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All the ideas for 'works', 'Ontological Dependence' and 'Frege philosophy of mathematics'

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59 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
Hegel produced modern optimism; he failed to grasp that consciousness never progresses [Hegel, by Cioran]
     Full Idea: Hegel is chiefly responsible for modern optimism. How could he have failed to see that consciousness changes only its forms and modalities, but never progresses.
     From: report of Georg W.F.Hegel (works [1812]) by E.M. Cioran - A Short History of Decay 5
1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / d. Nineteenth century philosophy
Hegel was the last philosopher of the Book [Hegel, by Derrida]
     Full Idea: Hegel was the last philosopher of the Book.
     From: report of Georg W.F.Hegel (works [1812]) by Jacques Derrida - Positions p.64
     A reaction: Reference to 'the Book' connects this to the great religions which rely on one holy text. The implication is that Hegel was proposing one big solution to all problems. It is doubtful if many philosophers before Hegel dreamt of that either.
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / c. Philosophy as generalisation
We understand things through their dependency relations [Fine,K]
     Full Idea: We understand a defined object (what it is) through the objects on which it depends.
     From: Kit Fine (Ontological Dependence [1995], II)
     A reaction: This places dependency relations right at the heart of our understanding of the world, and hence shifts traditional metaphysics away from existence and identity. The notion of explanation is missing from Fine's account.
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Hegel doesn't storm the heavens like the giants, but works his way up by syllogisms [Kierkegaard on Hegel]
     Full Idea: Hegel is a Johannes Climacus who does not storm the heavens, like the giants, by putting mountain upon mountain, but climbs aboard them by way of his syllogisms.
     From: comment on Georg W.F.Hegel (works [1812]) by Søren Kierkegaard - The Journals of Kierkegaard 2A
     A reaction: [Idea from SY] This appears to be an attempt at insulting Hegel for his timidity, but it seems to be describing the cautious approach which most modern philosophers take to be correct. [PG]
Metaphysics deals with the existence of things and with the nature of things [Fine,K]
     Full Idea: Metaphysics has two main areas of concern: one is with the nature of things, with what they are; and the other is with the existence of things, with whether they are.
     From: Kit Fine (Ontological Dependence [1995], I)
     A reaction: This paper is part of a movement which has shifted metaphysics to a third target - how things relate to one another. The possibility that this third aim should be the main one seems quite plausible to me.
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
For Hegel, things are incomplete, and contain external references in their own nature [Hegel, by Russell]
     Full Idea: The basis of Hegel's system is that what is incomplete must not be self-subsistent, and needs the support of other things; whatever has relations to things outside itself must contain some reference to those outside things in its own nature.
     From: report of Georg W.F.Hegel (works [1812]) by Bertrand Russell - Problems of Philosophy Ch.14
     A reaction: This leads to the idealist doctrine of 'internal relations'. It has some plausibility if you think about the physicist's definition of mass, which has to refer to forces etc. Presumably there is one essence for all of reality, instead of separate ones.
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
On the continent it is generally believed that metaphysics died with Hegel [Benardete,JA on Hegel]
     Full Idea: In continental Europe it is widely believed that the metaphysical game was played out in Hegel.
     From: comment on Georg W.F.Hegel (works [1812]) by José A. Benardete - Metaphysics: the logical approach Intro
2. Reason / B. Laws of Thought / 2. Sufficient Reason
Making sufficient reason an absolute devalues the principle of non-contradiction [Hegel, by Meillassoux]
     Full Idea: Hegel saw that the absolutization of the principle of sufficient reason (which marked the culmination of the belief in the necessity of what is) required the devaluation of the principle of non-contradiction.
     From: report of Georg W.F.Hegel (works [1812], 3) by Quentin Meillassoux - After Finitude; the necessity of contingency 3
     A reaction: I pass this on without understanding it, though a joint study of my collection of ideas on sufficient reason and non-contradiction might make it clear. [Let me know if you can explain it!]
2. Reason / C. Styles of Reason / 1. Dialectic
Rather than in three stages, Hegel presented his dialectic as 'negation of the negation' [Hegel, by Bowie]
     Full Idea: Hegel's 'dialectic' is often characterised in terms of the triad of thesis, antithesis and synthesis. This is, however, not the way he presents it. The core of the dialectic is rather what Hegel terms the 'negation of the negation'.
