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All the ideas for 'Mahaprajnaparamitashastra', 'Pragmatism and Deflationism' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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22 ideas

3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
Truth makes disagreements matter, or worth settling [Misak]
     Full Idea: The role of truth is to make disagreements matter, or to make sense of wanting to resolve disagreements.
     From: Cheryl Misak (Pragmatism and Deflationism [2007], 2)
     A reaction: [She cites Huw Price 2003] This suggests that the most important use of 'truth' is forensic. It is hard to make any sense of a law court without a robust sense of truth. Trial by jury, rather than some great personage, shows this value.
For pragmatists the loftiest idea of truth is just a feature of what remains forever assertible [Misak]
     Full Idea: For pragmatists there is an unseverable connection between making an assertion and claiming that it is true. ...Were we to get to a belief that is forever assertible...then we would have a true belief. There is nothing higher or better we could ask of it.
     From: Cheryl Misak (Pragmatism and Deflationism [2007], 1)
     A reaction: She is particularly drawing on Peirce. She says his 'ideal end of enquiry' idea is a small aspect of his view of truth, which is mainly given here. I had taken the pragmatic view of truth to be silly, but I may rethink.
'True' is used for emphasis, clarity, assertion, comparison, objectivity, meaning, negation, consequence... [Misak]
     Full Idea: 'P is true' is used to emphasise p, and avoid logic problems. The pragmatists says there are plenty of other uses: the aim of assertion or deliberation, the improvement of our views, distinguishing objectivity, explaining meaning, negation, consequence...
     From: Cheryl Misak (Pragmatism and Deflationism [2007], 2)
     A reaction: Pragmatism seems to break 'true' down into its many uses, rather than having a specific theory of truth. This might be where ordinary language philosophy (how is the word 'true' used) meets pragmatism (how is the concept [true] used).
'That's true' doesn't just refer back to a sentence, but implies sustained evidence for it [Misak]
     Full Idea: The pragmatist says 'That's so' or 'that's true' are not just 'pro-sentential', but carry with them the thought that evidence does currently speak in favour of the statement asserted, and the prediction that it will continue to speak in favour.
     From: Cheryl Misak (Pragmatism and Deflationism [2007], 3)
     A reaction: This is a very nice point made by a pragmatist against the flimsy view of truth held by various deflationary views. You ought to believe what is true, and stand by what you hold to be true.
Truth isn't a grand elusive property, if it is just the aim of our assertions and inquiries [Misak]
     Full Idea: If truth is what satisfies our aims in first-order assertion and inquiry (as the pragmatist says), then there is no search for an elusive property, or a metaphysical property, or a property which we cannot grasp.
     From: Cheryl Misak (Pragmatism and Deflationism [2007], 3)
     A reaction: This pragmatic approach is much more persuasive than the usual caricature of pragmatic truth (Idea 19097), but I'm beginning to wonder how you distinguish an 'inquiry' (or 'assertion') from other modes of thought. Do I smell a circularity?
Truth is proper assertion, but that has varying standards [Misak]
     Full Idea: The pragmatist will say that truth is proper assertion, but different discourses have different standards for proper assertion.
     From: Cheryl Misak (Pragmatism and Deflationism [2007], 4)
     A reaction: This remark shows that there is a pragmatic attitude towards truth behind most attempts to analyse the concept of assertion. When and why is assertion legitimate, and what motivates it?
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Disquotation is bivalent [Misak]
     Full Idea: The disquotational schema entails bivalence.
     From: Cheryl Misak (Pragmatism and Deflationism [2007], 2 n10)
     A reaction: A simple but interesting observation. Critics of Tarski observe that he depends on a bivalent logic.
Disquotations says truth is assertion, and assertion proclaims truth - but what is 'assertion'? [Misak]
     Full Idea: The point of the disquotational schema is that to say that a sentence is true is to assert it, and to assert a sentence is to say that it is true. We must then ask what it is to assert or endorse a proposition.
     From: Cheryl Misak (Pragmatism and Deflationism [2007], 4)
     A reaction: [She is referring to the views of Crispin Wright] Most people would say that we assert something because we think it is true, and truth is obviously prior. Clearly if it has been asserted, that was because someone thought it was true.
Disquotationalism resembles a telephone directory [Misak]
     Full Idea: Disquotationalism is more like a telephone directory than a theory.
     From: Cheryl Misak (Pragmatism and Deflationism [2007], 2 n7)
     A reaction: [She cites Wilfred Sellars 1962:33] The idea is that there is a schema - 'p' is true iff p - and that all the acceptable sentences of a language can be expressed in this way, making a vast but finite list. It seems to replace 'theories'.
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflating the correspondence theory doesn't entail deflating all the other theories [Misak]
     Full Idea: We must not move seamlessly from the thought that the correspondence theory must be deflated to the thought that any theory of truth must be deflated.
     From: Cheryl Misak (Pragmatism and Deflationism [2007], 2)
     A reaction: This rather good essay offers the idea that Peircean pragmatic approaches to truth can meet the deflationary desires of the opponents of correspondence, without jettisoning all the crucial naturalistic connections with reality. Interesting.
