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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
|
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
|
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
|
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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6408
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Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling]
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Full Idea:
In order to deduce the theorems of mathematics from purely logical axioms, Russell had to add three new axioms to those of standards logic, which were: the axiom of infinity, the axiom of choice, and the axiom of reducibility.
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From:
A.C. Grayling (Russell [1996], Ch.2)
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A reaction:
The third one was adopted to avoid his 'barber' paradox, but many thinkers do not accept it. The interesting question is why anyone would 'accept' or 'reject' an axiom.
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7091
|
The argument from analogy is not a strong inference, since the other being might be an actor or a robot [Grayling]
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Full Idea:
The argument from analogy is a weak one, because it does not logically guarantee the inference I draw to the other's inner states, for he might be dissimulating or acting, or may even be a cleverly contrived robot which feels nothing.
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From:
A.C. Grayling (Wittgenstein [1988], Ch.3)
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A reaction:
This gives the impression that for an argument to be strong it must logically guarantee its inference. It strikes me that analogy is a good reason for believing in other minds, but that is because I am looking for the best explanation, not logical proof.
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4993
|
If a bird captures a worm, we could say its behaviour is 'about' the worm [Kirk,R]
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Full Idea:
When a bird pulls a worm from the ground, then swallows it piece by piece, there is a sense in which its behaviour can be said to be about the worm.
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From:
Robert Kirk (Mind and Body [2003], §5.4)
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A reaction:
This is preparing the ground for a possible behaviourist account of intentionality. Reply: you could say rain is about puddles, or you could say we have adopted Dennett's 'intentional stance' to birds, but it tells us nothing about their psychology.
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4982
|
Dualism implies some brain events with no physical cause, and others with no physical effect [Kirk,R]
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Full Idea:
If the mind causes brain events, then they are not caused by other brain events, and such causal gaps should be detectable by scientists; there should also be a gap of brain-events which cause no other brain events, because they are causing mind events.
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From:
Robert Kirk (Mind and Body [2003], §2.5)
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A reaction:
This is the double causation problem which Spinoza had spotted (Idea 4862). Expressed this way, it seems a screamingly large problem for dualism. We should be able to discover some VERY strange physical activity in the brain.
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4991
|
Behaviourism seems a good theory for intentional states, but bad for phenomenal ones [Kirk,R]
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Full Idea:
For many kinds of mental states, notably intentional ones such as beliefs and desires, behaviourism is appealing, ..but for sensations and experiences such as pain, it seems grossly implausible.
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From:
Robert Kirk (Mind and Body [2003], §5.1)
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A reaction:
The theory does indeed make a bit more sense for intentional states, but it still strikes me as nonsense that there is no more to my belief that 'Whales live in the Atlantic' than a disposition to say something. WHY do I say this something?
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4994
|
Behaviourism offers a good alternative to simplistic unitary accounts of mental relationships [Kirk,R]
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Full Idea:
There is a temptation to think that 'aboutness', and the 'contents' of thoughts, and the relation of 'reference', are single and unitary relationships, but behaviourism offers an alternative approach.
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From:
Robert Kirk (Mind and Body [2003], §5.5)
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A reaction:
Personally I wouldn't touch behaviourism with a barge-pole (as it ducks the question of WHY certain behaviour occurs), but a warning against simplistic accounts of intentional states is good. I am sure there cannot be a single neat theory of refererence.
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4984
|
All meaningful psychological statements can be translated into physics [Kirk,R]
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Full Idea:
All psychological statements which are meaningful, that is to say, which are in principle verifiable, are translatable into propositions which do not involve psychological concepts, but only the concepts of physics.
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From:
Robert Kirk (Mind and Body [2003], §3.8)
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A reaction:
This shows how eliminativist behaviourism arises out of logical positivism (by only allowing what is verifiable). The simplest objection: we can't verify the mental states of others, because they are private, but they are still the best explanation.
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4997
|
It seems unlikely that most concepts are innate, if a theory must be understood to grasp them [Kirk,R]
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Full Idea:
It is widely accepted that for many concepts, if not all, grasping the concept requires grasping some theory, ...which makes difficulties for the view that concepts are not learned: for 'radical concept nativism', as Fodor calls it.
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From:
Robert Kirk (Mind and Body [2003], §7.3)
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A reaction:
Not a problem for traditional rationalist theories, where the whole theory can be innate along with the concept, but a big objection to modern more cautious non-holistic views (such as Fodor's). Does a bird have a concept AND theory of a nest?
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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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4995
|
Behaviourists doubt whether reference is a single type of relation [Kirk,R]
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Full Idea:
To most behaviourists it seems misguided to expect there to be a single relation that connects referring expressions with their referents.
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|
From:
Robert Kirk (Mind and Body [2003], §5.5)
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|
A reaction:
You don't need to be a behaviourist to feel this doubt. Think about names of real people, names of fictional people, reference to misunderstood items, or imagined items, or reference in dreams, or to mathematical objects, or negations etc.
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23262
|
Experience, sympathy and history are sensible grounds for laying claim to rights [Grayling]
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Full Idea:
Personal experience, social sympathies, and history together licence laying claim to rights …which we see to make good mutual as well as individual sense.
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|
From:
A.C. Grayling (The Good State [2020], 6)
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|
A reaction:
There are no such thing as natural rights, but there are clearly natural grounds on which it is very reasonable to base a claim for legal rights. If positive rights are just arbitrary, or expressions of power struggles, that is crazy.
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23259
|
There should be separate legislative, executive and judicial institutions [Grayling]
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|
Full Idea:
The obvious solution is where the legislative, executive and judicial powers are exercised by different institutions, distinguished by function. The executive is answerable to the legislative, and the judicial is controlled by neither.
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|
From:
A.C. Grayling (The Good State [2020], 3)
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|
A reaction:
Separation by institution, rather than merely by separate individuals exercising the powers. I agree (with Popper etc) that institutions are the way to secure long-term success and justice. Grayling says the judiciary must not paralyse government.
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7824
|
If suicide is lawful, but assisting suicide is unlawful, powerless people are denied their rights [Grayling]
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Full Idea:
An anomaly created by England's 1961 Suicide Act is that it is lawful to take one's own life, but unlawful to help anyone else to do it. This means anyone unable to commit suicide without help is denied one of their fundamental rights.
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|
From:
A.C. Grayling (What is Good? [2003], Ch.8)
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|
A reaction:
There is a difference, not really captured either by law or by reason, between tolerating an activity, and encouraging and helping it. I think the test question is "this activity is legal, but would you want your child to do it?"
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7819
|
Religion gives answers, comforts, creates social order, and panders to superstition [Grayling]
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Full Idea:
The four standard explanations given for religion are that it provides answer, that it gives comfort, that it makes for social order, and that it rests on mere superstition.
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|
From:
A.C. Grayling (What is Good? [2003], Ch.4)
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A reaction:
All four of these could be correct, though the first and fourth would be incompatible if religion gives correct answers. Why religion begins might be not the same as the reason why it continues.
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