13 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. |
| 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) |
| 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) |
| 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. |
| 12697 | Indivisibles are not parts, but the extrema of parts [Leibniz] |
| Full Idea: Indivisibles are not parts, but the extrema of parts. | |
| From: Gottfried Leibniz (Pacidius Philalethi dialogue [1676], A6.3.565-6), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 1 | |
| A reaction: This is incipient monadology, that the bottom level of division ceases to be parts of a thing, and arrives at a different order of entity, to explain the parts of things. Leibniz denies that this subdivision comes down to points. |