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All the ideas for 'The philosophical basis of intuitionist logic', 'Sentences' and 'Letters to Regius'

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10 ideas

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic

18073	Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher]
	Full Idea: Dummett argues that classical logic depends on the choice of the concept of truth as central to the theory of meaning, while for the intuitionist the concept of assertability occupies this position.
	From: report of Michael Dummett (The philosophical basis of intuitionist logic [1973]) by Philip Kitcher - The Nature of Mathematical Knowledge 06.5
	A reaction: Since I can assert any nonsense I choose, this presumably means 'warranted' assertability, which is tied to the concept of proof in mathematics. You can reason about falsehoods, or about uninterpreted variables. Can you 'assert' 'Fx'?

5. Theory of Logic / G. Quantification / 1. Quantification

19057	Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett]
	Full Idea: Classical quantification represents an infinite conjunction or disjunction, and the truth-value is determined by the infinite sum or product of the instances ....but this presupposes that all the instances already possess determinate truth-values.
	From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.246)
	A reaction: In the case of the universal quantifier, Dummett is doing no more than citing the classic empiricism objection to induction - that you can't make the universal claim if you don't know all the instances. The claim is still meaningful, though.

8. Modes of Existence / A. Relations / 1. Nature of Relations

18528	The single imagined 'interval' between things only exists in the intellect [Auriol]
	Full Idea: It appears that a single thing, which must be imagined as some sort of interval [intervallum] existing between two things, cannot exist in extramental reality, but only in the intellect.
	From: Peter Auriol (Sentences [1316], I fols318 v a-b), quoted by John Heil - The Universe as We Find It 7
	A reaction: This is the standard medieval denial of the existence of real relations. It contrasts with post-Russell ontology, which seems to admit relations as entities. Heil and Auriol and right.

9. Objects / D. Essence of Objects / 15. Against Essentialism

12251	Substantial forms are not understood, and explain nothing [Descartes]
	Full Idea: Clearly no explanation can be given by these substantial forms for any natural action, since their defenders admit that they are occult and that they do not understand them themselves, ...so they explain nothing.
	From: René Descartes (Letters to Regius [1642], 1642.01), quoted by David S. Oderberg - Real Essentialism 267 n5
	A reaction: [Oderberg gives refs for attack by Locke and Hume, p.66] Descartes' target is Aristotle's hylomorphism. The problem seems to be understanding what Aristotle meant, which is much more than mere 'shape'. More like 'controlling principle'.

19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions

19055	Stating a sentence's truth-conditions is just paraphrasing the sentence [Dummett]
	Full Idea: An ability to state the condition for the truth of a sentence is, in effect, no more than an ability to express the content of the sentence in other words.
	From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.224)
	A reaction: Alternatively, if you give something other than a paraphrase of the sentence as its meaning (such as a proof of its truth), then you seem to have departed from your target sentence. Can we reduce and eliminate our sentences in this way?

19056	If a sentence is effectively undecidable, we can never know its truth conditions [Dummett]
	Full Idea: If a sentence is effectively undecidable, the condition which must obtain for it to be true is not one which we are capable of recognising whenever it obtains, or of getting ourselves in a position to do so.
	From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.225)
	A reaction: The instances of 'undecidable' sentences are most clearly seen in mathematics, such as the Continuum Hypothesis or Goldbach's Conjecture, or anything involving vast infinite cardinals. But do you need precise truth-conditions for meaning?

19. Language / A. Nature of Meaning / 6. Meaning as Use

19054	Meaning as use puts use beyond criticism, and needs a holistic view of language [Dummett]
	Full Idea: If use constitutes meaning, it might seem that use is beyond criticism. ....But such an attitude can, ultimately, be supported onlly by the adoption of a holistic view of language.
	From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.218)
	A reaction: Dummett goes on to say that the rejection of the holistic view of mathematical meaning leads to his preference for intuitionistic logic.

26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter

16589	Prime matter lacks essence, but is only potentially and indeterminately a physical thing [Auriol]
	Full Idea: Prime matter has no essence, nor a nature that is determinate, distinct, and actual. Instead, it is pure potential, and determinable, so that it is indeterminately and indistinctly a material thing.
	From: Peter Auriol (Sentences [1316], II.12.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.1
	A reaction: Pasnau thinks Auriol has the best shot at explaining the vague idea of 'prime matter', with the thought that it exists, but indeterminateness is what gives it a lesser mode of existence. It strikes me as best to treat 'exist' as univocal.

28. God / A. Divine Nature / 4. Divine Contradictions

16651	God can do anything non-contradictory, as making straightness with no line, or lightness with no parts [Auriol]
	Full Idea: If someone says 'God could make straightness without a line, and roughness and lightness in weight without parts', …then show me the reason why God can do whatever does not imply a contradiction, yet cannot do these things.
	From: Peter Auriol (Sentences [1316], IV.12.2.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 11.4
	A reaction: How engagingly bonkers. The key idea preceding this is that God can do all sorts of things that are beyond our understanding. He is then obliged to offer some examples.

29. Religion / B. Monotheistic Religion / 4. Christianity / c. Angels

16772	An angelic mind would not experience pain, even when connected to a human body [Descartes, by Pasnau]
	Full Idea: Descartes points out that an angelic mind, even if causally connected to a human body, would not experience the same sort of bodily sensations; it would, instead, simply observe flesh being torn, like a piece of paper.
	From: report of René Descartes (Letters to Regius [1642], III:493) by Robert Pasnau - Metaphysical Themes 1274-1671 25.6
	A reaction: Does that mean that the angel could not have the experience even if it wanted to have it. So they can't pick up a cup either? So they can't make themselves known to us, even if they are desperate to? So the Annunciation never happened?