Combining Texts

All the ideas for 'fragments/reports', 'The philosophical basis of intuitionist logic' and 'Knowledge by Acquaintance and Description-1'

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8 ideas

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
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
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 / D. Universals / 2. Need for Universals
We know a universal in 'yellow differs from blue' or 'yellow resembles blue less than green does' [Russell]
     Full Idea: We are aware of the universal 'yellow'; this universal is the subject in such judgements as 'yellow differs from blue' or 'yellow resembles blue less than green does'.
     From: Bertrand Russell (Knowledge by Acquaintance and Description-1 [1911], 154), quoted by Bernard Linsky - Russell's Metaphysical Logic 2.3
     A reaction: This still seems one of the strongest examples in support of universals. You could hardly be talking about yellow tropes in such instances (even if the world does contain yellow tropes).
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
My 'acquaintance' with sense-data is nothing like my knowing New York [Williams,M on Russell]
     Full Idea: My 'acquaintance' with sense-data is nothing like my knowing New York.
     From: comment on Bertrand Russell (Knowledge by Acquaintance and Description-1 [1911]) by Michael Williams - Without Immediate Justification §4
     A reaction: This pinpoints a nice difficulty for Russell. Williams may misrepresent Russell's account of acquaintance, but that is probably because Russell is unclear, or uncertain. The problem is when Russell claims that his acquaintance gives knowledge.
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
By nature people are close to one another, but culture drives them apart [Hippias]
     Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature.
     From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
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?
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
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.