10035
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Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
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Full Idea:
'Mathematical Logic' is a precise and complete formulation of formal logic, and is both a section of mathematics covering classes, relations, symbols etc, and also a science prior to all others, with ideas and principles underlying all sciences.
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From:
Kurt Gödel (Russell's Mathematical Logic [1944], p.447)
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A reaction:
He cites Leibniz as the ancestor. In this database it is referred to as 'theory of logic', as 'mathematical' seems to be simply misleading. The principles of the subject are standardly applied to mathematical themes.
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10043
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Mathematical objects are as essential as physical objects are for perception [Gödel]
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Full Idea:
Classes and concepts may be conceived of as real objects, ..and are as necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions, with neither case being about 'data'.
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From:
Kurt Gödel (Russell's Mathematical Logic [1944], p.456)
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A reaction:
Note that while he thinks real objects are essential for mathematics, be may not be claiming the same thing for our knowledge of logic. If logic contains no objects, then how could mathematics be reduced to it, as in logicism?
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14193
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'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA]
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Full Idea:
Some deep essentialists resist the need to explain the structure under de re modal properties, taking them as primitive. One version (which we can call 'substance theory') takes them to fall under a sortal concept, with no further explanation.
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From:
L.A. Paul (In Defense of Essentialism [2006], §1)
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A reaction:
A very helpful identification of what Wiggins stands for, and why I disagree with him. The whole point of essences is to provide a notion that fits in with sciences, which means they must have an explanatory role, which needs structures.
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14195
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If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA]
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Full Idea:
If the substance essentialist holds that the sort an object belongs to determines its de re modal properties (rather than the other way round), then he needs to give an (ontological, not conceptual) explanation of what determines an object's sort.
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From:
L.A. Paul (In Defense of Essentialism [2006], §1)
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A reaction:
See Idea 14193 for 'substance essentialism'. I find it quite incredible that anyone could think that a thing's sort could determine its properties, rather than the other way round. Even if sortals are conventional, they are not arbitrary.
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14196
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Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA]
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Full Idea:
The explanation of material constitution given by substance essentialism is that there are multiple objects. A person is essentially human-shaped (falling under the human sort), while their hunk of tissue is accidentally human-shaped (as tissue).
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From:
L.A. Paul (In Defense of Essentialism [2006], §1)
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A reaction:
At this point sortal essentialism begins to look crazy. Persons are dubious examples (with sneaky dualism involved). A bronze statue is essentially harder to dent than a clay one, because of its bronze. If you remake it of clay, it isn't the same statue.
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14190
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Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA]
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Full Idea:
Essentialism says that objects have their properties essentially. 'Deep' essentialists take the (nontrivial) essential properties of an object to determine its nature. 'Shallow' essentialists substitute context-dependent truths for the independent ones.
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From:
L.A. Paul (In Defense of Essentialism [2006], Intro)
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A reaction:
If the deep essence determines a things nature, we should not need to say 'nontrivial'. This is my bete noire, the confusion of essential properties with necessary ones, where necessary properties (or predicates, at least) can indeed be trivial.
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9212
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Possible states of affairs are not propositions; a proposition can't be a state of affairs! [Fine,K]
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Full Idea:
Possible states of affairs have often been taken to be propositions, but this cannot be correct, since any possible state of affairs is possibly a state of affairs, but no proposition is possibly a state of affairs.
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From:
Kit Fine (The Problem of Possibilia [2003], 2)
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A reaction:
The point is, presumably, that the state of affairs cannot be the proposition itself, but (at least) what the proposition refers to. I can't see any objection to that.
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9213
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The actual world is a possible world, so we can't define possible worlds as 'what might have been' [Fine,K]
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Full Idea:
A possible world can't be defined (by Stalnaker and Plantinga) as a way the world might have been, because a possible world is possibly the world, yet no way the world might have been is possibly the world.
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From:
Kit Fine (The Problem of Possibilia [2003], 2)
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A reaction:
His point is that any definition of a possible world must cover the actual world, because that is one of them. 'Might have been' is not applicable to the actual world. It seems a fairly important starting point for discussion of possible worlds.
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14189
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'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA]
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Full Idea:
A 'modal realist' believes that there are many concrete worlds, while the 'actualist' believes in only one concrete world, the actual world. The 'ersatzist' is an actualist who takes nonactual possible worlds and their contents to be abstracta.
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From:
L.A. Paul (In Defense of Essentialism [2006], Intro)
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A reaction:
My view is something like that modal realism is wrong, and actualism is right, and possible worlds (if they really are that useful) are convenient abstract fictions, constructed (if we have any sense) out of the real possibilities in the actual world.
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