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All the ideas for 'fragments/reports', 'Truth Rehabilitated' and 'The philosophical basis of intuitionist logic'

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16 ideas

3. Truth / A. Truth Problems / 3. Value of Truth
Without truth, both language and thought are impossible [Davidson]
     Full Idea: Without a grasp of the concept of truth, not only language, but thought itself, is impossible.
     From: Donald Davidson (Truth Rehabilitated [1997], p.16)
     A reaction: Davidson never mentions animals, but I like this idea because it points to importance of truth for animals as well. I say that truth is relevant to any mind that makes judgements - and quite small animals (e.g. ants and spiders) make judgements.
Plato's Forms confused truth with the most eminent truths, so only Truth itself is completely true [Davidson]
     Full Idea: Plato's conflation of abstract universals with entities of supreme value reinforced the confusion of truth with the most eminent truths. …The only perfect exemplar of a Form is the Form itself, …and only truth itself is completely true.
     From: Donald Davidson (Truth Rehabilitated [1997], p.3)
     A reaction: Even non-subscribers to Plato often talk as if there were some grand thing called the Truth with a capital T, quite often used in a religious context. Truth is the hallmark of successful (non-fanciful) thought.
Truth can't be a goal, because we can neither recognise it nor confim it [Davidson]
     Full Idea: Since it is neither visible as a target, nor recognisable when achieved, there is no point in calling truth a goal. We should only aim at increasing confidence in our beliefs, by collecting further evidence or checking our calculations.
     From: Donald Davidson (Truth Rehabilitated [1997], P.6)
     A reaction: This is mainly aimed at pragmatists, but Davidson obviously subscribes (as do I) to their fallibilist view of knowledge.
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Correspondence can't be defined, but it shows how truth depends on the world [Davidson]
     Full Idea: Correspondence, while it is empty as a definition, does capture the thought that truth depends on how the world is.
     From: Donald Davidson (Truth Rehabilitated [1997], p.16)
     A reaction: Just don't try to give a precise account of the correspondence between two things (thoughts and facts) which are so utterly different in character.
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
When Tarski defines truth for different languages, how do we know it is a single concept? [Davidson]
     Full Idea: We have to wonder how we know that it is some single concept which Tarski indicates how to define for each of a number of well-behaved languages.
     From: Donald Davidson (Truth Rehabilitated [1997], P.11)
     A reaction: Davidson says that Tarski makes the assumption that it is a single concept, but fails to demonstrate the fact. This resembles Frege's Julius Caesar problem - of how you know whether your number definition has defined a number.
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Disquotation only accounts for truth if the metalanguage contains the object language [Davidson]
     Full Idea: Disquotation cannot pretend to give a complete account of the concept of truth, since it works only in the special case where the metalanguage contains the object language. Neither can contain their own truth predicate.
     From: Donald Davidson (Truth Rehabilitated [1997], p.10)
     A reaction: Presumably more sophisticated and complete accounts would need a further account of translation between languages - which explains Quine's interest in that topic. […see this essay, p.12]
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.
7. Existence / D. Theories of Reality / 8. Facts / e. Facts rejected
If we try to identify facts precisely, they all melt into one (as the Slingshot Argument proves) [Davidson]
     Full Idea: If we try to provide a serious semantics for reference to facts, we discover that they melt into one; there is no telling them apart. The relevant argument (the 'Slingshot') was credited to Frege by Alonso Church.
     From: Donald Davidson (Truth Rehabilitated [1997], p.5)
     A reaction: This sounds like good grounds for not attempting to be too precise. 'There are bluebells in my local wood' identifies a fact by words, but even an animal can distinguish this fact. Only a logician dreams of making its content precise.
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?
Knowing the potential truth conditions of a sentence is necessary and sufficient for understanding [Davidson]
     Full Idea: It is clear that someone who knows under what conditions a sentence would be true understands that sentence, …and if someone does not know under what conditions it would be true then they do not understand it.
     From: Donald Davidson (Truth Rehabilitated [1997], p.13)
     A reaction: I've always subscribed to this view. Langauge is meaningless if you can't relate it to reality, and I don't think there could be a language without an intuitive notion of truth.
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.
It could be that the use of a sentence is explained by its truth conditions [Davidson]
     Full Idea: It may be that sentences are used as they are because of their truth conditions, and they have the truth conditions they do because of how they are used.
     From: Donald Davidson (Truth Rehabilitated [1997], p.13)
     A reaction: I've always taken the attempt to explain meaning by use as absurd. It is similar to trying to explain mind in terms of function. In each case, what is the intrinsic nature of the thing, which makes that use or that function possible?
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
     Full Idea: Archelaus was the first person to say that the universe is boundless.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]
     Full Idea: Archelaus wrote that life on Earth began in a primeval slime.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus
     A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea.