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7527
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Analysis for Moore and Russell is carving up the world, not investigating language [Moore,GE, by Monk]
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Full Idea:
For Moore and Russell analysis is not - as is commonly understood now - a linguistic activity, but an ontological one. To analyse a proposition is not to investigate language, but to carve up the world so that it begins to make some sort of sense.
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From:
report of G.E. Moore (The Nature of Judgement [1899]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4
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A reaction:
A thought dear to my heart. The twentieth century got horribly side-tracked into thinking that ontology was an entirely linguistic problem. I suggest that physicists analyse physical reality, and philosophers analyse abstract reality.
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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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21342
|
A relation is internal if two things possessing the relation could not fail to be related [Moore,GE, by Heil]
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Full Idea:
Moore characterises internal relations modally, as those essential to their relata. If a and b are related R-wise, and R is an internal relation, a and b could not fail to be so related; otherwise R is external.
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From:
report of G.E. Moore (External and Internal Relations [1919]) by John Heil - Relations 'Internal'
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A reaction:
I don't think of Moore as an essentialist, but this fits the essentialist picture nicely, and is probably best paraphrased in terms of powers. Integers are the standard example of internal relations.
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6672
|
Moore's Paradox: you can't assert 'I believe that p but p is false', but can assert 'You believe p but p is false' [Moore,GE, by Lowe]
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Full Idea:
Moore's Paradox says it makes no sense to assert 'I believe that p, but p is false', even though it makes perfectly good sense to assert 'I used to believe p, but p is false' or 'You believe p, but p is false'.
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From:
report of G.E. Moore (works [1905]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.10
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A reaction:
I'm not sure if this really deserves the label of 'paradox'. I take it as drawing attention to the obvious fact that belief is commitment to truth. I think my assessment that p is true is correct, but your assessment is wrong. ('True' is not redundant!)
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6349
|
I can prove a hand exists, by holding one up, pointing to it, and saying 'here is one hand' [Moore,GE]
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Full Idea:
I can prove now that two human hands exist. How? By holding up my two hands, and saying, as I make a certain gesture with the right hand, 'Here is one hand', and adding, as I gesture with the left, 'and here is another'.
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From:
G.E. Moore (Proof of an External World [1939], p.1)
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A reaction:
The words need to be spoken, presumably, so that what he is doing fits into the linguistic conventions of what will normally be accepted as a proof. In fact, just holding the hand up seems enough. The proof begs the question of virtual reality.
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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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22302
|
Moor bypassed problems of correspondence by saying true propositions ARE facts [Moore,GE, by Potter]
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Full Idea:
Moore avoided the problematic correspondence between propositions and reality by identifying the former with the latter; the world consists of true propositions, and there is no difference between a true proposition and the fact that makes it true.
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From:
report of G.E. Moore (The Nature of Judgement [1899]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 28 'Refut'
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A reaction:
This is "the most platonic system of modern times", he wrote (letter 14.8.1898). He then added platonist ethics. This is a pernicious and absurd doctrine. The obvious problem is that false propositions can be indistinguishable, but differ in ontology.
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7526
|
Hegelians say propositions defy analysis, but Moore says they can be broken down [Moore,GE, by Monk]
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Full Idea:
Moore rejected the Hegelian view, that a proposition is a unity that defies analysis; instead, it is a complex that positively cries out to be broken up into its constituent parts, which parts Moore called 'concepts'.
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From:
report of G.E. Moore (The Nature of Judgement [1899]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4
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A reaction:
Russell was much influenced by this idea, though it may be found in Frege. Anglophone philosophers tend to side instantly with Moore, but the Hegel view must be pondered. An idea comes to us in a unified flash, before it is articulated.
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5903
|
'Right' means 'cause of good result' (hence 'useful'), so the end does justify the means [Moore,GE]
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Full Idea:
'Right' does and can mean nothing but 'cause of a good result', and is thus identical with 'useful', whence it follows that the end always will justify the means.
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From:
G.E. Moore (Principia Ethica [1903], §089)
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A reaction:
Of course, Moore does not identify utility with pleasure, as his notion of what is good concerns fairly Platonic ideals. Would Stalin's murders have been right if Russia were now the happiest nation on Earth?
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5907
|
Relationships imply duties to people, not merely the obligation to benefit them [Ross on Moore,GE]
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Full Idea:
Moore's 'Ideal Utilitarianism' seems to unduly simplify our relations to our fellows. My neighbours are merely possible beneficiaries by my action. But they also stand to me as promiser, creditor, husband, friend, which entails prima facie duties.
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From:
comment on G.E. Moore (Principia Ethica [1903]) by W. David Ross - The Right and the Good §II
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A reaction:
Perhaps it is better to say that we have obligations to benefit particular people, because of our obligations, and that we are confined to particular benefits which meet those obligations - not just any old benefit to any old person.
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