16 ideas
| 15118 | A successful Aristotelian 'definition' is what sciences produces after an investigation [Koslicki] |
| Full Idea: My current use of the Aristotelian term 'definition' is intended to correspond to what is typically accessible to a scientist only at the end of a successful investigation into the nature of a particular phenomenon. | |
| From: Kathrin Koslicki (Essence, Necessity and Explanation [2012], 13.3.1) | |
| A reaction: It is crucial to understand that Aristotle's definitions could be several hundred pages long. It has nothing to do with dictionary definitions. He proposes 'nominal' and 'real' definitions. |
| 15116 | Essences cause necessary features, and definitions describe those necessary features [Koslicki] |
| Full Idea: Since essences cause the other necessary features of a thing, so definitions, as the linguistic correlates of essences, explain, together with other axioms, the propositions describing those necessary features. | |
| From: Kathrin Koslicki (Essence, Necessity and Explanation [2012], 13.3.1) | |
| A reaction: This is nice and clear. Definitions are NOT essences - they are the linguistic correlates of essences, and mirror those essences. The necessary features are not the only things needing explanation. That picture is too passive. |
| 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) |
| 15110 | An essence and what merely follow from it are distinct [Koslicki] |
| Full Idea: We can distinguish (as Aristotle and Fine do) between what belongs to the essence of an object, and what merely follows from the essence of an object. | |
| From: Kathrin Koslicki (Essence, Necessity and Explanation [2012], 13.1) | |
| A reaction: This can help to clarify the confusions that result from treating necessary properties as if they were essential. |
| 15113 | Individuals are perceived, but demonstration and definition require universals [Koslicki] |
| Full Idea: Individual instances of a kind of phenomenon, in Aristotle's view, can only be perceived through sense-perception; but they are not the proper subject-matter of scientific demonstration and definition. | |
| From: Kathrin Koslicki (Essence, Necessity and Explanation [2012], 13.3.1) | |
| A reaction: A footnote (11) explains that this is because they involve syllogisms, which require universals. I take Aristotle, and anyone sensible, to rest on individual essences, but inevitably turn to generic essences when language becomes involved. |
| 15112 | If an object exists, then its essential properties are necessary [Koslicki] |
| Full Idea: If an object has a certain property essentially, then it follows that the object has the property necessarily (if it exists). | |
| From: Kathrin Koslicki (Essence, Necessity and Explanation [2012], 13.2) | |
| A reaction: She is citing Fine, who says that the converse (necessity implying essence) is false. I agree with that. I also willing to challenge the first bit. I suspect an object can retain identity and lose essence. Coma patient; broken clock; aged athlete. |
| 15111 | In demonstration, the explanatory order must mirror the causal order of the phenomena [Koslicki] |
| Full Idea: Demonstration encompasses more than deductive entailment, in that the explanatory order of priority represented in a successful demonstration must mirror precisely the causal order of priority present in the phenomena in question. | |
| From: Kathrin Koslicki (Essence, Necessity and Explanation [2012], 13.1) | |
| A reaction: She is referring to Aristotle's 'Posterior Analytics'. Put so clearly this sounds like an incredibly useful concept in discussing how we present good modern scientific explanations. Reinstating Aristotle is a major priority for philosophy! |
| 15115 | In a demonstration the middle term explains, by being part of the definition [Koslicki] |
| Full Idea: In a proper demonstrative argument, the middle term must be explanatory of the conclusion, in a very specific sense: the middle term must state what properly belongs to the definition of the kind of phenomenon in question. | |
| From: Kathrin Koslicki (Essence, Necessity and Explanation [2012], 13.3.1) | |
| A reaction: So 'All men are mortal, S is a man, so S is mortal'. The middle term is 'man', which gives a generic explanation for why S is mortal. Explanation as categorisation? I don't think this is the whole story of Aristotelian explanation. |
| 15117 | Greek uses the same word for 'cause' and 'explanation' [Koslicki] |
| Full Idea: The Greek does not disambiguate between 'cause' and 'explanation', since the same terms ('aitia' and 'aition') can be translated in both ways. | |
| From: Kathrin Koslicki (Essence, Necessity and Explanation [2012], 13.3.1 n15) | |
| A reaction: This is essential information if we are to understand Aristotle's Four Causes, which are quite baffling if we take 'causes' in the modern way. The are the Four Modes of Explanation. |
| 15114 | Discovering the Aristotelian essence of thunder will tell us why thunder occurs [Koslicki] |
| Full Idea: Both the question 'what is thunder?', and the question 'why does thunder occur?', for Aristotle, are answered simultaneously, once it has been discovered what the essence of thunder it, i.e. what it is to be thunder. | |
| From: Kathrin Koslicki (Essence, Necessity and Explanation [2012], 13.3.1 n10) | |
| A reaction: I take this idea to be pretty much the whole story about essences. |
| 5467 | Euler said nature is instrinsically passive, and minds cause change [Euler, by Ellis] |
| Full Idea: Euler thought the powers necessary for the maintenance of the changing universe would turn out to be just the passive ones of inertia and impenetrability. There are no active powers, he urged, other than those of God and living beings. | |
| From: report of Leonhard Euler (Letters to a German Princess [1765]) by Brian Ellis - The Philosophy of Nature: new essentialism Ch.4 | |
| A reaction: Very significant, I think, for revealing the religious framework behind early theories of natural laws. If there is nothing external to impose powers and movements on nature, the source must be sought within - hence essentialism. |