20 ideas
| 10017 | Truth in a model is more tractable than the general notion of truth [Hodes] |
| Full Idea: Truth in a model is interesting because it provides a transparent and mathematically tractable model - in the 'ordinary' rather than formal sense of the term 'model' - of the less tractable notion of truth. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: This is an important warning to those who wish to build their entire account of truth on Tarski's rigorously formal account of the term. Personally I think we should start by deciding whether 'true' can refer to the mental state of a dog. I say it can. |
| 10018 | Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes] |
| Full Idea: There is an enormous difference between the truth of sentences in the interpreted language of set theory and truth in some model for the disinterpreted skeleton of that language. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.132) | |
| A reaction: This is a warning to me, because I thought truth and semantics only entered theories at the stage of 'interpretation'. I must go back and get the hang of 'skeletal' truth, which sounds rather charming. [He refers to set theory, not to logic.] |
| 10015 | Higher-order logic may be unintelligible, but it isn't set theory [Hodes] |
| Full Idea: Brand higher-order logic as unintelligible if you will, but don't conflate it with set theory. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: [he gives Boolos 1975 as a further reference] This is simply a corrective, because the conflation of second-order logic with set theory is an idea floating around in the literature. |
| 10011 | Identity is a level one relation with a second-order definition [Hodes] |
| Full Idea: Identity should he considered a logical notion only because it is the tip of a second-order iceberg - a level 1 relation with a pure second-order definition. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) |
| 10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes] |
| Full Idea: A model is created when a language is 'interpreted', by assigning non-logical terms to objects in a set, according to a 'true-in' relation, but we must bear in mind that this 'interpretation' does not associate anything like Fregean senses with terms. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: This seems like a key point (also made by Hofweber) that formal accounts of numbers, as required by logic, will not give an adequate account of the semantics of number-terms in natural languages. |
| 10027 | Mathematics is higher-order modal logic [Hodes] |
| Full Idea: I take the view that (agreeing with Aristotle) mathematics only requires the notion of a potential infinity, ...and that mathematics is higher-order modal logic. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) | |
| A reaction: Modern 'modal' accounts of mathematics I take to be heirs of 'if-thenism', which seems to have been Russell's development of Frege's original logicism. I'm beginning to think it is right. But what is the subject-matter of arithmetic? |
| 10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
| Full Idea: Arithmetic should be able to face boldly the dreadful chance that in the actual world there are only finitely many objects. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.148) | |
| A reaction: This seems to be a basic requirement for any account of arithmetic, but it was famously a difficulty for early logicism, evaded by making the existence of an infinity of objects into an axiom of the system. |
| 10021 | It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes] |
| Full Idea: The mathematical object-theorist says a number is an object that represents a cardinality quantifier, with the representation relation as the entire essence of the nature of such objects as cardinal numbers like 4. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) | |
| A reaction: [compressed] This a classic case of a theory beginning to look dubious once you spell it our precisely. The obvious thought is to make do with the numerical quantifiers, and dispense with the objects. Do other quantifiers need objects to support them? |
| 10022 | Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes] |
| Full Idea: The dogmatic Frege is more right than wrong in denying that numerical terms can stand for numerical quantifiers, for there cannot be a language in which object-quantifiers and objects are simultaneously viewed as level zero. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.142) | |
| A reaction: Subtle. We see why Frege goes on to say that numbers are level zero (i.e. they are objects). We are free, it seems, to rewrite sentences containing number terms to suit whatever logical form appeals. Numbers are just quantifiers? |
| 10023 | Talk of mirror images is 'encoded fictions' about real facts [Hodes] |
| Full Idea: Talk about mirror images is a sort of fictional discourse. Statements 'about' such fictions are not made true or false by our whims; rather they 'encode' facts about the things reflected in mirrors. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.146) | |
| A reaction: Hodes's proposal for how we should view abstract objects (c.f. Frege and Dummett on 'the equator'). The facts involved are concrete, but Hodes is offering 'encoding fictionalism' as a linguistic account of such abstractions. He applies it to numbers. |
| 9264 | Persons are distinguished by a capacity for second-order desires [Frankfurt] |
| Full Idea: The essential difference between persons and other creatures is in the structure of the will, with their peculiar characteristic of being able to form 'second-order desires'. | |
| From: Harry G. Frankfurt (Freedom of the Will and concept of a person [1971], Intro) | |
