17 ideas
| 22820 | Early Romantics sought a plurality of systems, in a quest for freedom [Hösle] |
| Full Idea: It was an early Romantic idea that there is necessarily a plurality of systems in which individuality is expressed; for a complete system would destroy freedom. | |
| From: Vittorio Hösle (A Short History of German Philosophy [2013], 7) | |
| A reaction: I'm not clear why you are free because you are locked into system that differs from that of other people. True freedom seems to be either no system, or continually remaking one's own system. Why is such freedom valuable? Freedom v truth? |
| 17325 | Truth-maker theory can't cope with non-causal dependence [Liggins] |
| Full Idea: My charge is that truth-maker theory cannot be integrated into an attractive general account of non-causal dependence. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.6) | |
| A reaction: [You'll have to read Liggins to see why] |
| 17318 | Truthmakers for existence is fine; otherwise maybe restrict it to synthetic truths? [Liggins] |
| Full Idea: Many philosophers agree that true existential propositions have a truth-maker, but some go further, claiming that every true proposition has a truth-maker. More cautious theorists specify a class of truths, such as synthetic propositions. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.1) | |
| A reaction: [compressed; Armstrong is the ambitious one, and Rodriguez-Pereyra proposes the synthetic propositions] Presumably synthetic propositions can make negative assertions, which are problematic for truth-makers. |
| 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) |
| 17320 | Either p is true or not-p is true, so something is true, so something exists [Liggins] |
| Full Idea: Either p or not-p. If p, then the proposition 'p' is true. If not p, then the proposition 'not p' is true. Either way, something is true. Thus something exists. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.3 n5) | |
| A reaction: Liggins offers this dodgy argument as an objection to conceptual truths having truth-makers. |
| 17326 | The dependence of {Socrates} on Socrates involves a set and a philosopher, not facts [Liggins] |
| Full Idea: The dependence of {Socrates} on Socrates appears to involve a set and a philosopher, neither of which is a fact. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.6) | |
| A reaction: He points out that defenders of facts as the basis of dependence could find a suitable factual paraphrase here. Socrates is just Socrates, but the singleton has to be understood in a particular way to generate the dependence. |
| 17327 | Non-causal dependence is at present only dimly understood [Liggins] |
| Full Idea: Non-causal dependence is at present only dimly understood. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.8) | |
| A reaction: Not very helpful, you may be thinking, but it is always helpful to know where we have got to in the enquiry. |
| 17322 | Necessities supervene on everything, but don't depend on everything [Liggins] |
| Full Idea: Necessities supervene upon everything, but they do not depend on everything. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.4) | |
| A reaction: I'm not sure if merely existing together counts as sufficiently close to be 'supervenience'. If 2+2 necessitates 4, that hardly seems to 'supervene' on the Eiffel Tower. If so, how close must things be to qualify for supervenience? |
| 17324 | 'Because' can signal an inference rather than an explanation [Liggins] |
| Full Idea: 'Because' can signal an inference rather than an explanation. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.5) | |
| A reaction: Aristotle starts from words like 'why?', but it can be a deceptive approach to explanation. |
| 17321 | Value, constitution and realisation are non-causal dependences that explain [Liggins] |
| Full Idea: 'It is wrong because it produces pain for fun', and 'these constitute a table because they are arranged tablewise', and 'tea is poisonous because it contains arsenic' are clearly non-causal uses of 'because', and neither are they conceptual. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.4) | |
| A reaction: The general line seems to be that any form of determination will underwrite an explanation. He talks later of the 'wrongmaker' and 'poisonmaker' relationships to add to the 'truthmaker'. The table example is the 'object-maker' dependence relation. |
| 17323 | If explanations track dependence, then 'determinative' explanations seem to exist [Liggins] |
| Full Idea: If explanation often tracks dependence, then we have a theoretical reason to expect such explanations to exist. Let us call such explanations 'determinative'. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.4) | |
| A reaction: There seems to be an emerging understanding that this 'determination' relation is central to all of explanation - with causal explanations, for example, being a particular instance of it. I like it. These are real, not conventional, explanations. |
| 22819 | In the 18th century history came to be seen as progressive, rather than cyclical [Hösle] |
| Full Idea: The turning point in the history of the philosophy of history occurs in the eighteenth century, when the ancient cyclical model of Vico is superseded by the idea of progress. | |
| From: Vittorio Hösle (A Short History of German Philosophy [2013], 6) | |
| A reaction: He says that Hegel merely inherited this progressive view, rather than creating it. I'm not sure how widely held the cyclical view was. I don't recognise it in Shakespeare. Science and technology must have suggested progress. |