     From: report of Georg W.F.Hegel (works [1812]) by Andrew Bowie - Introduction to German Philosophy
     A reaction: Interestingly, this connects it to debates about intuitionist logic, which denies that double-negation necessarily makes a positive. Presumably Marx emphasised the first reading.
2. Reason / D. Definition / 4. Real Definition
Maybe two objects might require simultaneous real definitions, as with two simultaneous terms [Fine,K]
     Full Idea: In Wooster as the witless bachelor and Jeeves as the crafty manservant, and one valet to the other, we will have the counterpart, within the framework of real definition, to the simultaneous definition of two terms.
     From: Kit Fine (Ontological Dependence [1995], III)
     A reaction: This is wonderful grist to the mill of scientific essentialism, which endeavours to produce an understanding through explanation of the complex interactions of nature.
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
     Full Idea: The standard sense of a 'contextual definition' permits the eliminating of the defined expression, by transforming any sentence containing it into an equivalent one not containing it.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.11)
     A reaction: So the whole definition might be eliminated by a single word, which is not equivalent to the target word, which is embedded in the original expression. Clearly contextual definitions have some problems
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
     Full Idea: For sentential or first-order logic, the logical truths are represented by valid formulas; in higher-order logics, by sentences formulated in purely logical terms.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 3)
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
Negation of negation doubles back into a self-relationship [Hegel, by Houlgate]
     Full Idea: For Hegel, the 'negation of negation' is negation that, as it were, doubles back on itself and 'relates itself to itself'.
     From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - An Introduction to Hegel 6 'Space'
     A reaction: [ref VNP 1823 p.108] Glad we've cleared that one up.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
A prime number is one which is measured by a unit alone [Dummett]
     Full Idea: A prime number is one which is measured by a unit alone.
     From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 11)
     A reaction: We might say that the only way of 'reaching' or 'constructing' a prime is by incrementing by one till you reach it. That seems a pretty good definition. 64, for example, can be reached by a large number of different routes.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
     Full Idea: It is essential to a quantitative domain of any kind that there should be an operation of adding its elements; that this is more fundamental thaat that they should be linearly ordered by magnitude is apparent from cyclic domains like that of angles.
     From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit')
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A number is a multitude composed of units [Dummett]
     Full Idea: A number is a multitude composed of units.
     From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 2)
     A reaction: This is outdated by the assumption that 0 and 1 are also numbers, but if we say one is really just the 'unit' which is preliminary to numbers, and 0 is as bogus a number as i is, we might stick with the original Greek distinction.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
     Full Idea: A child understands 'there are just as many nuts as apples' as easily by pairing them off as by counting them.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12)
     A reaction: I find it very intriguing that you could know that two sets have the same number, without knowing any numbers. Is it like knowing two foreigners spoke the same words, without understanding them? Or is 'equinumerous' conceptually prior to 'number'?
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The identity of a number may be fixed by something outside structure - by counting [Dummett]
     Full Idea: The identity of a mathematical object may sometimes be fixed by its relation to what lies outside the structure to which it belongs. It is more fundamental to '3' that if certain objects are counted, there are three of them.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5)
     A reaction: This strikes me as Dummett being pushed (by his dislike of the purely abstract picture given by structuralism) back to a rather empiricist and physical view of numbers, though he would totally deny that.
Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
     Full Idea: The number 0 is not differentiated from 1 by its position in a progression, otherwise there would be no difference between starting with 0 and starting with 1. That is enough to show that numbers are not identifiable just as positions in structures.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5)
     A reaction: This sounds conclusive, but doesn't feel right. If numbers are a structure, then where you 'start' seems unimportant. Where do you 'start' in St Paul's Cathedral? Starting sounds like a constructivist concept for number theory.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
     Full Idea: The two frequent modern objects to logicism are that set theory is not part of logic, or that it is of no interest to 'reduce' a mathematical theory to another, more complex, one.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18)
     A reaction: Dummett says these are irrelevant (see context). The first one seems a good objection. The second one less so, because whether something is 'complex' is a quite different issue from whether it is ontologically more fundamental.
7. Existence / A. Nature of Existence / 3. Being / b. Being and existence
An object's 'being' isn't existence; there's more to an object than existence, and its nature doesn't include existence [Fine,K]
     Full Idea: It seems wrong to identify the 'being' of an object, its being what it is, with its existence. In one respect existence is too weak; for there is more to an object than mere existence; also too strong, for an object's nature need not include existence.
