|
7950
|
Philosophy tries to explain how the actual is possible, given that it seems impossible [Macdonald,C]
|
|
Full Idea:
Philosophical problems are problems about how what is actual is possible, given that what is actual appears, because of some faulty argument, to be impossible.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.6)
|
|
A reaction:
[She is discussing universals when she makes this comment] A very appealing remark, given that most people come into philosophy because of a mixture of wonder and puzzlement. It is a rather Wittgensteinian view, though, that we must cure our own ills.
|
|
7923
|
'Did it for the sake of x' doesn't involve a sake, so how can ontological commitments be inferred? [Macdonald,C]
|
|
Full Idea:
In 'She did it for the sake of her country' no one thinks that the expression 'the sake' refers to an individual thing, a sake. But given that, how can we work out what the ontological commitments of a theory actually are?
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.1)
|
|
A reaction:
For these sorts of reasons it rapidly became obvious that ordinary language analysis wasn't going to reveal much, but it is also a problem for a project like Quine's, which infers an ontology from the terms of a scientific theory.
|
|
10044
|
Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro]
|
|
Full Idea:
Russell adduces two reasons against the extensional view of classes, namely the existence of the null class (which cannot very well be a collection), and the unit classes (which would have to be identical with their single elements).
|
|
From:
report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Structure and Ontology p.459
|
|
A reaction:
Gödel believes in the reality of classes. I have great sympathy with Russell, when people start to claim that sets are not just conveniences to help us think about things, but actual abstract entities. Is the singleton of my pencil is on this table?
|
|
21707
|
Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
|
|
Full Idea:
Russell did not view logic as an uninterpreted calculus awaiting interpretations [the modern view]. Rather, logic is a single 'interpreted' body of a priori truths, of propositions rather than sentence forms - but maximally general and topic neutral.
|
|
From:
report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 1
|
|
A reaction:
This is the view which Wittgenstein challenged, saying logic is just conventional. Linsky claims that Russell's logicism is much more plausible, once you understand his view of logic.
|
|
8683
|
Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend]
|
|
Full Idea:
Unlike Frege, Russell and Whitehead were not realists about mathematical objects, and whereas Frege thought that only arithmetic and analysis are branches of logic, they think the vast majority of mathematics (including geometry) is essentially logical.
|
|
From:
report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.1
|
|
A reaction:
If, in essence, Descartes reduced geometry to algebra (by inventing co-ordinates), then geometry ought to be included. It is characteristic of Russell's hubris to want to embrace everything.
|
|
10093
|
The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman]
|
|
Full Idea:
Russell and Whitehead's ramified theory of types worked not with sets, but with propositional functions (similar to Frege's concepts), with a more restrictive assignment of variables, insisting that bound, as well as free, variables be of lower type.
|
|
From:
report of B Russell/AN Whitehead (Principia Mathematica [1913]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.3
|
|
A reaction:
I don't fully understand this (and no one seems much interested any more), but I think variables are a key notion, and there is something interesting going on here. I am intrigued by ordinary language which behaves like variables.
|
|
8691
|
The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead]
|
|
Full Idea:
The Russell/Whitehead type theory reduces mathematics to a consistent founding discipline, but is criticised for not really being logic. They could not prove the existence of infinite sets, and introduced a non-logical 'axiom of reducibility'.
|
|
From:
comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.6
|
|
A reaction:
To have reduced most of mathematics to a founding discipline sounds like quite an achievement, and its failure to be based in pure logic doesn't sound too bad. However, it seems to reduce some maths to just other maths.
|
|
10305
|
In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead]
|
|
Full Idea:
In the system of 'Principia Mathematica', it is not only the axioms of infinity and reducibility which go beyond pure logic, but also the initial conception of a universal domain of individuals and of a domain of predicates.
|
|
From:
comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.267) by Paul Bernays - On Platonism in Mathematics p.267
|
|
A reaction:
This sort of criticism seems to be the real collapse of the logicist programme, rather than Russell's paradox, or Gödel's Incompleteness Theorems. It just became impossible to stick strictly to logic in the reduction of arithmetic.
|
|
8746
|
To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro]
|
|
Full Idea:
Russell insisted on the vicious circle principle, and thus rejected impredicative definitions, which resulted in an unwieldy ramified type theory, with the ad hoc axiom of reducibility. Ramsey's simpler theory was impredicative and avoided the axiom.
|
|
From:
report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2
|
|
A reaction:
Nowadays the theory of types seems to have been given up, possibly because it has no real attraction if it lacks the strict character which Russell aspired to.
|
|
7944
|
Reduce by bridge laws (plus property identities?), by elimination, or by reducing talk [Macdonald,C]
|
|
Full Idea:
There are four kinds of reduction: the identifying of entities of two theories by means of bridge or correlation laws; the elimination of entities in favour of the other theory; reducing by bridge laws and property identities; and merely reducing talk.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.3 n5)
|
|
A reaction:
[She gives references] The idea of 'bridge laws' I regard with caution. If bridge laws are ceteris paribus, they are not much help, and if they are strict, or necessary, then there must be an underlying reason for that, which is probably elimination.
