|
14782
|
Philosophy is an experimental science, resting on common experience [Peirce]
|
|
Full Idea:
Philosophy, although it uses no microscopes or other apparatus of special observation, is really an experimental science, resting on that experience which is common to us all.
|
|
From:
Charles Sanders Peirce (The Nature of Mathematics [1898], I)
|
|
A reaction:
The 'experimental' either implies that thought-experiments are central to the subject, or that philosophers are discussing the findings of scientists, but at a high level of theory and abstraction. Peirce probably means the latter. I can't disagree.
|
|
9143
|
Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Fine,K, by Cook/Ebert]
|
|
Full Idea:
Fine distinguishes 'implicit definitions', where we must know it is satisfiable before it is deployed, 'creative definitions', where objects are introduced in virtue of the definition, ..and 'contextual definitions', based on established vocabulary.
|
|
From:
report of Kit Fine (The Limits of Abstraction [2002], 060) by R Cook / P Ebert - Notice of Fine's 'Limits of Abstraction' 3
|
|
A reaction:
Fine is a fan of creative definition. This sounds something like the distinction between cutting nature at the perceived joints, and speculating about where new joints might be inserted. Quite a helpful thought.
|
|
14788
|
Mathematics is close to logic, but is even more abstract [Peirce]
|
|
Full Idea:
The whole of the theory of numbers belongs to logic; or rather, it would do so, were it not, as pure mathematics, pre-logical, that is, even more abstract than logic.
|
|
From:
Charles Sanders Peirce (The Nature of Mathematics [1898], IV)
|
|
A reaction:
Peirce seems to flirt with logicism, but rejects in favour of some subtler relationship. I just don't believe that numbers are purely logical entities.
|
|
14193
|
'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA]
|
|
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.
|
|
From:
L.A. Paul (In Defense of Essentialism [2006], §1)
|
|
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.
|
|
14195
|
If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA]
|
|
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.
|
|
From:
L.A. Paul (In Defense of Essentialism [2006], §1)
|
|
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.
|
|
14196
|
Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA]
|
|
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).
|
|
From:
L.A. Paul (In Defense of Essentialism [2006], §1)
|
|
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.
|
|
14190
|
Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA]
|
|
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.
|
|
From:
L.A. Paul (In Defense of Essentialism [2006], Intro)
|
|
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.
|
|
14189
|
'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA]
|
|
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.
|
|
From:
L.A. Paul (In Defense of Essentialism [2006], Intro)
|
|
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.
|
|
14789
|
Experience is indeed our only source of knowledge, provided we include inner experience [Peirce]
|
|
Full Idea:
If Mill says that experience is the only source of any kind of knowledge, I grant it at once, provided only that by experience he means personal history, life. But if he wants me to admit that inner experience is nothing, he asks what cannot be granted.
|
|
From:
Charles Sanders Peirce (The Nature of Mathematics [1898])
|
|
A reaction:
Notice from Idea 14785 that Peirce has ideas in mind, and not just inner experiences like hunger. Empiricism certainly begins to look more plausible if we expand the notion of experience. It must include what we learned from prior experience.
|
|
9144
|
Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert]
|
|
Full Idea:
Fine says creative definitions can found mathematics. His 'procedural postulationism' says one stipulates not truths, but certain procedures for extending a domain. The procedures can be stated without invoking an abstract ontology.
|
|
From:
report of Kit Fine (The Limits of Abstraction [2002], 100) by R Cook / P Ebert - Notice of Fine's 'Limits of Abstraction' 4
|
|
A reaction:
(For creative definitions, see Idea 9143) This sounds close in spirit to fictionalism, but with the emphasis on the procedure (which can presumably be formalized) rather than a pure act of imaginative creation.
|
|
10141
|
Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K]
|
|
Full Idea:
Many different kinds of mathematical objects (natural numbers, the reals, points, lines, figures, groups) can be regarded as forms of abstraction, with special theories having their basis in a general theory of abstraction.
|
|
From:
Kit Fine (The Limits of Abstraction [2002], I.4)
|
|
A reaction:
This result, if persuasive, would be just the sort of unified account which the whole problem of abstact ideas requires.
|
|
9142
|
Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert]
|
|
Full Idea:
Fine considers abstraction principles as instances of reconceptualization (rather than implicit definition, or using the Context Principle). This centres not on reference, but on new senses emerging from analysis of a given sense.
|
|
From:
report of Kit Fine (The Limits of Abstraction [2002], 035) by R Cook / P Ebert - Notice of Fine's 'Limits of Abstraction' 2
|
|
A reaction:
Fine develops an argument against this view, because (roughly) the procedure does not end in a unique result. Intuitively, the idea that abstraction is 'reconceptualization' sounds quite promising to me.
|