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9193
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ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
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Full Idea:
ZF set theory is a first-order axiomatization. Variables range over sets, there are no second-order variables, and primitive predicates are just 'equals' and 'member of'. The axiom of extensionality says sets with the same members are identical.
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From:
Michael Dummett (The Philosophy of Mathematics [1998], 7)
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A reaction:
If the eleven members of the cricket team are the same as the eleven members of the hockey team, is the cricket team the same as the hockey team? Our cricket team is better than our hockey team, so different predicates apply to them.
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9195
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Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
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Full Idea:
It must not be concluded from the rejection of excluded middle that intuitionistic logic operates with three values: true, false, and neither true nor false. It does not make use of true and false, but only with a construction being a proof.
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From:
Michael Dummett (The Philosophy of Mathematics [1998], 8.1)
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A reaction:
This just sounds like verificationism to me, with all its problems. It seems to make speculative statements meaningless, which can't be right. Realism has lots of propositions which are assumed to be true or false, but also unknowable.
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9186
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First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
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Full Idea:
First-order logic is distinguished by generalizations (quantification) only over objects: second-order logic admits generalizations or quantification over properties or kinds of objects, and over relations between them, and functions defined over them.
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From:
Michael Dummett (The Philosophy of Mathematics [1998], 3.1)
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A reaction:
Second-order logic was introduced by Frege, but is (interestingly) rejected by Quine, because of the ontological commitments involved. I remain unconvinced that quantification entails ontological commitment, so I'm happy.
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9187
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Logical truths and inference are characterized either syntactically or semantically [Dummett]
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Full Idea:
There are two ways of characterizing logical truths and correct inference. Proof-theoretic or syntactic characterizations, if the formalization admits of proof or derivation; and model-theoretic or semantic versions, being true in all interpretations.
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From:
Michael Dummett (The Philosophy of Mathematics [1998], 3.1)
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A reaction:
Dummett calls this distinction 'fundamental'. The second one involves truth, and hence meaning, where the first one just responds to rules. ..But how can you have a notion of correctly following a rule, without a notion of truth?
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6248
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Reason is too slow and doubtful to guide all actions, which need external and moral senses [Hutcheson]
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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.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §VII.III)
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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.
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6239
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We dislike a traitor, even if they give us great benefit [Hutcheson]
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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.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §I.VI)
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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.
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6240
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The moral sense is not an innate idea, but an ability to approve or disapprove in a disinterested way [Hutcheson]
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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.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §I.VIII)
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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?
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6242
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We cannot choose our moral feelings, otherwise bribery could affect them [Hutcheson]
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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.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §II.IV)
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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.
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6244
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Human nature seems incapable of universal malice, except what results from self-love [Hutcheson]
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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.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §II.VII)
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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.
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6243
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As death approaches, why do we still care about family, friends or country? [Hutcheson]
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Full Idea:
How comes it that we do not lose, at the approach of death, all concern for our families, friends, or country?
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §II.V)
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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?
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6241
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Contempt of danger is just madness if it is not in some worthy cause [Hutcheson]
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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.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §II.I)
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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.
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6245
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That action is best, which procures the greatest happiness for the greatest number [Hutcheson]
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Full Idea:
That action is best, which procures the greatest happiness for the greatest number; and that worst, which, in like manner, occasions misery.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §III.VIII)
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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.
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6251
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The loss of perfect rights causes misery, but the loss of imperfect rights reduces social good [Hutcheson]
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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.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §VII.VI)
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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.
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6249
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If goodness is constituted by God's will, it is a tautology to say God's will is good [Hutcheson]
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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'.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §VII.V)
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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?
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