|
|
7967
|
Being taller is an external relation, but properties and substances have internal relations [Macdonald,C]
|
|
Full Idea:
The relation of being taller than is an external relation, since it relates two independent material substances, but the relation of instantiation or exemplification is internal, in that it relates a substance with a property.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.6)
|
|
A reaction:
An interesting revival of internal relations. To be plausible it would need clear notions of 'property' and 'substance'. We are getting a long way from physics, and I sense Ockham stropping his Razor. How do you individuate a 'relation'?
|
|
7934
|
Tropes are abstract (two can occupy the same place), but not universals (they have locations) [Macdonald,C]
|
|
Full Idea:
Tropes are abstract entities, at least in the sense that more than one can be in the same place at the same time (e.g. redness and roundness). But they are not universals, because they have unique and particular locations.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.3)
|
|
A reaction:
I'm uneasy about the reification involved in this kind of talk. Does a coin possess a thing called 'roundness', which then has to be individuated, identified and located? I am drawn to the two extreme views, and suspicious of compromise.
|
|
7972
|
Tropes are abstract particulars, not concrete particulars, so the theory is not nominalist [Macdonald,C]
|
|
Full Idea:
Trope 'Nominalism' is not a version of nominalism, because tropes are abstract particulars, rather than concrete particulars. Of course, a trope account of the relations between particulars and their properties has ramifications for concrete particulars.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.6 n16)
|
|
A reaction:
Cf. Idea 7971. At this point the boundary between nominalist and realist theories seems to blur. Possibly that is bad news for tropes. Not many dilemmas can be solved by simply blurring the boundary.
|
|
7960
|
Trope Nominalism is the only nominalism to introduce new entities, inviting Ockham's Razor [Macdonald,C]
|
|
Full Idea:
Of all the nominalist solutions, Trope Nominalism is the only one that tries to solve the problem at issue by introducing entities; all the others try to get by with concrete particulars and sets of them. This might invite Ockham's Razor.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.6)
|
|
A reaction:
We could reply that tropes are necessities. The issue seems to be a key one, which is whether our fundamental onotology should include properties (in some form or other). I am inclined to exclude them (Ideas 3322, 3906, 4029).
|
|
7951
|
Numerical sameness is explained by theories of identity, but what explains qualitative identity? [Macdonald,C]
|
|
Full Idea:
We can distinguish between numerical identity and qualitative identity. Numerical sameness is explained by a theory of identity, but what explains qualitative sameness?
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.6)
|
|
A reaction:
The distinction is between type and token identity. Tokens are particulars, and types are sets, so her question comes down to the one of what entitles something to be a member of a set? Nothing, if sets are totally conventional, but they aren't.
|
|
7971
|
Real Nominalism is only committed to concrete particulars, word-tokens, and (possibly) sets [Macdonald,C]
|
|
Full Idea:
All real forms of Nominalism should hold that the only objects relevant to the explanation of generality are concrete particulars, words (i.e. word-tokens, not word-types), and perhaps sets.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.6 n16)
|
|
A reaction:
The addition of sets seems controversial (see Idea 7970). The context is her rejection of the use of tropes in nominalist theories. I would doubt whether a theory still counted as nominalist if it admitted sets (e.g. Quine).
|
|
7961
|
A 'thing' cannot be in two places at once, and two things cannot be in the same place at once [Macdonald,C]
|
|
Full Idea:
The so-called 'laws of thinghood' govern particulars, saying that one thing cannot be wholly present at different places at the same time, and two things cannot occupy the same place at the same time.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.6)
|
|
A reaction:
Is this an empirical observation, or a tautology? Or might it even be a priori synthetic? What happens when two water drops or clouds merge? Or an amoeba fissions? In what sense is an image in two places at once? Se also Idea 2351.
|
|
7926
|
We 'individuate' kinds of object, and 'identify' particular specimens [Macdonald,C]
|
|
Full Idea:
We can usefully refer to 'individuation conditions', to distinguish objects of that kind from objects not of that kind, and to 'identity conditions', to distinguish objects within that kind from one another.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.2)
|
|
A reaction:
So we individuate types or sets, and identify tokens or particulars. Sounds good. Should be in every philosopher's toolkit, and on every introductory philosophy course.
|
|
7932
|
A phenomenalist cannot distinguish substance from attribute, so must accept the bundle view [Macdonald,C]
|
|
Full Idea:
Commitment to the view that only what can be an object of possible sensory experience can exist eliminates the possibility of distinguishing between substance and attribute, leaving only one alternative, namely the bundle view.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.3)
|
|
A reaction:
Phenomenalism strikes me as a paradigm case of confusing ontology with epistemology. Presumably physicists (even empiricist ones) are committed to the 'interior' of quarks and electrons, but no one expects to experience them.
