21 ideas
| 19100 | 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. |
| 19094 | 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. |
| 19099 | '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). |
| 19103 | '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. |
| 19105 | 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? |
| 19108 | 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? |
| 19101 | 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. |
| 19106 | 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. |
| 19096 | 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'. |
| 19098 | 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. |
| 19104 | 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. |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| Full Idea: A 'linear ordering' (or 'total ordering') on A is a binary relation R meeting two conditions: R is transitive (of xRy and yRz, the xRz), and R satisfies trichotomy (either xRy or x=y or yRx). | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:62) |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| Full Idea: To know if A ∈ B, we look at the set A as a single object, and check if it is among B's members. But if we want to know whether A ⊆ B then we must open up set A and check whether its various members are among the members of B. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:04) | |
| A reaction: This idea is one of the key ideas to grasp if you are going to get the hang of set theory. John ∈ USA ∈ UN, but John is not a member of the UN, because he isn't a country. See Idea 12337 for a special case. |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| Full Idea: The 'ordered pair' <x,y> is defined to be {{x}, {x,y}}; hence it can be proved that <u,v> = <x,y> iff u = x and v = y (given by Kuratowski in 1921). ...The definition is somewhat arbitrary, and others could be used. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:36) | |
| A reaction: This looks to me like one of those regular cases where the formal definitions capture all the logical behaviour of the concept that are required for inference, while failing to fully capture the concept for ordinary conversation. |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| Full Idea: Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ. A man with an empty container is better off than a man with nothing. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1.03) |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| Full Idea: It might be thought at first that the empty set would be a rather useless or even frivolous set to mention, but from the empty set by various set-theoretic operations a surprising array of sets will be constructed. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:02) | |
| A reaction: This nicely sums up the ontological commitments of mathematics - that we will accept absolutely anything, as long as we can have some fun with it. Sets are an abstraction from reality, and the empty set is the very idea of that abstraction. |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| Full Idea: Given any x we have the singleton {x}, which is defined by the pairing axiom to be {x,x}. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 2:19) | |
| A reaction: An interesting contrivance which is obviously aimed at keeping the axioms to a minimum. If you can do it intuitively with a new axiom, or unintuitively with an existing axiom - prefer the latter! |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| Full Idea: It was observed by several people that for a satisfactory theory of ordinal numbers, Zermelo's axioms required strengthening. The Axiom of Replacement was proposed by Fraenkel and others, giving rise to the Zermelo-Fraenkel (ZF) axioms. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:15) |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| Full Idea: For functions, we know that for any y there exists an appropriate x, but we can't yet form a function H, as we have no way of defining one particular choice of x. Hence we need the axiom of choice. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:48) |
| 19109 | 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |