14 ideas
10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection. | |
From: Leon Horsten (Philosophy of Mathematics [2007], §2.4) |
10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'. | |
From: Leon Horsten (Philosophy of Mathematics [2007], §5.2) |
10885 | Computer proofs don't provide explanations [Horsten] |
Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds. | |
From: Leon Horsten (Philosophy of Mathematics [2007], §5.3) |
10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept. | |
From: Leon Horsten (Philosophy of Mathematics [2007], §2.3) |
15797 | All structures are dispositional, objects are dispositions sets, and events manifest dispositions [Fetzer] |
Full Idea: I propose a dispositional ontology for the physical world, according to which a) every structural property is a dispositional one, b) a physical object is an ordered set of dispositions, and c) every event manifests a dispositional property of the world. | |
From: J.H. Fetzer (A World of Dispositions [1977], Intro) | |
A reaction: Mumford says this is consistent with ontology as a way of describing the world, rather than being facts about the world. I like Fetzer's sketch, which sounds to have a lot in common with 'process philosophy'. |
15800 | All events and objects are dispositional, and hence all structural properties are dispositional [Fetzer] |
Full Idea: Every atomic event in the world's history is a manifestation of some dispositional property of the world and every physical object is an instantiation of some set of dispositions; hence, every structural property is dispositional in kind. | |
From: J.H. Fetzer (A World of Dispositions [1977], 5) | |
A reaction: I quite like this drastic view, but there remains the intuition that there must always be something which has the disposition. That may be because I have not yet digested the lessons of modern physics. |
14221 | Serious essentialism says everything has essences, they're not things, and they ground necessities [Shalkowski] |
Full Idea: Serious essentialism is the position that a) everything has an essence, b) essences are not themselves things, and c) essences are the ground for metaphysical necessity and possibility. | |
From: Scott Shalkowski (Essence and Being [2008], 'Intro') | |
A reaction: If a house is being built, it might acquire an identity first, and only get an essence later. Essences can be physical, but if you extract them you destroy thing thing of which they were the essence. Does all of this apply to abstract 'things'. |
14222 | Essences are what it is to be that (kind of) thing - in fact, they are the thing's identity [Shalkowski] |
Full Idea: The route into essentialism is, first, a recognition that the essence of a thing is "what it is to be" that (kind of) thing; the essence of a thing is just its identity. | |
From: Scott Shalkowski (Essence and Being [2008], 'Essent') | |
A reaction: The first half sounds right, and very Aristotelian. The second half is dramatically different, controversial, and far less plausible. Slipping in 'kind of' is also highly dubious. This remark shows, I think, some confusion about essences. |
14226 | We distinguish objects by their attributes, not by their essences [Shalkowski] |
Full Idea: In ordinary contexts, we distinguish objects not by their essences but by their attributes. | |
From: Scott Shalkowski (Essence and Being [2008], 'Ess and Know') | |
A reaction: Hence we have a gap between what bestows identity intrinsically, and how we bestow identity conventionally. If you could grasp the essence of something, you might predict a new attribute, as yet unobserved. |
14225 | Critics say that essences are too mysterious to be known [Shalkowski] |
Full Idea: According to critics, the thorniest problem for essentialism is the question of our knowledge of essence. It is usually at this point that terms of abuse such as 'dark', 'mysterious', and 'occult' are wheeled out. | |
From: Scott Shalkowski (Essence and Being [2008], 'Ess and Know') | |
A reaction: I'm inclined to think that the existence of essences can be fairly conclusively inferred, but that attributing a precise identity to them is the biggest challenge. |
14223 | De dicto necessity has linguistic entities as their source, so it is a type of de re necessity [Shalkowski] |
Full Idea: De dicto necessity is a species of de re necessity. Anyone prone to countenance de dicto necessity must recognise mental and/or linguistic entities, thus counting each of them as a res to which necessity attaches. | |
From: Scott Shalkowski (Essence and Being [2008], 'Essent') | |
A reaction: This seems to rest on the Kit Fine thought that analytic necessities seem to derive from the essences of words such as 'bachelor'. I like this idea: all necessity is de re, but some of the 'things' are words. |
14224 | Equilateral and equiangular aren't the same, as we have to prove their connection [Shalkowski] |
Full Idea: That 'all and only equilateral triangles are equiangular' required proof, and not for mere curiosity, is grounds for thinking that being an equilateral triangle is not the same property as being an equiangular triangle. | |
From: Scott Shalkowski (Essence and Being [2008], 'Serious') | |
A reaction: If you start with equiangularity, does equilateralness then require proof? This famous example is of two concepts which seem to be coextensional, but seem to have a different intension. Does a dependence relation drive a wedge between them? |
15798 | Kinds are arrangements of dispositions [Fetzer] |
Full Idea: Kinds of things are specific arrangements of dispositions. | |
From: J.H. Fetzer (A World of Dispositions [1977], 2) | |
A reaction: A 'disposition' doesn't seem quite the right word for what is basic to the physical world, though Harré and Madden make a good case for the 'fields' of physic being understood in that way. I prefer 'power', though that doesn't solve anything. |
15799 | Lawlike sentences are general attributions of disposition to all members of some class [Fetzer] |
Full Idea: Lawlike sentences are conceived as logically general dispositional statements attributing permanent dispositional properties to every member of a reference class. ...Their basic form is that of subjunctive generalizations. | |
From: J.H. Fetzer (A World of Dispositions [1977], 3) | |
A reaction: I much prefer talk of 'lawlike sentences' to talk of 'laws'. At least they imply that the true generalisations about nature are fairly fine-grained. Why not talk of 'generalisations' instead of 'laws'? Fetzer wants dispositions to explain everything. |