18 ideas
| 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) |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 22246 | A train of reasoning must be treated as all happening simultaneously [Recanati] |
| Full Idea: For logic purposes, a train of reasoning has to be construed as synchronic. | |
| From: François Recanati (Mental Files in Flux [2016], 5.2) | |
| A reaction: If we are looking for a gulf between logic and the real world this is a factor to be considered, along with Nietzsche's observation about necessary simplification. [ref to Kaplan 'Afterthoughts' 1989, 584-5] |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 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) |
| 22247 | Indexicality is not just a feature of language; examples show it also occurs in thought [Recanati] |
| Full Idea: People once took indexicality to be exclusively a property of language, ....but a series of examples seemed to establish that the thought expressed by uttering an indexical sentence is itself indexical (and is thus 'essential'). | |
| From: François Recanati (Mental Files in Flux [2016], 6.1) | |
| A reaction: Perry's example of not realising it is him leaking the sugar in a supermarket is the best known example. Was this a key moment for realising that philosophy of thought is (pace Dummett) more important than philosophy of language? |
| 22248 | How can we communicate indexical thoughts to people not in the right context? [Recanati] |
| Full Idea: Indexical thoughts create an obvious problem with regard to communication. How can we manage to communicate such thoughts to those who are not in the right context? | |
| From: François Recanati (Mental Files in Flux [2016], 7.1) | |
| A reaction: One answer is that you often cannot communicate them. If I write on a wall 'I am here now', that doesn't tell the next passer-by very much. But 'it's raining here' said in a telephone call works fine - if you know the location of the caller. |
| 22242 | Mental files are concepts, which are either collections or (better) containers [Recanati] |
| Full Idea: Mental files are entries in the mental encyclopedia, that is, concepts. Some, following Grice, say they are information collections, but I think of them as containers. Collections are determined by their elements, but containers have independent identity. | |
| From: François Recanati (Mental Files in Flux [2016], Pref) | |
| A reaction: [compressed] [Grice reference is 'Vacuous Names' (1969)] I agree with Recanati. The point is that you can invoke a file by a label, even when you don't know what the content is. |
| 22243 | The Frege case of believing a thing is both F and not-F is explained by separate mental files [Recanati] |
| Full Idea: Frege's Constraint says if a subject believes an object is both F and not-F (as in 'Frege cases'), then the subject thinks of that object under distinct modes of presentation. Having distinct mental files of the object is sufficient to generate this. | |
| From: François Recanati (Mental Files in Flux [2016], Pref) | |
| A reaction: [compressed] When you look at how many semantic puzzles (notably from Frege and Kripke) are solved by the existence of labelled mental files, the case for them is overwhelming. |
| 22245 | A linguistic expression refers to what its associated mental file refers to [Recanati] |
| Full Idea: Mental files determine the reference of linguistic expressions: an expression refers to what the mental file associated with it refers to (at the time of tokening). | |
| From: François Recanati (Mental Files in Flux [2016], 5) | |
| A reaction: Invites the question of how mental files manage to refer, prior to the arrival of a linguistic expression. A mental file is usually fully of descriptions, but it might be no more than a label. |
| 22250 | There are speakers' thoughts and hearers' thoughts, but no further thought attached to the utterance [Recanati] |
| Full Idea: There is the speaker's thought and the thought formed by the hearer. That is all there is. We don't need an additional entity, the thought expressed by the utterance. | |
| From: François Recanati (Mental Files in Flux [2016], 7.2) | |
| A reaction: This fits my view of propositions nicely. They are the two 'thoughts'. The notion of some further abstract 'proposition' with its own mode of independent existence strikes me as ontologically absurd. |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
| A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
| 22249 | The Naive view of communication is that hearers acquire exactly the thoughts of the speaker [Recanati] |
| Full Idea: The Naive Conception of Communication rests on the idea that communication is the replication of thoughts: the thought the hearer entertains when he understands what the speaker is saying is the very thought which the speaker expressed. | |
| From: François Recanati (Mental Files in Flux [2016], 7.1) | |
| A reaction: It is hard to believe that any modern thinker would believe such a view, given holistic views of language etc. |