Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Will Kymlicka and Penelope Maddy

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119 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
'Forcing' can produce new models of ZFC from old models [Maddy]
     Full Idea: Cohen's method of 'forcing' produces a new model of ZFC from an old model by appending a carefully chosen 'generic' set.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.4)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy]
     Full Idea: A possible axiom is the Large Cardinal Axiom, which asserts that there are more and more stages in the cumulative hierarchy. Infinity can be seen as the first of these stages, and Replacement pushes further in this direction.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.5)
New axioms are being sought, to determine the size of the continuum [Maddy]
     Full Idea: In current set theory, the search is on for new axioms to determine the size of the continuum.
     From: Penelope Maddy (Believing the Axioms I [1988], §0)
     A reaction: This sounds the wrong way round. Presumably we seek axioms that fix everything else about set theory, and then check to see what continuum results. Otherwise we could just pick our continuum, by picking our axioms.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
The Axiom of Extensionality seems to be analytic [Maddy]
     Full Idea: Most writers agree that if any sense can be made of the distinction between analytic and synthetic, then the Axiom of Extensionality should be counted as analytic.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.1)
     A reaction: [Boolos is the source of the idea] In other words Extensionality is not worth discussing, because it simply tells you what the world 'set' means, and there is no room for discussion about that. The set/class called 'humans' varies in size.
Extensional sets are clearer, simpler, unique and expressive [Maddy]
     Full Idea: The extensional view of sets is preferable because it is simpler, clearer, and more convenient, because it individuates uniquely, and because it can simulate intensional notions when the need arises.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.1)
     A reaction: [She cites Fraenkel, Bar-Hillet and Levy for this] The difficulty seems to be whether the extensional notion captures our ordinary intuitive notion of what constitutes a group of things, since that needs flexible size and some sort of unity.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
     Full Idea: The Axiom of Infinity is a simple statement of Cantor's great breakthrough. His bold hypothesis that a collection of elements that had lurked in the background of mathematics could be infinite launched modern mathematics.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.5)
     A reaction: It also embodies one of those many points where mathematics seems to depart from common sense - but then most subjects depart from common sense when they get more sophisticated. Look what happened to art.
Infinite sets are essential for giving an account of the real numbers [Maddy]
     Full Idea: If one is interested in analysis then infinite sets are indispensable since even the notion of a real number cannot be developed by means of finite sets alone.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.5)
     A reaction: [Maddy is citing Fraenkel, Bar-Hillel and Levy] So Cantor's great breakthrough (Idea 13021) actually follows from the earlier acceptance of the real numbers, so that's where the departure from common sense started.
Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy]
     Full Idea: The axiom of infinity: that there are infinite sets is to claim that completed infinite collections can be treated mathematically. In its standard contemporary form, the axioms assert the existence of the set of all finite ordinals.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.3)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
     Full Idea: The Power Set Axiom is indispensable for a set-theoretic account of the continuum, ...and in so far as those attempts are successful, then the power-set principle gains some confirmatory support.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.6)
     A reaction: The continuum is, of course, notoriously problematic. Have we created an extra problem in our attempts at solving the first one?
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy]
     Full Idea: In the presence of other axioms, the Axiom of Foundation is equivalent to the claim that every set is a member of some Vα.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.3)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Efforts to prove the Axiom of Choice have failed [Maddy]
     Full Idea: Jordain made consistent and ill-starred efforts to prove the Axiom of Choice.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.7)
     A reaction: This would appear to be the fate of most axioms. You would presumably have to use a different system from the one you are engaged with to achieve your proof.
Modern views say the Choice set exists, even if it can't be constructed [Maddy]
     Full Idea: Resistance to the Axiom of Choice centred on opposition between existence and construction. Modern set theory thrives on a realistic approach which says the choice set exists, regardless of whether it can be defined, constructed, or given by a rule.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.7)
     A reaction: This seems to be a key case for the ontology that lies at the heart of theory. Choice seems to be an invaluable tool for proofs, so it won't go away, so admit it to the ontology. Hm. So the tools of thought have existence?
