11 ideas
| 15327 | Kripke's semantic theory has actually inspired promising axiomatic theories [Kripke, by Horsten] |
| Full Idea: Kripke has a semantic theory of truth which has inspired promising axiomatic theories of truth. | |
| From: report of Saul A. Kripke (Outline of a Theory of Truth [1975]) by Leon Horsten - The Tarskian Turn 01.2 | |
| A reaction: Feferman produced an axiomatic version of Kripke's semantic theory. |
| 15343 | Kripke offers a semantic theory of truth (involving models) [Kripke, by Horsten] |
| Full Idea: One of the most popular semantic theories of truth is Kripke's theory. It describes a class of models which themselves involve a truth predicate (unlike Tarski's semantic theory). | |
| From: report of Saul A. Kripke (Outline of a Theory of Truth [1975]) by Leon Horsten - The Tarskian Turn 02.3 | |
| A reaction: The modern versions explored by Horsten are syntactic versions of this, derived from Feferman's axiomatisation of the Kripke theory. |
| 14966 | The Tarskian move to a metalanguage may not be essential for truth theories [Kripke, by Gupta] |
| Full Idea: Kripke established that, contrary to the prevalent Tarskian dogma, attributions of truth do not always force a move to a metalanguage. | |
| From: report of Saul A. Kripke (Outline of a Theory of Truth [1975], 5.1) by Anil Gupta - Truth | |
| A reaction: [Gupta also cites Martin and Woodruff 1975] |
| 14967 | Certain three-valued languages can contain their own truth predicates [Kripke, by Gupta] |
| Full Idea: Kripke showed via a fixed-point argument that certain three-valued languages can contain their own truth predicates. | |
| From: report of Saul A. Kripke (Outline of a Theory of Truth [1975]) by Anil Gupta - Truth | |
| A reaction: [Gupta also cites Martin and Woodruff 1975] It is an odd paradox that truth can only be included if one adds a truth-value of 'neither true nor false'. The proposed three-valued system is 'strong Kleene logic'. |
| 16328 | Kripke classified fixed points, and illuminated their use for clarifications [Kripke, by Halbach] |
| Full Idea: Kripke's main contribution was …his classification of the different consistent fixed points and the discussion of their use for discriminating between ungrounded sentences, paradoxical sentences, and so on. | |
| From: report of Saul A. Kripke (Outline of a Theory of Truth [1975]) by Volker Halbach - Axiomatic Theories of Truth 15.1 |
| 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) |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |