21 ideas
| 14001 | People who use science to make philosophical points don't realise how philosophical science is [Markosian] |
| Full Idea: When people give arguments from scientific theories to philosophical conclusions, there is usually a good deal of philosophy built into the relevant scientific theories. | |
| From: Ned Markosian (A Defense of Presentism [2004], 3.9) | |
| A reaction: I love this remark, being thoroughly fed up with knowledgeable scientists who are naďve about philosophy, and think their current theory demolishes long-lasting aporiai. They are up to their necks in philosophy. |
| 13991 | Presentism has the problem that if Socrates ceases to exist, so do propositions about him [Markosian] |
| Full Idea: Presentism has a problem with singular propositions about non-present objects. ...When Socrates popped out of existence, according to Presentism, all those singular propositions about him also popped out of existence. | |
| From: Ned Markosian (A Defense of Presentism [2004], 2.1) | |
| A reaction: He seems to treat propositions in a Russellian way, as things which exist independently of thinkers, which I struggle to grasp. Markosian offers various strategies for this [§3.5]. |
| 8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
| Full Idea: We have something like perception of the objects of set theory, shown by the axioms forcing themselves on us as being true. I don't see why we should have less confidence in this kind of perception (i.e. mathematical intuition) than in sense perception. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.483), quoted by Michčle Friend - Introducing the Philosophy of Mathematics 2.4 | |
| A reaction: A famous strong expression of realism about the existence of sets. It is remarkable how the ingredients of mathematics spread themselves before the mind like a landscape, inviting journeys - but I think that just shows how minds cope with abstractions. |
| 9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
| Full Idea: Gödel proved the classical relative consistency of the axiom V = L (which implies the axiom of choice and the generalized continuum hypothesis). This established the full independence of the continuum hypothesis from the other axioms. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Hilary Putnam - Mathematics without Foundations | |
| A reaction: Gödel initially wanted to make V = L an axiom, but the changed his mind. Maddy has lots to say on the subject. |
| 18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
| Full Idea: The set-theoretical paradoxes are hardly any more troublesome for mathematics than deceptions of the senses are for physics. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.271), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 03.4 |
| 10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
| Full Idea: Gödel proved that the Continuum Hypothesis was not inconsistent with the axioms of set theory. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15 |
| 13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
| Full Idea: Gödel proved that (if set theory is consistent) we cannot refute the continuum hypothesis, and Cohen proved that (if set theory is consistent) we cannot prove it either. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by William D. Hart - The Evolution of Logic 10 |
| 10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
| Full Idea: Evidently the 'given' underlying mathematics is closely related to the abstract elements contained in our empirical ideas. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], Suppl) | |
| A reaction: Yes! The great modern mathematical platonist says something with which I can agree. He goes on to hint at a platonic view of the structure of the empirical world, but we'll let that pass. |
| 14002 | Possible worlds must be abstract, because two qualitatively identical worlds are just one world [Markosian] |
| Full Idea: Possible worlds are just abstract objects that play a certain role in philosophers' talk about modality. They are ways things could be. That's why there are no two abstract possible worlds which are qualitatively identical. They count as one world. | |
| From: Ned Markosian (A Defense of Presentism [2004], 3.10) | |
| A reaction: Brilliant! This looks like the best distinction between concrete and abstract. If two concreta are identical they remain two; if two abstracta are identical they are one (like numbers, or logical connectives with the same truth table). |
| 14000 | 'Grabby' truth conditions first select their object, unlike 'searchy' truth conditions [Markosian] |
| Full Idea: We can talk of 'grabby' truth conditions (where an object is grabbed before predication) and 'searchy' truth conditions (where the object is included in what is being asserted). | |
| From: Ned Markosian (A Defense of Presentism [2004], 3.8) | |
| A reaction: [He credits Tom Ryckman with the terminology] I am inclined to think that the whole of language is 'searchy', even when it appears to be blatantly 'grabby'. Even ostensive reference is an act of hope rather than certainty. |
| 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. |
| 13990 | Presentism is the view that only present objects exist [Markosian] |