A large array of theorems depend on the Axiom of Choice [Maddy]
     Full Idea: Many theorems depend on the Axiom of Choice, including that a countable union of sets is countable, and results in analysis, topology, abstract algebra and mathematical logic.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.7)
     A reaction: The modern attitude seems to be to admit anything if it leads to interesting results. It makes you wonder about the modern approach of using mathematics and logic as the cutting edges of ontological thinking.
The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
     Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original.
     From: Penelope Maddy (Defending the Axioms [2011], 1.3)
     A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Axiom of Reducibility: propositional functions are extensionally predicative [Maddy]
     Full Idea: The Axiom of Reducibility states that every propositional function is extensionally equivalent to some predicative proposition function.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1)
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
     Full Idea: The Iterative Conception (Zermelo 1930) says everything appears at some stage. Given two objects a and b, let A and B be the stages at which they first appear. Suppose B is after A. Then the pair set of a and b appears at the immediate stage after B.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.3)
     A reaction: Presumably this all happens in 'logical time' (a nice phrase I have just invented!). I suppose we might say that the existence of the paired set is 'forced' by the preceding sets. No transcendental inferences in this story?
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
     Full Idea: The 'limitation of size' is a vague intuition, based on the idea that being too large may generate the paradoxes.
     From: Penelope Maddy (Believing the Axioms I [1988], §1.3)
     A reaction: This is an intriguing idea to be found right at the centre of what is supposed to be an incredibly rigorous system.
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
The master science is physical objects divided into sets [Maddy]
     Full Idea: The master science can be thought of as the theory of sets with the entire range of physical objects as ur-elements.
     From: Penelope Maddy (Sets and Numbers [1981], II)
     A reaction: This sounds like Quine's view, since we have to add sets to our naturalistic ontology of objects. It seems to involve unrestricted mereology to create normal objects.
Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
     Full Idea: Maddy dispenses with pure sets, by sketching a strong set theory in which everything is either a physical object or a set of sets of ...physical objects. Eventually a physiological story of perception will extend to sets of physical objects.
     From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3
     A reaction: This doesn't seem to find many supporters, but if we accept the perception of resemblances as innate (as in Hume and Quine), it is isn't adding much to see that we intrinsically see things in groups.
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Henkin semantics is more plausible for plural logic than for second-order logic [Maddy]
     Full Idea: Henkin-style semantics seem to me more plausible for plural logic than for second-order logic.
     From: Penelope Maddy (Second Philosophy [2007], III.8 n1)
     A reaction: Henkin-style semantics are presented by Shapiro as the standard semantics for second-order logic.
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
     Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation.
     From: Penelope Maddy (Defending the Axioms [2011], 3.3)
     A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics.
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
'Propositional functions' are propositions with a variable as subject or predicate [Maddy]
     Full Idea: A 'propositional function' is generated when one of the terms of the proposition is replaced by a variable, as in 'x is wise' or 'Socrates'.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1)
     A reaction: This implies that you can only have a propositional function if it is derived from a complete proposition. Note that the variable can be in either subject or in predicate position. It extends Frege's account of a concept as 'x is F'.
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
     Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers.
     From: Penelope Maddy (Defending the Axioms [2011], 1.3)
If two mathematical themes coincide, that suggest a single deep truth [Maddy]
     Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth.
     From: Penelope Maddy (Defending the Axioms [2011], 5.3ii)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
Cantor and Dedekind brought completed infinities into mathematics [Maddy]
     Full Idea: Both Cantor's real number (Cauchy sequences of rationals) and Dedekind's cuts involved regarding infinite items (sequences or sets) as completed and subject to further manipulation, bringing the completed infinite into mathematics unambiguously.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1 n39)
     A reaction: So it is the arrival of the real numbers which is the culprit for lumbering us with weird completed infinites, which can then be the subject of addition, multiplication and exponentiation. Maybe this was a silly mistake?
