14 ideas
| 18902 | Correspondence theories can't tell you what truths correspond to [Davidson] |
| Full Idea: The real objection to correspondence theories is that such theories fail to provide entities to which truth vehicles (as statements, sentence, or utterances) can be said to correspond. | |
| From: Donald Davidson (The Structure and Content of Truth [1990], p.304), quoted by Fred Sommers - Intellectual Autobiography Notes 23 | |
| A reaction: This is the remark which provoked Sommers to come out with Idea 18901, which strikes me as rather profound. |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 1630 | We can only see an alien language in terms of our own thought structures (e.g. physical/abstract) [Quine] |
| Full Idea: We are prone to talk about physical and abstract objects. It is hard to know how else to talk, because we are bound to adapt any alien pattern to our own in the very process of understanding or translating the alien sentences. | |
| From: Willard Quine (Speaking of Objects [1960], pt.I,p.1) |
| 5747 | "No entity without identity" - our ontology must contain items with settled identity conditions [Quine, by Melia] |
| Full Idea: Quine's well-known slogan "no entity without identity" means that no object should be admitted into our ontology unless its identity conditions, the conditions that say which object it is, have been settled. | |
| From: report of Willard Quine (Speaking of Objects [1960]) by Joseph Melia - Modality Ch.4 | |
| A reaction: This invites science fiction scenarios, where we admit the existence of something before we have a clue what it is (whether it is physical, hallucination, divine..). Quine's slogan seems attractive but optimistic. How 'settled'? |
| 7925 | There is no proper identity concept for properties, and it is hard to distinguish one from two [Quine] |
| Full Idea: The lack of a proper identity concept for attributes (properties) is a lack that philosophers feel impelled to supply; for, what sense is there in saying there are attributes when there is no sense in saying when there is one attribute and when two? | |
| From: Willard Quine (Speaking of Objects [1960], IV) | |
| A reaction: This strikes me as being a really crucial question. There is a mistaken tendency to take any possible linguistic predicate as implying a natural property. I sympathise with the sceptics here (see Ideas 4029, 3906, 3322). How to individuate properties? |
| 13387 | Our conceptual scheme becomes more powerful when we posit abstract objects [Quine] |
| Full Idea: There is no denying the access of power that accrues to our conceptual scheme through the positing of abstract objects. | |
| From: Willard Quine (Speaking of Objects [1960], §5) | |
| A reaction: This seems right, both in its use of the word 'posit', and in its general pragmatic claim. So why? If they enable us to grapple with the world better, it must be because of their power of generalisation. They are nets thrown over chunks of reality. |
| 8277 | I prefer 'no object without identity' to Quine's 'no entity without identity' [Lowe on Quine] |
| Full Idea: To adapt Quine's famous slogan ('no entity without identity'), I prefer to say 'no object without identity'. | |
| From: comment on Willard Quine (Speaking of Objects [1960], p.52) by E.J. Lowe - The Possibility of Metaphysics 7.1 | |
| A reaction: Quine was trying to make us all more scientific, but Lowe is closer to common sense. The sky is an entity, most of us would say, but with very shaky identity-conditions. A wave of the sea is a good example. |
| 1631 | You could know the complete behavioural conditions for a foreign language, and still not know their beliefs [Quine] |
| Full Idea: We could know the necessary and sufficient stimulatory conditions of every possible act of utterance, in a foreign language, and still not know how to determine what objects the speakers of that language believe in. | |
| From: Willard Quine (Speaking of Objects [1960], pt.III,p.11) | |
| A reaction: I just don't believe this, because the same scepticism then creeps into discussions of native speakers of a single language, and all communcation is blighted - which is nonsense. |
| 1632 | Translation of our remote past or language could be as problematic as alien languages [Quine] |
| Full Idea: Translation of our remote past or future discourse into the terms we now know could be about as tenuous and arbitrary a projection as translation of a heathen language was seen to be. | |
| From: Willard Quine (Speaking of Objects [1960], pt.V,p.25) | |
| A reaction: Is he seriously saying that we can't understand Shakespeare, because holism implies that we would have to be Elizabethans? So scholarship is in vain? Is yesterday the 'past'? |