| Full Idea: According to Presentism, if we were to make an accurate list of all the things that exist (within the range of our most unrestricted quantifiers) there would not be a single non-present object on the list. | |
| From: Ned Markosian (A Defense of Presentism [2004], 1) | |
| A reaction: An immediate problem that needs examing is what constitutes an 'object'. It had better not range over time (like an journey). It would be hard to fit a description like 'the oldest man in England'. |
| 13992 | Presentism says if objects don't exist now, we can't have attitudes to them or relations with them [Markosian] |
| Full Idea: If there are no non-present objects (according to Presentism), then no one can now stand in any relation to any non-present object. You cannot now 'admire' Socrates, and no present event has a causal relation to Washington crossing the Delaware. | |
| From: Ned Markosian (A Defense of Presentism [2004], 2.2) | |
| A reaction: You can have an overlapping causal chain that gets you back to Washington, and a causal chain can connect Socrates to our thoughts about him (as in baptismal reference). A simple reply needs an 'overlap' though. |
| 13994 | Presentism seems to entail that we cannot talk about other times [Markosian] |
| Full Idea: It is very natural to talk about times, ...but Presentism seems to entail that we never say anything about any such times. | |
| From: Ned Markosian (A Defense of Presentism [2004], 2.4) | |
| A reaction: I'm beginning to think that Markosian is in the grips of a false notion of proposition, as something that exists independently of thinkers, and is entailed by the facts and objects of reality. This is not what language does. |
| 13995 | Serious Presentism says things must exist to have relations and properties; Unrestricted version denies this [Markosian] |
| Full Idea: Mark Hinchliff distinguishes between 'Serious' Presentism (objects only have relations and properties when they exist) and 'Unrestricted' Presentism (objects can have relations and properties even when they don't exist). | |
| From: Ned Markosian (A Defense of Presentism [2004], 3.1) | |
| A reaction: [Hinchliff 1996:124-6] Markosian votes for the Serious version, as being the only true Presentism. I think he is muddling language and reality, predicates and properties. |
| 13996 | Maybe Presentists can refer to the haecceity of a thing, after the thing itself disappears [Markosian] |
| Full Idea: Some Presentists (such as Adams) believe that a haecceity (a property unique to some entity) continues to exist even after its object ceases to exist. A sentence about Socrates still expresses a proposition, about 'Socraticity'. | |
| From: Ned Markosian (A Defense of Presentism [2004], 3.4) | |
| A reaction: [Adams 1986] This is rather puzzling. In what sense could a haecceity 'exist' to be referred to? Existence, but not as we know it, Jim. This smacks of medieval theology. |
| 13997 | Maybe Presentists can paraphrase singular propositions about the past [Markosian] |
| Full Idea: Maybe Presentists can paraphrase singular propositions about the past, into purely general past- and future-tensed sentences. | |
| From: Ned Markosian (A Defense of Presentism [2004], 3.5) | |
| A reaction: I'm not clear why Markosian worries about singular propositions, but is happy with general ones. Surely the latter refer as much as the former to what doesn't exist? Markosian objects that the paraphrase has a different meaning. |
| 13993 | Special Relativity denies the absolute present which Presentism needs [Markosian] |
| Full Idea: The objection to Presentism from Special Relativity is this: 1) Relativity is true, 2) so there is no absolute simultaneity, 3) so there is no absolute presentness, but 4) Presentism entails absolute presentness, so 5) Presentism is false. | |
| From: Ned Markosian (A Defense of Presentism [2004], 3.9) | |
| A reaction: I don't accept this objection. There may be accounts that can give Relativity one present (Idea 12689-90). Maybe Einstein was too instrumentalist in his account. Maybe we can have Presentism with multiple present moments. |
| 13998 | Objects in the past, like Socrates, are more like imaginary objects than like remote spatial objects [Markosian] |
| Full Idea: Maybe putative non-present objects like Socrates have more in common with putative non-actual objects like Santa Claus than they have in common with objects located elsewhere in space, like Alpha Centauri. | |
| From: Ned Markosian (A Defense of Presentism [2004], 3.7) | |
| A reaction: We can see Alpha Centauri, so we need an example beyond some 'event horizon'. He credits Arthur Prior with this line of thought. He seems to me to drift towards a Descriptive Theory of Reference (shock!). Does the nature of reference change with death? |
| 13999 | People are mistaken when they think 'Socrates was a philosopher' says something [Markosian] |
| Full Idea: People sometimes think that 'Socrates was a philosopher' expresses something like a true, singular proposition about Socrates. They're making a mistake, but still, this explains why they think it is true. | |
| From: Ned Markosian (A Defense of Presentism [2004], 3.8) | |
| A reaction: A classic error theory, about our talk of the past. Personally I would say that the sentence really is true, and that needing a tangible object to refer to is a totally bogus requirement. 'I wonder if there are any scissors in the house?' |