17 ideas
| 17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
| Full Idea: I uphold the belief that for clear questions posed by reason, reason can also find clear answers. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Koellner - On the Question of Absolute Undecidability 1.5 | |
| A reaction: [written in 1961] This contradicts the implication normally taken from his much earlier Incompleteness Theorems. |
| 18928 | If maximalism is necessary, then that nothing exists has a truthmaker, which it can't have [Cameron] |
| Full Idea: I think truthmaker theory is contingently true. [n24] If there could have been nothing, what makes that true? But if truthmaker maximalism is a necessary truth, there's necessarily something. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 4 n24) | |
| A reaction: Truthmaking is beginning to feel like Gödel's Theorems. You can 'make' lots and lots of truths ('prove' in Gödel), but there will be truths that elude the making. Truthmaker theory itself will be one example. So is Maximalism another one? |
| 18931 | Determinate truths don't need extra truthmakers, just truthmakers that are themselves determinate [Cameron] |
| Full Idea: I reject saying there must be an additional truthmaker for 'Determinately, p': rather, I say that the truthmaker for p must simply be a determinate existent rather than a mere existent. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 6) | |
| A reaction: As he puts it (quite persuasively), God doesn't need to add an extra truthmaker for a determinate truth. Cameron rejects Necessitarianism. He uses 'determinate' fairly uncritically. What makes the truth of the truthmaker's determinacy? |
| 18932 | The facts about the existence of truthmakers can't have a further explanation [Cameron] |
| Full Idea: The orthodox truthmaker theorist thinks the facts concerning the existence of the truthmakers do not admit of further explanation. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 6) | |
| A reaction: It is fairly obvious, I suppose, that not every truth can have a truthmaker, just as the verification principle could not be verified, and you can't perceive your perception in order to check it. Could God withdraw the power of truthmaking? |
| 18923 | The present property 'having been F' says nothing about a thing's intrinsic nature [Cameron] |
| Full Idea: The property 'being such as to have been a child' is suspicious because it points beyond its instances in the sense that a thing's presently having that property tells us nothing about the present intrinsic nature of the thing. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 2) | |
| A reaction: This is his objection to what he calls the 'Lucretian' strategy, which tries to make history into a property of present reality. That is implausible, I think, because there is no test for the property, apart from knowledge of the past. Reality is tensed? |
| 18926 | One temporal distibution property grounds our present and past truths [Cameron] |
| Full Idea: Temporal distributional properties are fundamental - it is exactly the same property that is grounding the truth about how the bearer now is that is grounding truths about how the bearer was. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 4) | |
| A reaction: Some kind of slight of hand is going on here, though he does a nice job of confronting all possible objections. This is the sort of metaphysics you come up with when you stake everything on the dubious notion of a 'property'. |
| 18929 | We don't want present truthmakers for the past, if they are about to cease to exist! [Cameron] |
| Full Idea: Whilst not logically inconsistent, it would be bad if it could now be true that ten years ago there was a sea battle, but that five years ago it wasn't true that five years before that there was a sea battle. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 4) | |
| A reaction: Nicely makes the point that you can't let the past rely on truthmakers in the present, if those truthmakers are about to go out of existence. So you need a sustained truthmaker, without giving up presentism. Enter 'temporally distributed properties'? |
| 9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
| Full Idea: Gödel proved the completeness of standard formalizations of first-order logic, including Frege's original one. However, an implication of his famous theorem on the incompleteness of arithmetic is that second-order logic is incomplete. | |
| From: report of Kurt Gödel (works [1930]) by Michael Dummett - The Philosophy of Mathematics 3.1 | |
| A reaction: This must mean that it is impossible to characterise arithmetic fully in terms of first-order logic. In which case we can only characterize the features of abstract reality in general if we employ an incomplete system. We're doomed. |
| 10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
| Full Idea: At that time (c.1930) a concept of objective mathematical truth as opposed to demonstrability was viewed with greatest suspicion and widely rejected as meaningless. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 28.2 | |
| A reaction: [quoted from a letter] This is the time of Ramsey's redundancy account, and before Tarski's famous paper of 1933. It is also the high point of Formalism, associated with Hilbert. |
| 17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
| Full Idea: Gödel was quick to point out that his original incompleteness theorems did not produce instances of absolute undecidability and hence did not undermine Hilbert's conviction that for every precise mathematical question there is a discoverable answer. | |
| From: report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro | |
| A reaction: The normal simplistic view among philosophes is that Gödel did indeed decisively refute the optimistic claims of Hilbert. Roughly, whether Hilbert is right depends on which axioms of set theory you adopt. |
| 17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
| Full Idea: Eventually Gödel ...expressed the hope that there might be a generalised completeness theorem according to which there are no absolutely undecidable sentences. | |
| From: report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro | |
| A reaction: This comes as a bit of a shock to those who associate him with the inherent undecidability of reality. |
| 10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
| Full Idea: The concept of truth of sentences in a language cannot be defined in the language. This is the true reason for the existence of undecidable propositions in the formal systems containing arithmetic. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 21.6 | |
| A reaction: [from a letter by Gödel] So they key to Incompleteness is Tarski's observations about truth. Highly significant, as I take it. |
| 18924 | Being polka-dotted is a 'spatial distribution' property [Cameron] |
| Full Idea: Spatial distribution properties say how things are across a region of space, such as being polka-dotted. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 3) | |
| A reaction: I think the routine fallacy of inferring properties from predicates is buried here. We truthfully describe it as 'polka-dotted', but that doesn't mean we must reify polka-dottedness, and see it as a feature of the world. What is a 'jumbled' space? |
| 18930 | Change is instantiation of a non-uniform distributional property, like 'being red-then-orange' [Cameron] |
| Full Idea: What change is on the account being offered is to instantiate a non-uniform distributional property. Being red at one time and orange at a later time is to be analysed as instantiating the distributional property 'being red-then-orange'. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 4) | |
| A reaction: One of those moments when you begin to doubt whether 'being analysed' successfully actually adds much to our wisdom. His property sounds suspiciously 'gruesome' - i.e. subject to the vagaries of how we chose to describe the thing. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |
| 18927 | Surely if things extend over time, then time itself must be extended? [Cameron] |
| Full Idea: If there are temporally extended entities - and there are - then there must be extended regions of time for those entities to extend in. Hence presentism is false. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 4) | |
| A reaction: [Cameron is playing devil's advocate] Something has to be weird here, and I take it to be the fact that the past no longer exists, and yet it is fixed and supports truths. Get over it. My childhood has gone. Totally. Irrevocably. |