26 ideas
| 22496 | Wisdom only implies the knowledge achievable in any normal lifetime [Foot] |
| Full Idea: Wisdom implies no more knowledge and understanding than anyone of normal capacity can and should acquire in the course of an ordinary life. | |
| From: Philippa Foot (Natural Goodness [2001], 5) | |
| A reaction: Have philosophers stopped talking about wisdom precisely because you now need three university degrees to be considered even remotely good at phillosophy? Hence wisdom is an inferior attainment, because Foot is right. |
| 10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
| Full Idea: Second-order logic raises doubts because of its ontological commitment to the set-theoretic hierarchy, and the allegedly problematic epistemic status of the second-order consequence relation. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §1) | |
| A reaction: The 'epistemic' problem is whether you can know the truths, given that the logic is incomplete, and so they cannot all be proved. Rossberg defends second-order logic against the second problem. A third problem is that it may be mathematics. |
| 10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
| Full Idea: Henkin semantics (for second-order logic) specifies a second domain of predicates and relations for the upper case constants and variables. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This second domain is restricted to predicates and relations which are actually instantiated in the model. Second-order logic is complete with this semantics. Cf. Idea 10756. |
| 10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
| Full Idea: In addition to standard and Henkin semantics for second-order logic, one might also employ substitutional or game-theoretical or topological semantics, or Boolos's plural interpretation, or even a semantics inspired by Lesniewski. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This is helpful in seeing the full picture of what is going on in these logical systems. |
| 10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
| Full Idea: Logical consequence is intuitively taken to be a semantic notion, ...and it is therefore the formal semantics, i.e. the model theory, that captures logical consequence. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: If you come at the issue from normal speech, this seems right, but if you start thinking about the necessity of logical consequence, that formal rules and proof-theory seem to be the foundation. |
| 10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
| Full Idea: Deductive consequence, written Γ|-S, is loosely read as 'the sentence S can be deduced from the sentences Γ', and semantic consequence Γ|=S says 'all models that make Γ true make S true as well'. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: We might read |= as 'true in the same model as'. What is the relation, though, between the LHS and the RHS? They seem to be mutually related to some model, but not directly to one another. |
| 10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
| Full Idea: A proof-theorist could insist that the logical form of a sentence is exhibited by the logical constants that it contains. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: You have to first get to the formal logical constants, rather than the natural language ones. E.g. what is the truth table for 'but'? There is also the matter of the quantifiers and the domain, and distinguishing real objects and predicates from bogus. |
| 10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
| Full Idea: A standard model is a set of objects called the 'domain', and an interpretation function, assigning objects in the domain to names, subsets to predicate letters, subsets of the Cartesian product of the domain with itself to binary relation symbols etc. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: The model actually specifies which objects have which predicates, and which objects are in which relations. Tarski's account of truth in terms of 'satisfaction' seems to be just a description of those pre-decided facts. |
| 10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
| Full Idea: A mathematical theory is 'categorical' if, and only if, all of its models are isomorphic. Such a theory then essentially has just one model, the standard one. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: So the term 'categorical' is gradually replacing the much-used phrase 'up to isomorphism'. |
| 10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
| Full Idea: All that should be required to get a semantics relative to which a given deductive system is complete is a sufficiently cunning model-theorist. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §5) |
| 10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
| Full Idea: No deductive system is semantically incomplete in and of itself; rather a deductive system is incomplete with respect to a specified formal semantics. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This important point indicates that a system might be complete with one semantics and incomplete with another. E.g. second-order logic can be made complete by employing a 'Henkin semantics'. |
| 19508 | Contextualism needs a semantics for knowledge sentences that are partly indexical [Schiffer,S] |
| Full Idea: Contextualist semantics must capture the 'indexical' nature of knowledge claims, the fact that different utterances of a knowledge sentence with no apparent indexical terms can express different propositions. | |
| From: Stephen Schiffer (Contextualist Solutions to Scepticism [1996], p.325), quoted by Keith DeRose - The Case for Contextualism 1.5 | |
| A reaction: Schiffer tries to show that this is too difficult, and DeRose defends contextualism against the charge. |
| 19509 | The indexical aspect of contextual knowledge might be hidden, or it might be in what 'know' means [Schiffer,S] |
| Full Idea: One might have a 'hidden-indexical' theory of knowledge sentences: they contain constituents that are not the semantic values of any terms; ...or 'to know' itself might be indexical, as in 'I know[easy] I have hands' or 'I know[tough] I have hands'. | |
| From: Stephen Schiffer (Contextualist Solutions to Scepticism [1996], p.326-7), quoted by Keith DeRose - The Case for Contextualism 1.5 | |
| A reaction: [very compressed] Given the choice, I would have thought it was in 'know', since to say 'either you know p or you don't' sounds silly to me. |
| 23694 | All criterions of practical rationality derive from goodness of will [Foot] |
| Full Idea: I want to say, baldly, that there is no criterion for practical rationality that is not derived from that of goodness of will. | |
| From: Philippa Foot (Natural Goodness [2001], 1) | |
| A reaction: Where does that put the successful and clever criminal? Presumably they are broadly irrational, but narrowly rational - but that is not very clear distinction. She says Kant's concept of the good will is too pure, and unrelated to human good. |
