9 ideas
| 17833 | The first-order ZF axiomatisation is highly non-categorical [Hallett,M] |
| Full Idea: The first-order Sermelo-Fraenkel axiomatisation is highly non-categorical. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1213) |
| 17834 | Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M] |
| Full Idea: The non-categoricity of the axioms which Zermelo demonstrates reveals an incompleteness of a sort, ....for this seems to show that there will always be a set (indeed, an unending sequence) that the basic axioms are incapable of revealing to be sets. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1215) | |
| A reaction: Hallett says the incompleteness concerning Zermelo was the (transfinitely) indefinite iterability of the power set operation (which is what drives the 'iterative conception' of sets). |
| 17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M] |
| Full Idea: Unlike earlier writers (such as Fraenkel), Zermelo clearly allows that there might be ur-elements (that is, objects other than the empty set, which have no members). Indeed he sees in this the possibility of widespread application of set-theory. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217) |
| 17836 | The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M] |
| Full Idea: In 1938, Gödel showed that ZF plus the General Continuum Hypothesis is consistent if ZF is. Cohen showed that ZF and not-GCH is also consistent if ZF is, which finally shows that neither GCH nor ¬GCH can be proved from ZF itself. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217) |
| 6451 | Visual sense data are an inner picture show which represents the world [Blackburn] |
| Full Idea: In the case of vision, sense data are a kind of inner picture show which itself only indirectly represents aspects of the external world. | |
| From: Simon Blackburn (Oxford Dictionary of Philosophy [1994], p.347) | |
| A reaction: I'm unsure whether this is correct. Russell says the 'roughness' of the table is the sense datum. If it is even a possibility that there are unsensed sense-data, then they cannot be an aspect of the mind, as Blackburn is suggesting they are. |
| 2866 | A true belief might be based on a generally reliable process that failed on this occasion [Blackburn] |
| Full Idea: Reliabilism is open to the counterexample that a belief may be the result of some generally reliable process (a pressure gauge) which was in fact malfunctioning on this occasion, when we would be reluctant to attribute knowledge to the subject. | |
| From: Simon Blackburn (Oxford Dictionary of Philosophy [1994], p.327) | |
| A reaction: Russell's stopped clock that tells the right time twice a day. A good objection. Coming from a reliable source is very good criterion for good justification, but it needs critical assessment. |
| 14080 | Are causal descriptions part of the causal theory of reference, or are they just metasemantic? [Kaplan, by Schaffer,J] |
| Full Idea: Kaplan notes that the causal theory of reference can be understood in two quite different ways, as part of the semantics (involving descriptions of causal processes), or as metasemantics, explaining why a term has the referent it does. | |
| From: report of David Kaplan (Dthat [1970]) by Jonathan Schaffer - Deflationary Metaontology of Thomasson 1 | |
| A reaction: [Kaplan 'Afterthought' 1989] The theory tends to be labelled as 'direct' rather than as 'causal' these days, but causal chains are still at the heart of the story (even if more diffused socially). Nice question. Kaplan takes the meta- version as orthodox. |
| 2864 | The main objection to intuitionism in ethics is that intuition is a disguise for prejudice or emotion [Blackburn] |
| Full Idea: Critics say that intuitionism in ethics explains nothing, but may merely function as a disguise for prejudice or passion. | |
| From: Simon Blackburn (Oxford Dictionary of Philosophy [1994], p.198) | |
| A reaction: If someone claims to have an important moral intuition about something, you should carefully assess the person who has the intuition. I would trust some people a lot. |
| 2865 | Critics of prescriptivism observe that it is consistent to accept an ethical verdict but refuse to be bound by it [Blackburn] |
| Full Idea: Critics of prescriptivism have noted the problem that whilst accepting a command seems tantamount to setting oneself to obey it, accepting an ethical verdict is, unfortunately, consistent with refusing to be bound by it. | |
| From: Simon Blackburn (Oxford Dictionary of Philosophy [1994], p.300) | |
| A reaction: We nearly all of us accept that our behaviour should be better than it actually is, so we accept the oughts but fail to act. Actually 'refusing', though, sounds a bit contradictory. |