17896
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We need to know the meaning of 'and', prior to its role in reasoning [Prior,AN, by Belnap]
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Full Idea:
For Prior, so the moral goes, we must first have a notion of what 'and' means, independently of the role it plays as premise and as conclusion.
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From:
report of Arthur N. Prior (The Runabout Inference Ticket [1960]) by Nuel D. Belnap - Tonk, Plonk and Plink p.132
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A reaction:
The meaning would be given by the truth tables (the truth-conditions), whereas the role would be given by the natural deduction introduction and elimination rules. This seems to be the basic debate about logical connectives.
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17898
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Prior's 'tonk' is inconsistent, since it allows the non-conservative inference A |- B [Belnap on Prior,AN]
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Full Idea:
Prior's definition of 'tonk' is inconsistent. It gives us an extension of our original characterisation of deducibility which is not conservative, since in the extension (but not the original) we have, for arbitrary A and B, A |- B.
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From:
comment on Arthur N. Prior (The Runabout Inference Ticket [1960]) by Nuel D. Belnap - Tonk, Plonk and Plink p.135
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A reaction:
Belnap's idea is that connectives don't just rest on their rules, but also on the going concern of normal deduction.
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18247
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Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]
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Full Idea:
In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities.
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From:
report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6
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A reaction:
This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer.
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12453
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Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer]
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Full Idea:
Neo-intuitionism sees the falling apart of moments, reunited while remaining separated in time, as the fundamental phenomenon of human intellect, passing by abstracting to mathematical thinking, the intuition of bare two-oneness.
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From:
Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80)
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A reaction:
[compressed] A famous and somewhat obscure idea. He goes on to say that this creates one and two, and all the finite ordinals.
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8728
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Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]
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Full Idea:
Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths.
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From:
Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2
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A reaction:
Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time!
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15201
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That Queen Anne is dead is a 'general fact', not a fact about Queen Anne [Prior,AN]
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Full Idea:
The fact that Queen Anne has been dead for some years is not, in the strict sense of 'about', a fact about Queen Anne; it is not a fact about anyone or anything - it is a general fact.
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From:
Arthur N. Prior (Changes in Events and Changes in Things [1968], p.13), quoted by Robin Le Poidevin - Past, Present and Future of Debate about Tense 1 b
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A reaction:
He distinguishes 'general facts' (states of affairs, I think) from 'individual facts', involving some specific object. General facts seem to be what are expressed by negative existential truths, such as 'there is no Loch Ness Monster'. Useful.
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16697
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Time is independent of motion, because God could stop everything for a short or long time [Crathorn, by Pasnau]
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Full Idea:
Suppose God annihilates everything, and then creates something new. The vacant interval could last a shorter or longer time, so there are facts about time independent of facts about motion.
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From:
report of William Crathorn (Sentences [1335], I.16, concl.2) by Robert Pasnau - Metaphysical Themes 1274-1671 18.2
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A reaction:
Not very persuasive if God is in some way 'timeless'. Crathorn would have loved Shoemaker's argument, where motionless time is the best explanation, rather than a possible explanation.
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22899
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'Thank goodness that's over' is not like 'thank goodness that happened on Friday' [Prior,AN]
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Full Idea:
One says 'thank goodness that is over', ..and it says something which it is impossible which any use of any tenseless copula with a date should convey. It certainly doesn't mean the same as 'thank goodness that occured on Friday June 15th 1954'.
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From:
Arthur N. Prior (Changes in Events and Changes in Things [1968]), quoted by Adrian Bardon - Brief History of the Philosophy of Time 4 'Pervasive'
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A reaction:
[Ref uncertain] This seems to be appealing to ordinary usage, in which tenses have huge significance. If we take time (with its past, present and future) as primitive, then tenses can have full weight. Did tenses mean anything at all to Einstein?
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