| 23686 | Moral reason is not just neutral, because morality is part of the standard of rationality [Foot, by Hacker-Wright] |
| Full Idea: In her late period she again reverses her thoughts on moral rationalism; …rather than a neutral rationality which fulfils desires, she argues that morality ought to be thought of as part of the standard of rationality itself. | |
| From: report of Philippa Foot (Natural Goodness [2001]) by John Hacker-Wright - Philippa Foot's Moral Thought Intro | |
| A reaction: This comes much closer to the Greek and Aristotelian concept of logos. They saw morality as inseparable from our judgements about how the world is. All 'sensible' thinking will involve what is good for humanity. |
| 23693 | Practical rationality must weigh both what is morally and what is non-morally required [Foot] |
| Full Idea: Different considerations are on a par, in that judgement about what is required by practical rationality must take account of their interaction: of the weight of the ones we call non-moral as well as those we call moral. | |
| From: Philippa Foot (Natural Goodness [2001], 1) | |
| A reaction: Her final settled view of rationalism in morality, it seems. The point is that moral considerations are not paramount, because she sees possible justifications for ignoring moral rules (like 'don't lie') in certain practical situations. |
| 23687 | Moral virtues arise from human nature, as part of what makes us good human beings [Foot, by Hacker-Wright] |
| Full Idea: In her later work she offers a view of the relationship of morality to human nature, arguing that the moral virtues are part of what makes us good as human beings. | |
| From: report of Philippa Foot (Natural Goodness [2001]) by John Hacker-Wright - Philippa Foot's Moral Thought Intro | |
| A reaction: In this phase she talks explicitly of the Aristotelian idea that successful function is the grounding of what is good for any living being, including humans. |
| 22493 | Sterility is a human defect, but the choice to be childless is not [Foot] |
| Full Idea: Lack of capacity to reproduce is a defect in a human being. But choice of childlessness and even celibacy is not thereby shown to be defective choice, because human good is not the same as plant or animal good. | |
| From: Philippa Foot (Natural Goodness [2001], 3) | |
| A reaction: Is failure to reproduce a defect in an animal? If goodness and virtue derive from function, it is hard to see how deliberate childlessness could be a human good, even if it is not a defect. Choosing to terminate a hereditary defect seems good. |
| 22492 | Virtues are as necessary to humans as stings are to bees [Foot] |
| Full Idea: Virtues play a necessary part in the life of human beings as do stings in the life of a bee. | |
| From: Philippa Foot (Natural Goodness [2001], 2) | |
| A reaction: This presumably rests on the Aristotelian idea that humans are essentially social (as opposed to solitary humans who choose to be social, perhaps in a contractual way, as Plato implies). |
| 22491 | Moral evaluations are not separate from facts, but concern particular facts about functioning [Foot] |
| Full Idea: A moral evaluation does not stand over against the statement of a matter of fact, but rather has to do with facts about a particular subject matter, as do evaluations of such things as sight and hearing in animals. | |
| From: Philippa Foot (Natural Goodness [2001], 1) | |
| A reaction: She avoids the word 'function', and only deals with living creatures, but she uses a 'good knife' as an example, and this Aristotelian view clearly applies to any machine which has a function. |
| 22497 | Deep happiness usually comes from the basic things in life [Foot] |
| Full Idea: Possible objects of deep happiness seem to be things that are basic in human life, such as home, and family, and work, and friendship. | |
| From: Philippa Foot (Natural Goodness [2001], 6) | |
| A reaction: I've not encountered discussion of 'deep' happiness before. I heard of an old man in tears because he had just seen a Purple Emperor butterfly for the first time. She makes it sound very conservative. How about mountaineering achievements? |
| 22498 | Happiness is enjoying the pursuit and attainment of right ends [Foot] |
| Full Idea: In my terminology 'happiness' is understood as the enjoyment of good things, meaning the enjoyment in attaining, and in pursuing, right ends. | |
| From: Philippa Foot (Natural Goodness [2001], 6) | |
| A reaction: A modified version of Aristotle's view, which she contrasts with McDowell's identification of happiness with the life of virtue. They all seem to have an optimistic hope that the pleasure in being a bit wicked is false happiness. |
| 23695 | Good actions can never be justified by the good they brings to their agent [Foot] |
| Full Idea: There is no good case for assessing the goodness of human action by reference only to good that each person brings to himself. | |
| From: Philippa Foot (Natural Goodness [2001], 1) | |
| A reaction: She observes that even non-human animals often act for non-selfish reasons. The significance of this is its rejection of her much earlier view that virtues are justified by the good they bring their possessor. |
| 22499 | We all know that just pretending to be someone's friend is not the good life [Foot] |
| Full Idea: We know perfectly well that it is not true that the best life would consist in successfully pretending friendship: having friends to serve one but without being a real friend oneself. | |
| From: Philippa Foot (Natural Goodness [2001], 7) | |
| A reaction: For some skallywags the achieving of something for nothing seems to be very much the good life, but not many of them want to exploit people who are seen to be their friends. |
| 22495 | Someone is a good person because of their rational will, not their body or memory [Foot] |
| Full Idea: To speak of a good person is to speak of an individual not in respect of his body, or of faculties such as sight and memory, but as concerns his rational will (his 'will as controllable by reason'). | |
| From: Philippa Foot (Natural Goodness [2001], 5) | |
| A reaction: She more or less agrees with Kant that the only truly good moral thing is a good will, though she has plenty of other criticisms of his views. |
| 22502 | Refraining from murder is not made good by authenticity or self-fulfilment [Foot] |
| Full Idea: If a stranger should come on us when we are sleeping he will not think it all right to kill us. …In human life as it is, this kind of action is not made good by authenticity or self-fulfilment in the one who does it. | |
| From: Philippa Foot (Natural Goodness [2001], 7) | |
| A reaction: A rare swipe from Foot at existentialism, which she hardly ever mentions. I find it hard to see these existential virtues as in any way moral. It means nothing to other citizens whether one of their number is 'authentic'. |