Deflationism isn't a theory of truth, but an account of its role in natural language [Misak]
     Full Idea: Deflationist theories are not theories of truth, or theories of what truth is. ...They are theories which try to explain the role that 'true' plays in natural languages.
     From: Cheryl Misak (Pragmatism and Deflationism [2007], 3)
     A reaction: [She cites Dorothy Grover 2001,2002] If so, then the modern axiomatic theory of truth sounds appealing, because it tries to give a fuller and more precise account than a mere list is disquotations could possibly give.
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn]
     Full Idea: Frege (1893) considered a definite description to be a genuine singular term (as we do), so that a sentence like 'The present King of France is bald' would have the same logical form as 'Harry Truman is bald'.
     From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by M Fitting/R Mendelsohn - First-Order Modal Logic
     A reaction: The difficulty is what the term refers to, and they embrace a degree of Meinongianism - that is that non-existent objects can still have properties attributed to them, and so can be allowed some sort of 'existence'.
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
     Full Idea: The contradiction in Frege's system is due to the presence of second-order quantification, ..and Frege's explanation of the second-order quantifier, unlike that which he provides for the first-order one, appears to be substitutional rather than objectual.
     From: comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], §25) by Michael Dummett - Frege philosophy of mathematics Ch.17
     A reaction: In Idea 9871 Dummett adds the further point that Frege lacks a clear notion of the domain of quantification. At this stage I don't fully understand this idea, but it is clearly of significance, so I will return to it.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers are ratios of quantities, such as lengths or masses [Frege]
     Full Idea: If 'number' is the referent of a numerical symbol, a real number is the same as a ratio of quantities. ...A length can have to another length the same ratio as a mass to another mass.
     From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], III.1.73), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's'
     A reaction: This is part of a critique of Cantor and the Cauchy series approach. Interesting that Frege, who is in the platonist camp, is keen to connect the real numbers with natural phenomena. He is always keen to keep touch with the application of mathematics.
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
     Full Idea: It cannot be demanded that everything be proved, because that is impossible; but we can require that all propositions used without proof be expressly declared as such, so that we can see distinctly what the whole structure rests upon.
     From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], p.2), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 'What'
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
     Full Idea: Frege opts for his famous definition of numbers in terms of extensions of the concept 'equal to the concept F', but he then (in 'Grundgesetze') needs a theory of extensions or classes, which he provided by means of Basic Law V.
     From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' §1
Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
     Full Idea: Cantor pointed out explicitly to Frege that it is a mistake to take the notion of a set (i.e. of that which has a cardinal number) to simply mean the extension of a concept. ...Frege's later assumption of this was an act of recklessness.
     From: comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by William W. Tait - Frege versus Cantor and Dedekind III
     A reaction: ['recklessness' is on p.61] Tait has no sympathy with the image of Frege as an intellectual martyr. Frege had insufficient respect for a great genius. Cantor, crucially, understood infinity much better than Frege.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
My Basic Law V is a law of pure logic [Frege]
     Full Idea: I hold that my Basic Law V is a law of pure logic.
     From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], p.4), quoted by Penelope Maddy - Naturalism in Mathematics I.1
     A reaction: This is, of course, the notorious law which fell foul of Russell's Paradox. It is said to be pure logic, even though it refers to things that are F and things that are G.
7. Existence / D. Theories of Reality / 4. Anti-realism
The anti-realism debate concerns whether indefeasibility is a plausible aim of inquiry [Misak]
     Full Idea: If indefeasibility turns out to be something we can't sensibly aim at in a kind of inquiry, then the judgements that arise from that kind of 'inquiry' are not truth-apt. It is here that the realism/anti-realism debate resides.
     From: Cheryl Misak (Pragmatism and Deflationism [2007], 4)
     A reaction: A very interesting way of presenting the issue, one that makes the debate sound (to me) considerably more interesting than hitherto. I may start using the word 'indefeasible' rather a lot, in my chats with the anti-realist philosophical multitude.
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
     Full Idea: In later Frege, a concept could be taken as a particular case of a function, mapping every object on to one of the truth-values (T or F), according as to whether, as we should ordinarily say, that object fell under the concept or not.
     From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by Michael Dummett - The Philosophy of Mathematics 3.5
     A reaction: As so often in these attempts at explanation, this sounds circular. You can't decide whether an object truly falls under a concept, if you haven't already got the concept. His troubles all arise (I say) because he scorns abstractionist accounts.
Frege took the study of concepts to be part of logic [Frege, by Shapiro]
     Full Idea: Frege took the study of concepts and their extensions to be within logic.
     From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by Stewart Shapiro - Foundations without Foundationalism 7.1
     A reaction: This is part of the plan to make logic a universal language (see Idea 13664). I disagree with this, and with the general logicist view of the position of logic. The logical approach thins concepts out. See Deleuze/Guattari's horror at this.
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
     Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
     From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
     A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').