Completed infinities resulted from giving foundations to calculus [Maddy]
     Full Idea: The line of development that finally led to a coherent foundation for the calculus also led to the explicit introduction of completed infinities: each real number is identified with an infinite collection of rationals.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.3)
     A reaction: Effectively, completed infinities just are the real numbers.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
     Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals.
     From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
Infinity has degrees, and large cardinals are the heart of set theory [Maddy]
     Full Idea: The stunning discovery that infinity comes in different degrees led to the theory of infinite cardinal numbers, the heart of contemporary set theory.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1)
     A reaction: It occurs to me that these huge cardinals only exist in set theory. If you took away that prop, they would vanish in a puff.
For any cardinal there is always a larger one (so there is no set of all sets) [Maddy]
     Full Idea: By the mid 1890s Cantor was aware that there could be no set of all sets, as its cardinal number would have to be the largest cardinal number, while his own theorem shows that for any cardinal there is a larger.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1)
     A reaction: There is always a larger cardinal because of the power set axiom. Some people regard that with suspicion.
An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy]
     Full Idea: An 'inaccessible' cardinal is one that cannot be reached by taking unions of small collections of smaller sets or by taking power sets.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.5)
     A reaction: They were introduced by Hausdorff in 1908.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
Theorems about limits could only be proved once the real numbers were understood [Maddy]
     Full Idea: Even the fundamental theorems about limits could not [at first] be proved because the reals themselves were not well understood.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.2)
     A reaction: This refers to the period of about 1850 (Weierstrass) to 1880 (Dedekind and Cantor).
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
The extension of concepts is not important to me [Maddy]
     Full Idea: I attach no decisive importance even to bringing in the extension of the concepts at all.
     From: Penelope Maddy (Naturalism in Mathematics [1997], §107)
     A reaction: He almost seems to equate the concept with its extension, but that seems to raise all sorts of questions, about indeterminate and fluctuating extensions.
In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy]
     Full Idea: In the ZFC cumulative hierarchy, Frege's candidates for numbers do not exist. For example, new three-element sets are formed at every stage, so there is no stage at which the set of all three-element sets could he formed.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.2)
     A reaction: Ah. This is a very important fact indeed if you are trying to understand contemporary discussions in philosophy of mathematics.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
Frege solves the Caesar problem by explicitly defining each number [Maddy]
     Full Idea: To solve the Julius Caesar problem, Frege requires explicit definitions of the numbers, and he proposes his well-known solution: the number of Fs = the extension of the concept 'equinumerous with F' (based on one-one correspondence).
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1)
     A reaction: Why do there have to be Fs before there can be the corresponding number? If there were no F for 523, would that mean that '523' didn't exist (even if 522 and 524 did exist)?
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy]
     Full Idea: If you wonder why multiplication is commutative, you could prove it from the Peano postulates, but the proof offers little towards an answer. In set theory Cartesian products match 1-1, and n.m dots when turned on its side has m.n dots, which explains it.
     From: Penelope Maddy (Sets and Numbers [1981], II)
     A reaction: 'Turning on its side' sounds more fundamental than formal set theory. I'm a fan of explanation as taking you to the heart of the problem. I suspect the world, rather than set theory, explains the commutativity.
Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy]
     Full Idea: The standard account of the relationship between numbers and sets is that numbers simply are certain sets. This has the advantage of ontological economy, and allows numbers to be brought within the epistemology of sets.
     From: Penelope Maddy (Sets and Numbers [1981], III)
     A reaction: Maddy votes for numbers being properties of sets, rather than the sets themselves. See Yourgrau's critique.
Numbers are properties of sets, just as lengths are properties of physical objects [Maddy]
     Full Idea: I propose that ...numbers are properties of sets, analogous, for example, to lengths, which are properties of physical objects.
     From: Penelope Maddy (Sets and Numbers [1981], III)
     A reaction: Are lengths properties of physical objects? A hole in the ground can have a length. A gap can have a length. Pure space seems to contain lengths. A set seems much more abstract than its members.
A natural number is a property of sets [Maddy, by Oliver]
     Full Idea: Maddy takes a natural number to be a certain property of sui generis sets, the property of having a certain number of members.
