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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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4125
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Hare says I acquire an agglomeration of preferences by role-reversal, leading to utilitarianism [Hare, by Williams,B]
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Full Idea:
In Hare's theory I apply a "role-reversal test", and then acquire an actual agglomeration of preferences that apply to the hypothetical situation. The result is utilitarianism.
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From:
report of Richard M. Hare (Moral Thinking: Its Levels,Method and Point [1981]) by Bernard Williams - Ethics and the Limits of Philosophy Ch.5
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A reaction:
It hits that traditional stumbling block, of why I should care about the preferences of others. Pure reason and empathy are the options (Kant or Hume). I may, however, lack both.
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4126
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If we have to want the preferences of the many, we have to abandon our own deeply-held views [Williams,B on Hare]
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Full Idea:
Hare's version of utilitarianism requires an agent to abandon any deeply held principle or conviction if a large enough aggregate of contrary preferences, of whatever kind, favours a contrary action.
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From:
comment on Richard M. Hare (Moral Thinking: Its Levels,Method and Point [1981]) by Bernard Williams - Ethics and the Limits of Philosophy Ch.5
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A reaction:
This nicely attacks any impersonal moral theory, whether it is based on reason or preferences. But where did my personal ideals come from?
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4127
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If morality is to be built on identification with the preferences of others, I must agree with their errors [Williams,B on Hare]
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Full Idea:
If there is to be total identification with others, then if another's preferences are mistaken, the preferences I imagine myself into are equally mistaken, and if 'identification' is the point, they should remain mistaken.
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From:
comment on Richard M. Hare (Moral Thinking: Its Levels,Method and Point [1981]) by Bernard Williams - Ethics and the Limits of Philosophy Ch.5
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A reaction:
Yes. The core of morality must be judgement. Robots can implement universal utilitarian rules, but they could end up promoting persecutions of minorities.
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22483
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A judgement is presciptive if we expect it to be acted on [Hare]
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Full Idea:
We say something prescriptive if and only if, for some act A, some situation S and some person R, if P were to assent (orally) to what we say, and not, in S, do A, he logically must be assenting insincerely.
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From:
Richard M. Hare (Moral Thinking: Its Levels,Method and Point [1981], p.21), quoted by Philippa Foot - Does Moral Subjectivism Rest on a Mistake? p.190
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A reaction:
Foot offers this as Hare's most explicit definition. The use of algebra strikes me as ludicrous. In logic letters have the virtue of not shifting their meaning during an argument, but that is not required here.
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