21 ideas
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) |
16755 | The possible Aristotelian view that forms are real and active principles is clearly wrong [Fine,K, by Pasnau] |
Full Idea: Aristotle seems to have a possible basis for the belief [in individual forms], namely that forms are real and active principles in the world, which is denied by any right-minded modern. | |
From: report of Kit Fine (A Puzzle Concerning Matter and Form [1994], p.19) by Robert Pasnau - Metaphysical Themes 1274-1671 24.3 n8 | |
A reaction: Pasnau says this is the view of forms promoted by the scholastics, whereas Aristotle's own view should be understood as 'metaphysical'. |
6248 | Reason is too slow and doubtful to guide all actions, which need external and moral senses [Hutcheson] |
Full Idea: We boast of our mighty reason above other animals, but its processes are too slow, too full of doubt, to serve us in every exigency, either for our preservation, without external senses, or to influence our actions for good without the moral sense. | |
From: Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §VII.III) | |
A reaction: This idea was taken up by Hume, and it must have influence Hume's general scepticism about the importance of reason. What this idea misses is the enormous influence of prior reasoning on our quick decisions. |
6238 | We approve of actions by a superior moral sense [Hutcheson] |
Full Idea: By a superior sense, which I call a moral one, we approve the actions of others. | |
From: Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], Intro) | |
A reaction: This tries to present moral insight as being on a par with the famous five senses. This doesn't seem quite right to me; separate parts of me can operate individual senses, but the whole of me is required for moral judgements, based on evidence. |
6239 | We dislike a traitor, even if they give us great benefit [Hutcheson] |
Full Idea: Let us consider if a traitor, who would sell his own country to us, may not often be as advantageous to us, as an hero who defends us: and yet we can love the treason, and hate the traitor. | |
From: Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §I.VI) | |
A reaction: A nice example, which certainly refutes any claim that morality is entirely and directly self-interested. High-minded idealism, though, is not the only alternative explanation. We admire loyalty, but not loyalty to, say, Hitler. |
6240 | The moral sense is not an innate idea, but an ability to approve or disapprove in a disinterested way [Hutcheson] |
Full Idea: The moral sense is not an innate idea or knowledge, but a determination of our minds to receive the simple ideas of approbation or condemnation, from actions observed, antecedent to any opinions of advantage or loss to redound to ourselves. | |
From: Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §I.VIII) | |
A reaction: This may claim a pure moral intuition, but it is also close to Kantian universalising of the rules for behaviour. It is also a variation on Descartes' 'natural light' of reason. Of course, if we say the ideas are 'received', where are they received from? |
6242 | We cannot choose our moral feelings, otherwise bribery could affect them [Hutcheson] |
Full Idea: Neither benevolence nor any other affection or desire can be directly raised by volition; if they could, then we could be bribed into any affection whatsoever toward any object. | |
From: Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §II.IV) | |
A reaction: Of course, notoriously, the vast mass of people have often been bribed to love a politician, by low taxes, or bread and circuses. Still, you cannot choose to love or admire someone, you just do. Not much free will there. |
6247 | Everyone feels uneasy when seeing others in pain, unless the others are evil [Hutcheson] |
Full Idea: Every mortal is made uneasy by any grievous misery he sees another involved in, unless the person be imagined morally evil. | |
From: Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §V.VIII) | |
A reaction: This is the natural compassion on which Hume built his moral theory. This remark emphasises that a concern for justice is just as important as a compassion for pain. Kant was more interested in what we deserve than in what we get. |
6244 | Human nature seems incapable of universal malice, except what results from self-love [Hutcheson] |
Full Idea: Human nature seems scarce capable of malicious disinterested hatred, or an ultimate desire of the misery of others, when we imagine them not pernicious to us, or opposite to our interests; ..that is only the effect of self-love, not disinterested malice. | |
From: Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §II.VII) | |
A reaction: I suppose it is true that even the worst criminals brooding in prison don't wish the entire population of some foreign country to die in pain. Only a very freakish person would wish the human race were extinct. A very nice observation. |
6243 | As death approaches, why do we still care about family, friends or country? [Hutcheson] |
Full Idea: How comes it that we do not lose, at the approach of death, all concern for our families, friends, or country? | |
From: Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §II.V) | |
A reaction: A nice question. No doubt some people do cease to care, but on the whole it raises the 'last round' problem in social contract theory, which is why fulfil your part of a bargain if it is too late to receive the repayment afterwards? |
6246 | My action is not made good by a good effect, if I did not foresee and intend it [Hutcheson] |
Full Idea: No good effect, which I did not actually foresee and intend, makes my action morally good. | |
From: Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §III.XII) | |
A reaction: This is one of the parents of utilitarianism repudiating pure consequentialism. Bentham sharply divided the action (which is consequentialist) from the person (who has useful intentions, but is not particulary important); this division is misleading. |
6241 | Contempt of danger is just madness if it is not in some worthy cause [Hutcheson] |
Full Idea: Mere courage, or contempt of danger, if we conceive it to have no regard to the defence of the innocent, or repairing of wrongs or self-interest, would only entitle its possessor to bedlam. | |
From: Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §II.I) | |
A reaction: If many criminals would love to rob a bank, but only a few have the nerve to attempt it, we can hardly deny that the latter exhibit a sort of courage. The Greeks say that good sense must be involved, but few of them were so moral about courage. |
6245 | That action is best, which procures the greatest happiness for the greatest number [Hutcheson] |
Full Idea: That action is best, which procures the greatest happiness for the greatest number; and that worst, which, in like manner, occasions misery. | |
From: Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §III.VIII) | |
A reaction: The first use of a phrase taken up by Bentham. This is not just an anticipation of utilitarianism, it is utilitarianism, with all its commitment to consequentialism (but see Idea 6246), and to the maximising of happiness. It is a brilliant idea. |
6251 | The loss of perfect rights causes misery, but the loss of imperfect rights reduces social good [Hutcheson] |
Full Idea: Perfect rights are necessary to the public good, and it makes those miserable whose rights are thus violated; …imperfect rights tend to the improvement and increase of good in a society, but are not necessary to prevent universal misery. | |
From: Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §VII.VI) | |
A reaction: This is a very utilitarian streak in Hutcheson, converting natural law into its tangible outcome in actual happiness or misery. The distinction here is interesting (taken up by Mill), but there is a very blurred borderline. |
6250 | We say God is good if we think everything he does aims at the happiness of his creatures [Hutcheson] |
Full Idea: We call the Deity morally good, when we apprehend that his whole providence tends to the universal happiness of his creatures. | |
From: Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §VII.V) | |
A reaction: From the point of view of eternity, we might accept that God aims at some even greater good than the happiness of a bunch of miserable little creatures whose bad behaviour merits little reward. The greater good needs to be impressive, though. |
6249 | If goodness is constituted by God's will, it is a tautology to say God's will is good [Hutcheson] |
Full Idea: To call the laws of the supreme Deity good or holy or just, if these be constituted by laws, or the will of a superior, must be an insignificant tautology, amounting to no more than 'God wills what he wills' or 'His will is conformable to his will'. | |
From: Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §VII.V) | |
A reaction: This argues not only against God as the source of morality, but also against any rules, such as those of the Categorical Imperative. Why should I follow the Categorical Imperative? What has value must dictate the rules. Is obedience the highest value? |