| A reaction: There are problems with this - notably that all strategies of this kind just shift the problem up to the next order, without solving it - but this still strikes me as a very promising line of thinking when trying to understand ourselves. See Idea 9266. |
| 9266 | A person essentially has second-order volitions, and not just second-order desires [Frankfurt] |
| Full Idea: It is having second-order volitions, and not having second-order desires generally, that I regard as essential to being a person. | |
| From: Harry G. Frankfurt (Freedom of the Will and concept of a person [1971], §II) | |
| A reaction: Watson criticises Frankfurt for just pushing the problem up to the the next level, but Frankfurt is not offering to explain the will. He merely notes that this structure produces the sort of behaviour which is characteristic of persons, and he is right. |
| 9267 | Free will is the capacity to choose what sort of will you have [Frankfurt] |
| Full Idea: The statement that a person enjoys freedom of the will means that he is free to want what he wants to want. More precisely, he is free to will what he wants to will, or to have the will he wants. | |
| From: Harry G. Frankfurt (Freedom of the Will and concept of a person [1971], §III) | |
| A reaction: A good proposal. It covers kleptomaniacs and drug addicts quite well. Thieves have second-order desires (to steal) of which kleptomaniacs are incapable. There is actually no such thing as free will, but this sort of thing will do. |
| 9265 | The will is the effective desire which actually leads to an action [Frankfurt] |
| Full Idea: A person's will is the effective desire which moves (or will or would move) a person all the way to action. The will is not coextensive with what an agent intends to do, since he may do something else instead. | |
| From: Harry G. Frankfurt (Freedom of the Will and concept of a person [1971], §I) | |
| A reaction: Essentially Hobbes's view, but with an arbitrary distinction added. If the desire is only definitely a 'will' if it really does lead to action, then it only becomes the will after the action starts. The error is thinking that will is all-or-nothing. |
| 20015 | Freedom of action needs the agent to identify with their reason for acting [Frankfurt, by Wilson/Schpall] |
| Full Idea: Frankfurt says that basic issues concerning freedom of action presuppose and give weight to a concept of 'acting on a desire with which the agent identifies'. | |
| From: report of Harry G. Frankfurt (Freedom of the Will and concept of a person [1971]) by Wilson,G/Schpall,S - Action 1 | |
| A reaction: [the cite Frankfurt 1988 and 1999] I'm not sure how that works when performing a grim duty, but it sounds quite plausible. |
| 9270 | A 'wanton' is not a person, because they lack second-order volitions [Frankfurt] |
| Full Idea: I use the term 'wanton' to refer to agents who have first-order desires but who are not persons because, whether or not they have desires of the second-order, they have no second-order volitions. | |
| From: Harry G. Frankfurt (Freedom of the Will and concept of a person [1971], §II) | |
| A reaction: He seems to be describing someone who behaves like an animal, performing actions without ever stopping to think about them. Presumably some persons occasionally become wantons, if, for example, they have an anger problem. |
| 9269 | A person may be morally responsible without free will [Frankfurt] |
| Full Idea: It is not true that a person is morally responsible for what he has done only if his will was free when he did it. He may be morally responsible for having done it even though his will was not free at all. | |
| From: Harry G. Frankfurt (Freedom of the Will and concept of a person [1971], §IV) | |
| A reaction: Frankfurt seems to be one of the first to assert this break with the traditional view. Good for him. I take moral responsibility to hinge on an action being caused by a person, but not with a mystical view of what a person is. |
| 17371 | Some kinds are very explanatory, but others less so, and some not at all [Devitt] |
| Full Idea: Explanatory significance, hence naturalness, comes in degrees: positing some kinds may be very explanatory, positing others, only a little bit explanatory, positing others still, not explanatory at all. | |
| From: Michael Devitt (Natural Kinds and Biological Realism [2009], 4) | |
| A reaction: He mentions 'cousin' as a natural kind that is not very explanatory of anything. It interests us as humans, but not at all in other animals, it seems. ...Nice thought, though, that two squirrels might be cousins... |
| 17372 | The higher categories are not natural kinds, so the Linnaean hierarchy should be given up [Devitt] |
| Full Idea: The signs are that the higher categories are not natural kinds and so the Linnaean hierarchy must be abandoned. ...This is not abandoning a hierarchy altogether, it is not abandoning a tree of life. | |
| From: Michael Devitt (Natural Kinds and Biological Realism [2009], 6) | |
| A reaction: Devitt's underlying point is that the higher and more general kinds do not have an essence (a specific nature), which is the qualification to be a natural kind. They explain nothing. Essence is the hallmark of natural kinds. Hmmm. |
| 17373 | Species pluralism says there are several good accounts of what a species is [Devitt] |
| Full Idea: Species pluralism is the view that there are several equally good accounts of what it is to be a species. | |
| From: Michael Devitt (Natural Kinds and Biological Realism [2009], 7) | |
| A reaction: Devitt votes for it, and cites Dupré, among many other. Given the existence of rival accounts, all making good points, it is hard to resist this view. |