6 ideas
| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
| Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10) | |
| A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity. |
| 10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
| Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08) | |
| A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning. |
| 10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
| Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01) |
| 10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
| Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02) |
| 13120 | Chisholm divides things into contingent and necessary, and then individuals, states and non-states [Chisholm, by Westerhoff] |
| Full Idea: Chisholm's Ontological Categories: ENTIA - {Contingent - [Individual - (Boundaries)(Substances)] [States - (Events)]} {Necessary - [States] [Non-States - (Attributes)(Substance)]} | |
| From: report of Roderick Chisholm (A Realistic Theory of Categories [1996], p.3) by Jan Westerhoff - Ontological Categories §01 | |
| A reaction: [I am attempting a textual representation of a tree diagram! The bracket-styles indicate the levels.] |
| 8886 | Being a true justified belief is not a sufficient condition for knowledge [Gettier] |
| Full Idea: The claim that someone knows a proposition if it is true, it is believed, and the person is justified in their belief is false, in that the conditions do not state a sufficient condition for the claim. | |
| From: Edmund L. Gettier (Is Justified True Belief Knowledge? [1963], p.145) | |
| A reaction: This is the beginning of the famous Gettier Problem, which has motivated most epistemology for the last forty years. Gettier implies that justification is necessary, even if it is not sufficient. He gives two counterexamples. |