20 ideas
| 20728 | Metaphysics is hopeless with its present epistemology; common-sense realism is needed [Colvin] |
| Full Idea: Despair over metaphysics will not change until it has shaken off the incubus of a perverted epistemology, which has left thought in a hopeless tangle - until common-sense critical realism is made the starting point for investigating reality. | |
| From: Stephen S. Colvin (The Common-Sense View of Reality [1902], p.144) | |
| A reaction: It seems to me that this is what has happened to analytic metaphysics since Kripke. Careful discussions about the nature of an object, or a category, or a property, are relying on unquestioned robust realism. Quite right too. |
| 10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
| Full Idea: The logic of ZF Set Theory is classical first-order predicate logic with identity. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.121) | |
| A reaction: This logic seems to be unable to deal with very large cardinals, precisely those that are implied by set theory, so there is some sort of major problem hovering here. Boolos is fairly neutral. |
| 10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
| Full Idea: Maybe the axioms of extensionality and the pair set axiom 'force themselves on us' (Gödel's phrase), but I am not convinced about the axioms of infinity, union, power or replacement. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.130) | |
| A reaction: Boolos is perfectly happy with basic set theory, but rather dubious when very large cardinals come into the picture. |
| 10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
| Full Idea: The naïve view of set theory (that any zero or more things form a set) is natural, but inconsistent: the things that do not belong to themselves are some things that do not form a set. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.127) | |
| A reaction: As clear a summary of Russell's Paradox as you could ever hope for. |
| 10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
| Full Idea: According to the iterative conception, every set is formed at some stage. There is a relation among stages, 'earlier than', which is transitive. A set is formed at a stage if and only if its members are all formed before that stage. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.126) | |
| A reaction: He gives examples of the early stages, and says the conception is supposed to 'justify' Zermelo set theory. It is also supposed to make the axioms 'natural', rather than just being selected for convenience. And it is consistent. |
| 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. |
| 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. |
| 10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
| Full Idea: The existence of infinitely many natural numbers seems to me no more troubling than that of infinitely many computer programs or sentences of English. There is, for example, no longest sentence, since any number of 'very's can be inserted. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: If you really resisted an infinity of natural numbers, presumably you would also resist an actual infinity of 'very's. The fact that it is unclear what could ever stop a process doesn't guarantee that the process is actually endless. |
| 10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
| Full Idea: To the best of my knowledge nothing in mathematics or science requires the existence of very high orders of infinity. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.122) | |
| A reaction: He is referring to particular high orders of infinity implied by set theory. Personally I want to wield Ockham's Razor. Is being implied by set theory a sufficient reason to accept such outrageous entities into our ontology? |
| 10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
| Full Idea: It is no surprise that we should be able to reason mathematically about many of the things we experience, for they are already 'abstract'. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: He has just given a list of exemplary abstract objects (Idea 10489), but I think there is a more interesting idea here - that our experience of actual physical objects is to some extent abstract, as soon as it is conceptualised. |
| 20726 | We can only distinguish self from non-self if there is an inflexible external reality [Colvin] |
| Full Idea: Were there no inflexible reality outside of the individual, opposing and limiting it, knowledge of the self and the non-self would never develop. | |
| From: Stephen S. Colvin (The Common-Sense View of Reality [1902], p.140) | |
| A reaction: Presumably opponents would have to say that such 'knowledge' is an illusion. This is in no way a conclusive argument, but I approach the problem of realism in quest of the best explanation, and this idea is important evidence. |
| 20727 | Common-sense realism rests on our interests and practical life [Colvin] |
| Full Idea: It is the determination of the external world from the practical standpoint, from the standpoint of interest, that may be defined as the common-sense view of reality. | |
| From: Stephen S. Colvin (The Common-Sense View of Reality [1902], p.141) | |
| A reaction: Probably more appropriately named the 'pragmatic' view of reality. Relying on what is 'practical' seems to offer some objectivity, but relying on 'interest' rather less so. Can I be an anti-realist when life goes badly, and a realist when it goes well? |
| 20729 | Arguments that objects are unknowable or non-existent assume the knower's existence [Colvin] |
| Full Idea: Arguments for the absolute unknowability or non-existence of an external object only works by assuming that another external object, an individual, is known completely in so far as that individual expresses a judgement about an external object. | |
| From: Stephen S. Colvin (The Common-Sense View of Reality [1902], p.145) | |
| A reaction: Anti-realism is a decay that eats into everything. You can't doubt all the externals without doubting all the internals as well. |
| 20730 | If objects are doubted because their appearances change, that presupposes one object [Colvin] |
| Full Idea: If objects are doubted because the same object appears differently at different times and circumstances, in order that this judgement shall have weight it must be assumed that the object under question is the same in its different presentations. | |
| From: Stephen S. Colvin (The Common-Sense View of Reality [1902], p.145) | |
| A reaction: [compressed] Scepticism could eat into the underlying object as well. Is the underlying object a 'substrate'? If so, what's that? Is the object just a bundle of a properties? If so, there is no underlying object. |
| 20731 | The idea that everything is relations is contradictory; relations are part of the concept of things [Colvin] |
| Full Idea: The doctrine [that all we can know is the relations between subject and object] is in its essence self-contradictory, since our very idea of thing implies that it is something in relation either actually or potentially. | |
| From: Stephen S. Colvin (The Common-Sense View of Reality [1902], p.150) | |
| A reaction: Ladyman and Ross try to defend an account of reality based entirely on relations. I'm with Colvin on this one. All accounts of reality based either on pure relations or pure functions have a huge hole in their theory. |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| Full Idea: It's a kind of lunacy to think that sound scientific philosophy demands that we think that we see ink-tracks but not words, i.e. word-types. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.128) | |
| A reaction: This seems to link him with Armstrong's mockery of 'ostrich nominalism'. There seems to be some ambiguity with the word 'see' in this disagreement. When we look at very ancient scratches on stones, why don't we always 'see' if it is words? |
| 10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
| Full Idea: I am rather a fan of abstract objects, and confident of their existence. Smaller numbers, sets and functions don't offend my sense of reality. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.128) | |
| A reaction: The great Boolos is rather hard to disagree with, but I disagree. Logicians love abstract objects, indeed they would almost be out of a job without them. It seems to me they smuggle them into our ontology by redefining either 'object' or 'exists'. |
| 10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
| Full Idea: We twentieth century city dwellers deal with abstract objects all the time, such as bank balances, radio programs, software, newspaper articles, poems, mistakes, triangles. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: I find this claim to be totally question-begging, and typical of a logician. The word 'object' gets horribly stretched in these discussions. We can create concepts which have all the logical properties of objects. Maybe they just 'subsist'? |
| 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). |