20 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) |
| 9175 | We may fix the reference of 'Cicero' by a description, but thereafter the name is rigid [Kripke] |
| Full Idea: We may fix the reference of 'Cicero' by use of some descriptive phrase, such as 'author of these works'. But once we have this reference fixed, we then use the name 'Cicero' rigidly to designate the man who in fact we have identified by his authorship. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.183) | |
| A reaction: Even supposedly rigid names can shift reference, as Evans's example of 'Madagascar' shows (Idea 9041). Reference is a much more social activity than Kripke is willing to admit. There is a 'tradition' of reference (Dummett) for the name 'Cicero'. |
| 9171 | The function of names is simply to refer [Kripke] |
| Full Idea: The function of names is simply to refer. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.167) | |
| A reaction: This is Kripke reverting to the John Stuart Mill view of names. If I say "you are a right Casanova" I don't simply refer to Casanova. In notorious examples like 'Homer' reference is fine, but the object of reference is a bit elusive. |
| 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) |
| 9174 | It is necessary that this table is not made of ice, but we don't know it a priori [Kripke] |
| Full Idea: Although the statement that this table (if it exists at all) was not made of ice, is necessary, it certainly is not something that we know a priori. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.180) | |
| A reaction: One of the key thoughts in modern philosophy. Kit Fine warns against treating it as a new and exciting toy, but it is a new and exciting toy. Scientific essentialism, which I so want to be true, is built on this proposal. |
| 9172 | A 'rigid designator' designates the same object in all possible worlds [Kripke] |
| Full Idea: By 'rigid designator' I mean a term that designates the same object in all possible worlds. | |
| From: Saul A. Kripke (Identity and Necessity [1971]) | |
| A reaction: I am persistently troubled by the case of objects which are slightly different in another possible world. Does 'Aristotle' refer to him as young or old? Might the very same man have had a mole on his cheek? |
| 9173 | We cannot say that Nixon might have been a different man from the one he actually was [Kripke] |
| Full Idea: It seems that we cannot say "Nixon might have been a different man from the man he in fact was", unless we mean it metaphorically. He might have been a different sort of person. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.176) | |
| A reaction: The problem is that being a 'different sort of person' could become more and more drastic, till Nixon is unrecognisable. I don't see how I can stipulate that a small and dim mouse is Richard Nixon, even in a possible world with magicians. |
| 9176 | Modal statements about this table never refer to counterparts; that confuses epistemology and metaphysics [Kripke] |
| Full Idea: Statements about the modal properties of this table never refer to counterparts. However, if someone confuses the epistemological problems and the metaphysical problems he will be well on the way to the counterpart theory of Lewis. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.184 n16) | |
| A reaction: I can't make out what we should say about a possible object which is very nearly this table. Kripke needs the table to have a clear and unwavering essence, but tables are not that sort of thing. How would Kripke define 'physical object'? |
| 9177 | Identity theorists must deny that pains can be imagined without brain states [Kripke] |
| Full Idea: The identity theorist has to hold that we are under some illusion in thinking that we can imagine that there could have been pains without brain states. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.190) | |
| A reaction: The origin of Robert Kirk's idea that there might be zombies. Kripke is wrong. Of course Kripke and his friends can imagine disembodied pains; the question is whether being able to imagine them makes them possible, which it doesn't. |
| 9178 | Pain, unlike heat, is picked out by an essential property [Kripke] |
| Full Idea: 'Heat' is a rigid designator, which is picked out by the contingent property of being felt in a certain way; pain, on the other hand, is picked out by an essential (indeed necessary and sufficient) property. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.190 n19) | |
| A reaction: Hm. I could pick out your pain by your contingent whimpering behaviour. I can spot my own potential pain by a combination of bodily damage and pain killing tablets. I suspect him of the same blunder as Descartes on this one. |
| 19271 | No rule can be fully explained [Kripke] |
| Full Idea: Every explanation of a rule could conceivably be misunderstood. | |
| From: Saul A. Kripke (Wittgenstein on Rules and Private Language [1982], 3) | |
| A reaction: This is Kripke's summary of what he takes to be Wittgenstein's scepticism about rules. |
| 19269 | 'Quus' means the same as 'plus' if the ingredients are less than 57; otherwise it just produces 5 [Kripke] |
| Full Idea: I will define 'quus' by x-quus-y = x + y, if x, y < 57, and otherwise it equals 5. Who is to say that this is not the function I previously meant by '+'? | |
| From: Saul A. Kripke (Wittgenstein on Rules and Private Language [1982], 2) | |
| A reaction: Kripke's famous example, to illustrate the big new scepticism introduced by Wittgenstein's questions about the rationality of following a rule. I suspect that you have to delve into psychology to understand rule-following, rather than logic. |
| 7305 | Kripke's Wittgenstein says meaning 'vanishes into thin air' [Kripke, by Miller,A] |
| Full Idea: Quine and Kripke's Wittgenstein attempt to argue that there are no facts about meaning, that the notion of meaning, as Kripke puts it, 'vanishes into thin air'. | |
| From: report of Saul A. Kripke (Wittgenstein on Rules and Private Language [1982]) by Alexander Miller - Philosophy of Language Pref | |
| A reaction: A tempting solution to the problem. If, though, it is possible for someone to say something that is self-evidently meaningless, or to accuse someone of speaking (deep down) without meaning, then that needs explaining. |
| 19270 | If you ask what is in your mind for following the addition rule, meaning just seems to vanish [Kripke] |
| Full Idea: What can there be in my mind that I make use of when I follow a general rule to add in the future? It seems that the entire idea of meaning vanishes into thin air. | |
| From: Saul A. Kripke (Wittgenstein on Rules and Private Language [1982], 2) | |
| A reaction: Introspection probably isn't the best way to investigate the phenomenon of meaning. Indeed it seems rather old-fashioned and Cartesian. Kripke says, though, that seeking 'tacit' rules is even worse [end of note 22]. |
| 11076 | Community implies assertability-conditions rather than truth-conditions semantics [Kripke, by Hanna] |
| Full Idea: If we take account of the fact that a speaker is in a community, then we must adopt an assertability-conditions semantics (based on what is legitimately assertible), and reject truth-conditional semantics (based on correspondence to the facts). | |
| From: report of Saul A. Kripke (Wittgenstein on Rules and Private Language [1982]) by Robert Hanna - Rationality and Logic 6.1 | |
| A reaction: [Part of Hanna's full summary of Kripke's argument] This sounds wrong to me. There are conditions where it is agreed that a lie should be told. Two people can be guilty of the same malapropism. |
| 11075 | The sceptical rule-following paradox is the basis of the private language argument [Kripke, by Hanna] |
| Full Idea: Kripke argues that the 'rule-following paradox' is essential to the more controversial private language argument, and introduces a radically new form of scepticism. | |
| From: report of Saul A. Kripke (Wittgenstein on Rules and Private Language [1982]) by Robert Hanna - Rationality and Logic 6.1 | |
| A reaction: It certainly seems that Kripke is right to emphasise the separateness of the two, as the paradox is quite persuasive, but the private language argument seems less so. |