     From: Kit Fine (Ontological Dependence [1995], I)
     A reaction: The word 'being' has been shockingly woolly, from Parmenides to Heidegger, but if you identify it with a thing's 'nature' that strikes me as much clearer (even if a little misty).
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
The dialectical opposition of being and nothing is resolved in passing to the concept of becoming [Hegel, by Scruton]
     Full Idea: The concept of being contains within itself it own negation - nothing - and the dialectical opposition between these two concepts is resolved only in the passage to a new concept, becoming, which contains the truth of the passage from nothing to being.
     From: report of Georg W.F.Hegel (works [1812]) by Roger Scruton - Short History of Modern Philosophy Ch.12
     A reaction: The idea that one concept 'contains' another, or that an opposition could be 'resolved' by a new concept, sounds doubtful to me. For most analytical philosophers, and for Aristotle, oppositions are contradictions, and cannot and should not be 'resolved'.
7. Existence / A. Nature of Existence / 5. Reason for Existence
Hegel gives an ontological proof of the existence of everything [Hegel, by Scruton]
     Full Idea: It would not be unfair to say that Hegel's metaphysics consists of an ontological proof of the existence of everything.
     From: report of Georg W.F.Hegel (works [1812]) by Roger Scruton - Short History of Modern Philosophy Ch.12
     A reaction: This is so gloriously far from David Hume that we must all find some appeal in it. The next question would be whether necessary existence has been proved. If so, given death, decay and entropy, what is it that has to exist? 2nd Law of Thermodynamics?
7. Existence / C. Structure of Existence / 4. Ontological Dependence
There is 'weak' dependence in one definition, and 'strong' dependence in all the definitions [Fine,K]
     Full Idea: An object 'weakly' depends upon another if it is ineliminably involved in one of its definitions; and it 'strongly' depends upon the other if it is ineliminably involved in all of its definitions.
     From: Kit Fine (Ontological Dependence [1995], III)
     A reaction: It is important to remember that a definition can be very long, and not just what might go into a dictionary.
A natural modal account of dependence says x depends on y if y must exist when x does [Fine,K]
     Full Idea: A natural account of dependence in terms of modality and existence is that one thing x will depend on another thing y just in case it is necessary that y exists if x exists (or in the symbolism of modal logic, □(Ex→Ey).
     From: Kit Fine (Ontological Dependence [1995], I)
     A reaction: He is going to criticise this view (which he traces back to Aristotle and Husserl). It immediately seems possible that there might be counterexamples. x might depend on y, but not necessarily depend on y. Necessities may not produce dependence.
An object depends on another if the second cannot be eliminated from the first's definition [Fine,K]
     Full Idea: The objects upon which a given object depends, according to the present account, are those which must figure in any of the logically equivalent definitions of the object. They will, in a sense, be ineliminable.
     From: Kit Fine (Ontological Dependence [1995], II)
     A reaction: This is Fine's main proposal for the dependency relationship, with a context of Aristotelian essences understood as definitions. Sounds pretty good to me.
Dependency is the real counterpart of one term defining another [Fine,K]
     Full Idea: The notion of one object depending upon another is the real counterpart to the nominal notion of one term being definable in terms of another.
     From: Kit Fine (Ontological Dependence [1995], II)
     A reaction: This begins to fill out the Aristotelian picture very nicely, since definitions are right at the centre of the nature of things (though a much more transitional part of the story than Fine seems to think).
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett]
     Full Idea: The distinction between concrete and abstract objects, or Frege's corresponding distinction between actual and non-actual objects, is not a sharp dichotomy, but resembles a scale upon which objects occupy a range of positions.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18)
     A reaction: This might seem right if you live (as Dummett chooses to) in the fog of language, but it surely can't be right if you think about reality. Is the Equator supposed to be near the middle of his scale? Either there is an equator, or there isn't.
7. Existence / D. Theories of Reality / 2. Realism
Realism is just the application of two-valued semantics to sentences [Dummett]
     Full Idea: Fully fledged realism depends on - indeed, may be identified with - an undiluted application to sentences of the relevant kind of straightforwards two-valued semantics.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
     A reaction: This is the sort of account you get from a whole-heartedly linguistic philosopher. Personally I would say that Dummett has got it precisely the wrong way round: I adopt a two-valued semantics because my metaphysics is realist.
