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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2748
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A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]
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Full Idea:
Nozick says Gettier cases aren't knowledge because the proposition would be believed even if false. Proper justification must be more sensitive to the truth ("track the truth").
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From:
report of Robert Nozick (Philosophical Explanations [1981], 3.1) by Jonathan Dancy - Intro to Contemporary Epistemology 3.1
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A reaction:
This is a bad idea. I see a genuine tree in my garden and believe it is there, so I know it. That I might have believed it if I was in virtually reality, or observing a mirror, won't alter that.
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16236
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Maybe our persistence conditions concern bodies, rather than persons [Olson, by Hawley]
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Full Idea:
Instead of attributing person-like persistence conditions to bodies, we could attribute body-like persistence conditions to persons, …so human persons are identical with human organisms.
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From:
report of Eric T. Olson (The Human Animal [1997]) by Katherine Hawley - How Things Persist 5.10
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A reaction:
In the case of pre-birth and advanced senility, Olson thinks we could have the body without the person, so person is a 'phase sortal' of bodies. A good theory, which seems to answer a lot of questions. 'Person' may be an abstraction.
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6669
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For 'animalism', I exist before I became a person, and can continue after it, so I am not a person [Olson, by Lowe]
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Full Idea:
According to 'animalism', I existed before I was a person and I may well go one existing for some time after I cease to be a person; hence, I am not essentially a person, but a human organism.
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From:
report of Eric T. Olson (The Human Animal [1997]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.10
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A reaction:
There is a very real sense in which an extremely senile person has 'ceased to exist' (e.g. as the person I used to love). On the whole, though, I think that Olson is right, and yet 'person' is an important concept. Neither concept is all-or-nothing.
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