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) |
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'? |
19722 | We could know the evidence for our belief without knowing why it is such evidence [Mittag] |
Full Idea: While one might understand the proposition entailed by one's evidence, one might have no idea how or why one's evidence entails it. This seems to imply one is not justified in believing the proposition on the basis of one's evidence. | |
From: Daniel M. Mittag (Evidentialism [2011], 'Evidential') | |
A reaction: An example might be seen if a layman tours a physics lab. This looks like a serious problem for evidentialism. Once you see why the evidence entails the proposition, you are getting closer to understanding than to knowledge. Explanation. |
19723 | Evidentialism can't explain that we accept knowledge claims if the evidence is forgotten [Mittag] |
Full Idea: If one came to believe p with good evidence, but has since forgotten that evidence, we might think one can continue to believe justifiably, but evidentialism appears unable to account for this. | |
From: Daniel M. Mittag (Evidentialism [2011], 'Forgotten') | |
A reaction: We would still think that the evidence was important, and we would need to trust the knower's claim that the forgotten evidence was good. So it doesn't seem to destroy the evidentialist thesis. |
19720 | Evidentialism concerns the evidence for the proposition, not for someone to believe it [Mittag] |
Full Idea: Evidentialism is not a theory about when one's believing is justified; it is a theory about what makes one justified in believing a proposition. It is a thesis regarding 'propositional justification', not 'doxastic justification'. | |
From: Daniel M. Mittag (Evidentialism [2011], 'Preliminary') | |
A reaction: Thus it is entirely about whether the evidence supports the proposition, and has no interest in who believes it or why. Knowledge is when you believe a true proposition which has good support. This could be internalist or externalist? |
19721 | Coherence theories struggle with the role of experience [Mittag] |
Full Idea: Traditional coherence theories seem unable to account for the role experience plays in justification. | |
From: Daniel M. Mittag (Evidentialism [2011], 'Evidence') | |
A reaction: I'm inclined to say that experience only becomes a justification when it has taken propositional (though not necessarily lingistic) form. That is, when you see it 'as' something. Uninterpreted shape and colour can justify virtually nothing. |
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. |