He doesn't mention bridge laws, which are presumably only required in more complicated cases of constitutive reduction.
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16061
|
If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow]
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Full Idea:
Logical supervenience, restricted to individuals, seems to imply strong reduction. It is said that where the B-facts logically supervene on the A-facts, the B-facts simply re-describe what the A-facts describe, and the B-facts come along 'for free'.
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From:
Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C)
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A reaction:
This seems to be taking 'logically' to mean 'analytically'. Presumably an entailment is logically supervenient on its premisses, and may therefore be very revealing, even if some people think such things are analytic.
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5514
|
Psychologists are interested in identity as a type of person, but philosophers study numerical identity [Parfit]
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Full Idea:
When psychologists discuss identity, they are typically concerned with the kind of person someone is, or wants to be (as in an 'identity crisis'). But when philosophers discuss identity, it is numerical identity they mean.
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From:
Derek Parfit (The Unimportance of Identity [1995], p.293)
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A reaction:
I think it is important to note that the philosophical problem breaks down into two areas: whether I have numerical identity with myself over time, and whether other people have it. It may be that two different sets of criteria will emerge.
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5521
|
If my brain-halves are transplanted into two bodies, I have continuity, and don't need identity [Parfit]
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Full Idea:
If the two halves of my brain are transplanted into different bodies just like mine, they cannot both be me, since that would make them the same person. ..But my relation to these two contains everything that matters, so identity is not what matters.
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From:
Derek Parfit (The Unimportance of Identity [1995], p.314)
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A reaction:
I challenge his concept of what 'matters'. He has a rather solipsistic view of the problem, and I take Parfit to be a rather unsociable person, since his friends and partner will be keenly interested in the identities of the new beings.
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1392
|
If we split like amoeba, we would be two people, neither of them being us [Parfit]
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Full Idea:
In the case of the man who, like an amoeba, divides….we can suggest that he survives as two different people without implying that he is those people.
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From:
Derek Parfit (Personal Identity [1971], §1)
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A reaction:
Maybe an amoeba is a homogeneous substance for which splitting is insignificant, but when a person has certain parts that are totally crucial, splitting them is catastrophic, and quite different. I'm not sure that splitting a self would leave persons.
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5519
|
It is fine to save two dying twins by merging parts of their bodies into one, and identity is irrelevant [Parfit]
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Full Idea:
If I am largely paralysed, and my twin brother is dying of brain disease, then if the operation to graft my head onto his body is offered, I should accept the operation, and it is irrelevant whether this person would be me.
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From:
Derek Parfit (The Unimportance of Identity [1995], p.308)
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A reaction:
Parfit notes that the brain is a particularly significant part of the process. The fact that I might cheerfully accept this offer without philosophical worries doesn't get rid of the question 'who is this person?' Who should they remain married to?
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5520
|
If two humans are merged surgically, the new identity is a purely verbal problem [Parfit]
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Full Idea:
If there is someone with my head and my brother's body, it is a merely verbal question whether that person will be me, and that is why, even if it won't be me, that doesn't matter. ..What matters is not identity, but the facts of which identity consists.
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From:
Derek Parfit (The Unimportance of Identity [1995], p.310)
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A reaction:
It strikes me that from the subjective psychological point of view identity is of little interest, but from the objective external viewpoint (e.g. the forensic one) such questions are highly significant, and rightly so.
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1391
|
Concern for our own lives isn't the source of belief in identity, it is the result of it [Parfit]
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Full Idea:
Egoism, and the fear not of near but of distant death, and the regret that so much of one's life should have gone by - these are not, I think, wholly natural or instinctive. They are strengthened by a false belief in stable identity.
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From:
Derek Parfit (Personal Identity [1971], §6)
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A reaction:
This raises some very nice questions, about the extent to which various aspects of self-concern are instinctive and natural, or culturally induced, and even totally misguided and false. I can worry about the distant death of my guinea pig, or my grandson.
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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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9762
|
We should focus less on subjects of experience, and more on the experiences themselves [Parfit]
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Full Idea:
It becomes more plausible, when thinking morally, to focus less upon the person, the subject of experiences, and instead to focus more upon the experiences themselves.
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From:
Derek Parfit (Reasons and Persons [1984], §116)
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A reaction:
This pinpoints how Parfit moves from a view of persons in terms of continuity of consciousness to a utilitarian morality. It brings out nicely what is wrong with utilitarianism - the reductio of a great ball of nice experiences, with no one having them.
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