14 ideas
| 22334 | Analysis must include definitions, search for simples, concept analysis, and Kant's analysis [Glock] |
| Full Idea: Under 'analysis' a minimum would include the Socratic quest for definitions, Descartes' search for simple natures, the empiricists' psychological resolution of complex ideas, and Kant's 'transcendental' analysis of our cognitive capacities. | |
| From: Hans-Johann Glock (What is Analytic Philosophy? [2008], 6.1) | |
| A reaction: This has always struck me, and I find the narrow focus on modern logic a very distorted idea of the larger project. The aim, I think, is to understand by taking things apart, in the spirit of figuring out how a watch works. |
| 16186 | The Barcan Formulas express how to combine modal operators with classical quantifiers [Simchen] |
| Full Idea: The Barcan Formula and its converse gives expression to the most straightforward way of combining modal operators with classical quantification. | |
| From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §1) |
| 16187 | The Barcan Formulas are orthodox, but clash with the attractive Actualist view [Simchen] |
| Full Idea: The Barcan Formulas are a threat to 'actualism' in modal metaphysics, which seems regrettable since the Formulas are validated by standard modal logics, but clash with the plausible and attractive actualist view (that there are no merely possible things). | |
| From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §1) | |
| A reaction: He notes that the Barcan Formulas 'appear to require quantification over possibilia'. So are you prepared to accept the 'possible elephant in your kitchen'? Conceptually yes, but actually no, I would have thought. So possibilia are conceptual. |
| 16190 | BF implies that if W possibly had a child, then something is possibly W's child [Simchen] |
| Full Idea: In accordance with the Barcan Formula we assume that if it is possible that Wittgenstein should have had a child, then something or other is possibly Wittgentein's child. | |
| From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §5) | |
| A reaction: Put like this it sounds unpersuasive. What is the something or other? Someone else's child? A dustbin? A bare particular? Wittgenstein's child? If it was the last one, how could it be Wittgenstein's child while only possibly being that thing? |
| 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) |
| 16188 | Serious Actualism says there are no facts at all about something which doesn't exist [Simchen] |
| Full Idea: Serious Actualism is the view that in possible circumstances in which something does not exist there are no facts about it of any kind, including its very non-existence | |
| From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §1 n4) | |
| A reaction: He suggests that the Converse Barcan Formula implies this view. It sounds comparable to the view of Presentism about time, that no future or past truthmakers exist right now. If a new square table were to exist, it would have four corners. |
| 22332 | German and British idealism is not about individual ideas, but the intelligibility of reality [Glock] |
| Full Idea: Neither German nor British Idealism reduced reality to episodes in the minds of individuals. Instsead, they insisted that reality is intelligible only because it is a manifestation of a divine spirit or rational principle. | |
| From: Hans-Johann Glock (What is Analytic Philosophy? [2008], 5.2) | |
| A reaction: They standardly reject Berkeley. Such Idealism seems either to be the design argument for God's existence, or neo-Stoicism (in its claim that nature is rational). Why not just say that nature seems to be intelligible, and stop there? |
| 22336 | We might say that the family resemblance is just a consequence of meaning-as-use [Glock] |
| Full Idea: Against Wittgenstein's family resemblance view one might evoke his own idea that the meaning of a word is its use, and that diversity of use entails diversity of meaning. | |
| From: Hans-Johann Glock (What is Analytic Philosophy? [2008], 8.2) | |
| A reaction: Wittgenstein might just accept the point. Diversity of concepts reflects diversity of usage. But how do you distinguish 'football is a game' from 'oy, what's your game?'. How does usage distinguish metaphorical from literal (if it does)? |
| 22335 | The variety of uses of 'game' may be that it has several meanings, and isn't a single concept [Glock] |
| Full Idea: The proper conclusion to draw from the fact that we explain 'game' in a variety of different ways is that it is not a univocal term, but has different, albeit related, meanings. | |
| From: Hans-Johann Glock (What is Analytic Philosophy? [2008], 8.2) | |
| A reaction: [He cites Rundle 1990] Potter says Wittgenstein insisted that 'game' is a single concept. 'Game' certainly slides off into metaphor, as in 'are you playing games with me?'. The multivocal view would still meet family resemblance on a narrower range. |