|
|
7929
|
A substance is either a bundle of properties, or a bare substratum, or an essence [Macdonald,C]
|
|
Full Idea:
The three main theories of substance are the bundle theory (Leibniz, Berkeley, Hume, Ayer), the bare substratum theory (Locke and Bergmann), and the essentialist theory.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.3)
|
|
A reaction:
Macdonald defends the essentialist theory. The essentialist view immediately appeals to me. Properties must be OF something, and the something must have the power to produce properties. So there.
|
|
7941
|
Each substance contains a non-property, which is its substratum or bare particular [Macdonald,C]
|
|
Full Idea:
A rival to the bundle theory says that, for each substance, there is a constituent of it that is not a property but is both essential and unique to it, this constituent being referred to as a 'bare particular' or 'substratum'.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.3)
|
|
A reaction:
This doesn't sound promising. It is unclear what existence devoid of all properties could be like. How could it 'have' its properties if it was devoid of features (it seems to need property-hooks)? It is an ontological black hole. How do you prove it?
|
|
7942
|
The substratum theory explains the unity of substances, and their survival through change [Macdonald,C]
|
|
Full Idea:
If there is a substratum or bare particular within a substance, this gives an explanation of the unity of substances, and it is something which can survive intact when a substance changes.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.3)
|
|
A reaction:
[v. compressed wording] Many problems here. The one that strikes me is that when things change they sometimes lose their unity and identity, and that seems to be decided entirely from observation of properties, not from assessing the substratum.
|
|
7943
|
A substratum has the quality of being bare, and they are useless because indiscernible [Macdonald,C]
|
|
Full Idea:
There seems to be no way of identifying a substratum as the bearer of qualities without qualifiying it as bare (having the property of being bare?), ..and they cannot be used to individuate things, because they are necessarily indiscernible.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.3)
|
|
A reaction:
The defence would probably be a priori, claiming an axiomatic necessity for substrata in our thinking about the world, along with a denial that bareness is a property (any more than not being a contemporary of Napoleon is a property).
|
|
12033
|
An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM]
|
|
Full Idea:
Trivially, the Identity of Indiscernibles says that two individuals, Castor and Pollux, cannot have all properties in common. For Castor must have the properties of being identical with Castor and not being identical with Pollux, which Pollux can't share.
|
|
From:
report of B Russell/AN Whitehead (Principia Mathematica [1913], I p.57) by Robert Merrihew Adams - Primitive Thisness and Primitive Identity 2
|
|
A reaction:
I suspect that either the property of being identical with itself is quite vacuous, or it is parasytic on primitive identity, or it is the criterion which is actually used to define identity. Either way, I don't find this claim very illuminating.
|
|
7927
|
At different times Leibniz articulated three different versions of his so-called Law [Macdonald,C]
|
|
Full Idea:
There are three distinct versions of Leibniz's Law, all traced to remarks made by Leibniz: the Identity of Indiscernibles (same properties, same thing), the Indiscernibility of Identicals (same thing, same properties), and the Substitution Principle.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.2)
|
|
A reaction:
The best view seems to be to treat the second one as Leibniz's Law (and uncontroversially true), and the first one as being an interesting but dubious claim.
|
|
10040
|
Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel]
|
|
Full Idea:
By analyzing the paradoxes to which Cantor's set theory had led, ..Russell brought to light the amazing fact that our logical intuitions (concerning such notions as truth, concept, being, class) are self-contradictory.
|
|
From:
report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.452
|
|
A reaction:
The main intuition that failed was, I take it, that every concept has an extension, that is, there are always objects which will or could fall under the concept.
|
|
7947
|
In continuity, what matters is not just the beginning and end states, but the process itself [Macdonald,C]
|
|
Full Idea:
What matters to continuity is not just the beginning and end states of the process by which a thing persists, perhaps through change, but the process itself.
|
|
From:
Cynthia Macdonald (Varieties of Things [2005], Ch.4)
|
|
A reaction:
This strikes me as being a really important insight. Compare Idea 4931. If this is the key to understanding mind and personal identity, it means that the concept of a 'process' must be a central issue in ontology. How do you individuate a process?
|
|
21725
|
The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B]
|
|
Full Idea:
The multiple relations theory of judgement proposes that assertions about propositions are dependent upon genuine facts involving belief and other attitude relations, subjects of those attitudes, and the constituents of the belief.
|
|
From:
report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 7.2
|
|
A reaction:
This seems to require a commitment to universals (especially relations) with which we can be directly acquainted. I prefer propositions, but as mental entities, not platonic entities.
|
|
23453
|
Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead]
|
|
Full Idea:
A 'proposition', in the sense in which a proposition is supposed to be the object of a judgement, is a false abstraction, because a judgement has several objects, not one.
|
|
From:
B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus 2E
|
|
A reaction:
This is the rejection of the 'Russellian' theory of propositions, in favour of his multiple-relations theory of judgement. But why don't the related objects add up to a proposition about a state of affairs?
|