7. Existence / E. Categories / 4. Category Realism
For Hegel, categories shift their form in the course of history [Hegel, by Houlgate]
     Full Idea: For Hegel, the categories of thought are not fixed, eternal forms that remain unchanged throughout history, but are concepts that alter their meaning in history.
     From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - An Introduction to Hegel 01
     A reaction: This results from a critique of Kant's rather rigid view of categories. This idea is very influential, and certainly counts among Hegel's better ideas.
Our concepts and categories disclose the world, because we are part of the world [Hegel, by Houlgate]
     Full Idea: For Hegel, the structure of our concepts and categories is identical with, and thus discloses, the structure of the world itself, because we ourselves are born into and so share the character of the world we encounter.
     From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - An Introduction to Hegel 01
     A reaction: This is a reasonable speculation, but it makes more sense in the context of natural selection, and an empiricist theory of concepts.
7. Existence / E. Categories / 5. Category Anti-Realism
Hegel said Kant's fixed categories actually vary with culture and era [Hegel, by Houlgate]
     Full Idea: Hegel's disagreement with Kant is that categories are not unambiguously universal forms of human understanding, but are conceived in subtly different ways in different cultures and in different historical epochs.
     From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - Hegel p.95
     A reaction: This may be Hegel's most influential idea. Though he hoped that categories would contain truth, by arising untrammelled from reason, and thereby matching reality. His successors seem to have given up on that hope, and settled for relativism.
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalism assumes unmediated mental contact with objects [Dummett]
     Full Idea: The nominalist superstition is based ultimately on the myth of the unmediated presentation of genuine concrete objects to the mind.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18)
     A reaction: Personally I am inclined to favour nominalism and a representative theory of perception, which acknowledges some 'mediation', but of a non-linguistic form. Any good theory here had better include animals, which seem to form concepts.
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
The existence of abstract objects is a pseudo-problem [Dummett]
     Full Idea: The existence of abstract objects is a pseudo-problem.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18)
     A reaction: This remark follows after Idea 9884, which says the abstract/concrete distinction is a sliding scale. Personally I take the distinction to be fairly sharp, and it is therefore probably the single most important problem in the whole of human thought.
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Abstract objects nowadays are those which are objective but not actual [Dummett]
     Full Idea: Objects which are objective but not actual are precisely what are now called abstract objects.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
     A reaction: Why can there not be subjective abstract objects? 'My favourites are x, y and z'. 'I'll decide later what my favourites are'. 'I only buy my favourites - nothing else'.
It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett]
     Full Idea: If someone argued that assuming the existence of the Equator explains nothing, and it has no causal powers, so everything would be the same if it didn't exist, so we needn't accept its existence, we should gape at the crudity of the misunderstanding.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
     A reaction: Not me. I would gape if someone argued that latitude 55° 14' (and an infinity of other lines) exists for the same reasons (whatever they may be) that the Equator exists. A mode of description can't create an object.
'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett]
     Full Idea: 'We've crossed the Equator' is judged true if we are nearer the other Pole, so it not for philosophers to deny that the Earth has an equator, and we see that the Equator is not a concept or relation or function, so it must be classified as an object.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
     A reaction: A lovely example of linguistic philosophy in action (and so much the worse for that, I would say). A useful label here, I suggest (unoriginally, I think), is that we should label such an item a 'semantic object', rather than a real object in our ontology.
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
Abstract objects need the context principle, since they can't be encountered directly [Dummett]
     Full Idea: To recognise that there is no objection in principle to abstract objects requires acknowledgement that some form of the context principle is correct, since abstract objects can neither be encountered nor presented.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16)
     A reaction: I take this to be an immensely important idea. I consider myself to be a philosopher of thought rather than a philosopher of language (Dummett's distinction, he being one of the latter). Thought connects to the world, but does it connect to abstracta?
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
We should understand identity in terms of the propositions it renders true [Fine,K]
     Full Idea: We should understand the identity or being of an object in terms of the propositions rendered true by its identity rather than the other way round.
     From: Kit Fine (Ontological Dependence [1995], I)
     A reaction: Behind this is an essentialist view of identity, rather than one connected with necessary properties.
9. Objects / D. Essence of Objects / 2. Types of Essence
How do we distinguish basic from derived esssences? [Fine,K]
     Full Idea: How and where are we to draw the line between what is basic to the essence and what is derived?
