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9390
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Logic guides thinking, but it isn't a substitute for it [Rumfitt]
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Full Idea:
Logic is part of a normative theory of thinking, not a substitute for thinking.
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From:
Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.13)
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A reaction:
There is some sort of logicians' dream, going back to Leibniz, of a reasoning engine, which accepts propositions and outputs inferences. I agree with this idea. People who excel at logic are often, it seems to me, modest at philosophy.
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11023
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The logical connectives are 'defined' by their introduction rules [Gentzen]
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Full Idea:
The introduction rules represent, as it were, the 'definitions' of the symbols concerned, and the elimination rules are no more, in the final analysis, than the consequences of these definitions.
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From:
Gerhard Gentzen (works [1938]), quoted by Stephen Read - Thinking About Logic Ch.8
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A reaction:
If an introduction-rule (or a truth table) were taken as fixed and beyond dispute, then it would have the status of a definition, since there would be nothing else to appeal to. So is there anything else to appeal to here?
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11213
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Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
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Full Idea:
To every logical symbol there belongs precisely one inference figure which 'introduces' the symbol ..and one which 'eliminates' it. The introductions represent the 'definitions' of the symbols concerned, and eliminations are consequences of these.
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From:
Gerhard Gentzen (works [1938], II.5.13), quoted by Ian Rumfitt - "Yes" and "No" III
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A reaction:
[1935 paper] This passage is famous, in laying down the basics of natural deduction systems of logic (ones using only rules, and avoiding axioms). Rumfitt questions whether Gentzen's account gives the sense of the connectives.
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9389
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Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt]
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Full Idea:
Vagueness in respect of membership is consistency with determinacy of the set's identity, so long as a set's identity is taken to consist, not in its having such-and-such members, but in its being the extension of a concept.
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From:
Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.5)
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A reaction:
I find this view of sets much more appealing than the one that identifies a set with its members. The empty set is less of a problem, as well as non-existents. Logicians prefer the extensional view because it is tidy.
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13193
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Active force is not just potential for action, since it involves a real effort or striving [Leibniz]
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Full Idea:
Active force should not be thought of as the simple and common potential [potentia] or receptivity to action of the schools. Rather, active force involves an effort [conatus] or striving [tendentia] toward action.
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From:
Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.252)
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A reaction:
This is why Leibniz is lured into making his active forces more and more animistic, till they end up like proto-minds (though never, remember, conscious and willing minds).
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13194
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God's laws would be meaningless without internal powers for following them [Leibniz]
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Full Idea:
To say that, in creation, God gave bodies a law for acting means nothing, unless, at the same time, he gave them something by means of which it could happen that the law is followed.
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From:
Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.253)
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A reaction:
This is the beginning of the modern rebellion against the medieval view of laws as imposed from outside on passive matter. Unfortunately for Leibniz, once you have postulated active internal powers, the external laws become redundant.
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13192
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Power is passive force, which is mass, and active force, which is entelechy or form [Leibniz]
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Full Idea:
The dynamicon or power [potentia] in bodies is twofold, passive and active. Passive force [vis] constitutes matter or mass [massa], and active force constitutes entelechy or form.
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From:
Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.252)
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A reaction:
This is explicitly equating the innate force understood in physics with Aristotelian form. The passive force is to explain the resistance of bodies. I like the equation of force with power. He says the entelechy is 'analogous' to a soul.
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