11 ideas
| 10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
| Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.4) |
| 10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
| Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.2) |
| 10885 | Computer proofs don't provide explanations [Horsten] |
| Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.3) |
| 10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
| Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.3) |
| 16129 | Evans argues (falsely!) that a contradiction follows from treating objects as vague [Evans, by Lowe] |
| Full Idea: Evans tries to derive a contradiction from the supposition that a given identity statement is of indeterminate truth-value. (As it happens, I consider that this argument is flawed) | |
| From: report of Gareth Evans (Can there be Vague Objects? [1978]) by E.J. Lowe - The Possibility of Metaphysics 1.3 | |
| A reaction: A priori, I wouldn't expect to be able to settle the question of whether there are any vague objects simply by following some logical derivation. Empirical examination, and conceptual analysis (or stipulation) have to be involved. |
| 16459 | Is it coherent that reality is vague, identities can be vague, and objects can have fuzzy boundaries? [Evans] |
| Full Idea: Maybe the world is vague, and vagueness is a necessary feature of any true description of it. Also identities may lack a determinate truth value because of their vagueness. Hence it is a fact that some objects have fuzzy boundaries. But is this coherent? | |
| From: Gareth Evans (Can there be Vague Objects? [1978]) | |
| A reaction: [compressed] Lewis quotes this introduction to the famous short paper, to show that Evans wasn't proposing a poor argument, but offering a reductio of the view that vagueness is 'ontic', or a feature of the world. |
| 16460 | Evans assumes there can be vague identity statements, and that his proof cannot be right [Evans, by Lewis] |
| Full Idea: The correct interpretation is that Evans trusts his reader (unwisely) to take for granted that there are vague identity statements, that a proof of the contrary cannot be right, and that the vagueness-in-describing view affords a diagnosis of the fallacy. | |
| From: report of Gareth Evans (Can there be Vague Objects? [1978]) by David Lewis - Vague Identity: Evans misunderstood p.319 | |
| A reaction: [Lowe 199:11 is a culprit!] Lewis put this interpretation to Evans, who replied 'Yes, yes, yes!'. |
| 16457 | There clearly are vague identity statements, and Evans's argument has a false conclusion [Evans, by Lewis] |
| Full Idea: One problem with Evans's argument that there are no such thing as vague identity statements is that its conclusion is plainly false. Example: 'Princeton = Princeton Borough', where it is unsettled what region 'Princeton' denotes. | |
| From: report of Gareth Evans (Can there be Vague Objects? [1978]) by David Lewis - Vague Identity: Evans misunderstood p.319 | |
| A reaction: Lewis endorses the view that vagueness is semantic. I certainly don't endorse Evans's argument, which hinges on a weird example of a property, as applied to Leibniz's Law. |
| 14484 | If a=b is indeterminate, then a=/=b, and so there cannot be indeterminate identity [Evans, by Thomasson] |
| Full Idea: We cannot accept the existence of vague objects, according to Evans's argument that there cannot be indeterminacy of identity. ...From the assumption that it is indeterminate whether a = b, we conclude, determinately, that it's not the case that a = b. | |
| From: report of Gareth Evans (Can there be Vague Objects? [1978]) by Amie L. Thomasson - Ordinary Objects 05.6 | |
| A reaction: I think we should keep intrinsic identity separate from identity between entities. A cloud can be clearly identified, while being a bit fuzzy. It is only when you ask whether we saw the same cloud that Evans's argument seems relevant. |
| 16224 | There can't be vague identity; a and b must differ, since a, unlike b, is only vaguely the same as b [Evans, by PG] |
| Full Idea: Two things can't be vaguely identical, because then a would have an indeterminacy which b lacks (namely, being perfectly identical to b), so by Leibniz's Law they can't be identical. | |
| From: report of Gareth Evans (Can there be Vague Objects? [1978], 4.7) by PG - Db (ideas) | |
| A reaction: [my summary of Katherine Hawley's summary (2001:118) of Evans] Hawley considers the argument to be valid. I have grave doubts about whether b's identity with b is the sort of property needed for an application of Liebniz's Law. |
| 11052 | Psychological logic can't distinguish justification from causes of a belief [Frege] |
| Full Idea: With the psychological conception of logic we lose the distinction between the grounds that justify a conviction and the causes that actually produce it. | |
| From: Gottlob Frege (Logic [1897] [1897]) | |
| A reaction: Thus Frege kicked the causal theory of justification well into touch long before it had even been properly formulated. That is not to say that there is no psychological aspect to logic, because there is. |