     From: Kit Fine (Ontological Dependence [1995], II)
     A reaction: He calls the basic essence 'constitutive' and the rest the 'consequential' essence. This question is obviously very challenging for the essentialist. See Idea 22.
Maybe some things have essential relationships as well as essential properties [Fine,K]
     Full Idea: It is natural to suppose, in the case of such objects as Wooster and Jeeves, that in addition to possessing constitutive essential properties they will also enter into constitutive essential relationships.
     From: Kit Fine (Ontological Dependence [1995], III)
     A reaction: I like this. If we are going to have scientific essences as structures of intrinsic powers, then the relationships between the parts of the essence must also be essential. That is the whole point - that the powers dictate the relationships.
9. Objects / D. Essence of Objects / 4. Essence as Definition
An object only essentially has a property if that property follows from every definition of the object [Fine,K]
     Full Idea: We can say that an object essentially has a certain property if its having that property follows from every definition of the object, while an object will definitively have a given property if its having that property follows from some definition of it.
     From: Kit Fine (Ontological Dependence [1995], III)
     A reaction: Presumably that will be every accurate definition. This nicely allows for the fact that at least nominal definitions may not be unique, and there is even room for real definitions not to be fully determinate (thus, how far should they extend?).
9. Objects / F. Identity among Objects / 2. Defining Identity
Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett]
     Full Idea: Husserl says the only ground for assuming the replaceability of one content by another is their identity; we are therefore not entitled to define their identity as consisting in their replaceability.
     From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by Michael Dummett - Frege philosophy of mathematics Ch.12
     A reaction: This is a direct challenge to Frege. Tricky to arbitrate, as it is an issue of conceptual priority. My intuition is with Husserl, but maybe the two are just benignly inerdefinable.
Frege introduced criteria for identity, but thought defining identity was circular [Dummett]
     Full Idea: In his middle period Frege rated identity indefinable, on the ground that every definition must take the form of an identity-statement. Frege introduced the notion of criterion of identity, which has been widely used by analytical philosophers.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.10)
     A reaction: The objection that attempts to define identity would be circular sounds quite plausible. It sounds right to seek a criterion for type-identity (in shared properties or predicates), but token-identity looks too fundamental to give clear criteria.
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
Hegel reputedly claimed to know a priori that there are five planets [Hegel, by Field,H]
     Full Idea: Hegel is reputed to have claimed to have deduced on a priori grounds that the number of planets is exactly five.
     From: report of Georg W.F.Hegel (works [1812]) by Hartry Field - Recent Debates on the A Priori 1
     A reaction: Even if this is a wicked travesty of Hegel, it will do nicely to represent the extremes of claims to a priori synthetic knowledge. Field doesn't offer any evidence. I would love it to be true.
18. Thought / D. Concepts / 4. Structure of Concepts / i. Conceptual priority
Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett]
     Full Idea: One powerful argument for a thesis that one notion is conceptually prior to another is the possibility of defining the first without reference to the second.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12)
     A reaction: You'd better check whether you can't also define the second without reference to the first before you rank their priority. And maybe 'conceptual priority' is conceptually prior to 'definition' (i.e. definition needs a knowledge of priority). Help!
An argument for conceptual priority is greater simplicity in explanation [Dummett]
     Full Idea: An argument for conceptual priority is greater simplicity in explanation.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12)
     A reaction: One might still have to decide priority between two equally simple (or complex) concepts. I begin to wonder whether 'priority' has any other than an instrumental meaning (according to which direction you wish to travel - is London before Edinburgh?).
18. Thought / E. Abstraction / 1. Abstract Thought
Abstract terms are acceptable as long as we know how they function linguistically [Dummett]
     Full Idea: To recognise abstract terms as perfectly proper items of a vocabulary depends upon allowing that all that is necessary for the lawful introduction of a range of expressions into the language is a coherent account of how they are to function in sentences.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16)
     A reaction: Why can't the 'coherent account' of the sentences include the fact that there must be something there for the terms to refer to? How else are we to eliminate nonsense words which obey good syntactical rules? Cf. Idea 9872.
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait]
     Full Idea: Dummett uses the term 'logical abstraction' for the construction of the abstract objects as equivalence classes, but it is not clear why we should call this construction 'logical'.
     From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by William W. Tait - Frege versus Cantor and Dedekind n 14
     A reaction: This is a good objection, and Tait offers a much better notion of 'logical abstraction' (as involving preconditions for successful inference), in Idea 9981.
We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett]
     Full Idea: We arrive at the concept of suicide by considering both occurrences in the sentence 'Cato killed Cato' of the proper name 'Cato' as simultaneously replaceable by another name, say 'Brutus', and so apprehending the pattern common to both sentences.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.14)
     A reaction: This is intended to illustrate Frege's 'logical abstraction' technique, as opposed to wicked psychological abstraction. The concept of suicide is the pattern 'x killed x'. This is a crucial example if we are to understand abstraction...
18. Thought / E. Abstraction / 8. Abstractionism Critique
To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett]
     Full Idea: To get units by abstraction, units arrived at by abstraction from forks must the identical to that abstracted from spoons, with no trace of individuality. But if spoons can no longer be differentiated from forks, they can't differ from one another either.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8)
     A reaction: [compressed] Dummett makes the point better than Frege did. Can we 'think of a fork insofar as it is countable, ignoring its other features'? What are we left thinking of? Frege says it must still be the whole fork. 'Nice fork, apart from the colour'.
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
     Full Idea: A Fregean semantics assumes a domain already determinately articulated into individual objects.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8)
     A reaction: A more interesting criticism than most of Dummett's other challenges to the Frege/Davidson view. I am beginning to doubt whether the semantics and the ontology can ever be divorced from the psychology, of thought, interests, focus etc.
23. Ethics / F. Existentialism / 1. Existentialism
Humans have no fixed identity, but produce and reveal their shifting identity in history [Hegel, by Houlgate]
     Full Idea: For Hegel, the absolute truth of humanity is that human beings have no fixed, given identity, but rather determine and produce their own identity and their world in history, and that they gradually come to the recognition of this fact in history.
     From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - An Introduction to Hegel 01
     A reaction: This quintessentially existentialist idea, most obvious in Sartre, seems to have originated with this view of Hegel's.
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
Hegel's Absolute Spirit is the union of human rational activity at a moment, and whatever that sustains [Hegel, by Eldridge]
     Full Idea: We may take Hegel's Absolute Spirit to be the union of collective, human rational activity at a historical moment with its proper object, the forms of social and individual life that the rational activity is devoted to understanding and sustaining.
     From: report of Georg W.F.Hegel (works [1812]) by Richard Eldridge - G.W.F. Hegel (aesthetics) 1
     A reaction: From this formulation it sounds as if the whole human race might have momentary union, but presumably it is more local 'peoples' that can exhibit this.
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Society isn’t founded on a contract, since contracts presuppose a society [Hegel, by Scruton]
     Full Idea: For Hegel, society cannot be founded on a contract, since contracts have no reality until society is in place.
     From: report of Georg W.F.Hegel (works [1812]) by Roger Scruton - Modern Philosophy:introduction and survey 28.2
     A reaction: Interesting, and reminiscent of the private language argument, but contracts surely start as deals between individuals (on a desert island?).
26. Natural Theory / A. Speculations on Nature / 1. Nature
When man wills the natural, it is no longer natural [Hegel]
     Full Idea: When man wills the natural, it is no longer natural.
     From: Georg W.F.Hegel (works [1812]), quoted by Rosalind Hursthouse - On Virtue Ethics Ch.4
     A reaction: Sounds good, though I'm not sure what it means. The application of the word 'natural' seems a bit arbitrary to me. No objective joint exists between the natural and unnatural. The default position has to be that everything is natural.
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]
     Full Idea: By what right do we assume that the limit of measurement is a point, and not an interval?
     From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit')
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
Hegel's entire philosophy is nothing but a monstrous amplification of the ontological proof [Schopenhauer on Hegel]
     Full Idea: Hegel's entire philosophy is nothing but a monstrous amplification of the ontological proof.
     From: comment on Georg W.F.Hegel (works [1812]) by Arthur Schopenhauer - Abstract of 'The Fourfold Root' Ch.II
     A reaction: All massive a priori metaphysics is summed up in this argument, which is right at the core of philosophy.
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Hegel said he was offering an encyclopaedic rationalisation of Christianity [Hegel, by Graham]
     Full Idea: Hegel claimed that his philosophy was nothing less than an encyclopaedic rationalisation of the Christian religion.
     From: report of Georg W.F.Hegel (works [1812]) by Gordon Graham - Eight Theories of Ethics Ch.5
     A reaction: Why did he pick Christianity to rationalise? How can you reason properly if you start with a dogma?