     From: report of Penelope Maddy (Realism in Mathematics [1990], 3 §2) by Alex Oliver - The Metaphysics of Properties
     A reaction: [I believe Maddy has shifted since then] Presumably this will make room for zero and infinities as natural numbers. Personally I want my natural numbers to count things.
Making set theory foundational to mathematics leads to very fruitful axioms [Maddy]
     Full Idea: The set theory axioms developed in producing foundations for mathematics also have strong consequences for existing fields, and produce a theory that is immensely fruitful in its own right.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.2)
     A reaction: [compressed] Second of Maddy's three benefits of set theory. This benefit is more questionable than the first, because the axioms may be invented because of their nice fruit, instead of their accurate account of foundations.
Unified set theory gives a final court of appeal for mathematics [Maddy]
     Full Idea: The single unified area of set theory provides a court of final appeal for questions of mathematical existence and proof.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.2)
     A reaction: Maddy's third benefit of set theory. 'Existence' means being modellable in sets, and 'proof' means being derivable from the axioms. The slightly ad hoc character of the axioms makes this a weaker defence.
Set theory brings mathematics into one arena, where interrelations become clearer [Maddy]
     Full Idea: Set theoretic foundations bring all mathematical objects and structures into one arena, allowing relations and interactions between them to be clearly displayed and investigated.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.2)
     A reaction: The first of three benefits of set theory which Maddy lists. The advantages of the one arena seem to be indisputable.
Identifying geometric points with real numbers revealed the power of set theory [Maddy]
     Full Idea: The identification of geometric points with real numbers was among the first and most dramatic examples of the power of set theoretic foundations.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.2)
     A reaction: Hence the clear definition of the reals by Dedekind and Cantor was the real trigger for launching set theory.
The line of rationals has gaps, but set theory provided an ordered continuum [Maddy]
     Full Idea: The structure of a geometric line by rational points left gaps, which were inconsistent with a continuous line. Set theory provided an ordering that contained no gaps. These reals are constructed from rationals, which come from integers and naturals.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.2)
     A reaction: This completes the reduction of geometry to arithmetic and algebra, which was launch 250 years earlier by Descartes.
Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
     Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness.
     From: Penelope Maddy (Defending the Axioms [2011], 3.4)
     A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics.
Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy]
     Full Idea: Our much loved mathematical knowledge rests on two supports: inexorable deductive logic (the stuff of proof), and the set theoretic axioms.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I Intro)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy]
     Full Idea: I am not suggesting a reduction of number theory to set theory ...There are only sets with number properties; number theory is part of the theory of finite sets.
     From: Penelope Maddy (Sets and Numbers [1981], V)
Sets exist where their elements are, but numbers are more like universals [Maddy]
     Full Idea: A set of things is located where the aggregate of those things is located, ...but a number is simultaneously located at many different places (10 in my hand, and a baseball team) ...so numbers seem more like universals than particulars.
     From: Penelope Maddy (Sets and Numbers [1981], III)
     A reaction: My gut feeling is that Maddy's master idea (of naturalising sets by building them from ur-elements of natural objects) won't work. Sets can work fine in total abstraction from nature.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
If mathematical objects exist, how can we know them, and which objects are they? [Maddy]
     Full Idea: The popular challenges to platonism in philosophy of mathematics are epistemological (how are we able to interact with these objects in appropriate ways) and ontological (if numbers are sets, which sets are they).
     From: Penelope Maddy (Sets and Numbers [1981], I)
     A reaction: These objections refer to Benacerraf's two famous papers - 1965 for the ontology, and 1973 for the epistemology. Though he relied too much on causal accounts of knowledge in 1973, I'm with him all the way.
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
     Full Idea: Maddy says that intuition alone does not support very much mathematics; more importantly, a naturalist cannot accept intuition at face value, but must ask why we are justified in relying on intuition.
     From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3
     A reaction: It depends what you mean by 'intuition', but I identify with her second objection, that every faculty must ultimately be subject to criticism, which seems to point to a fairly rationalist view of things.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
     Full Idea: Maddy proposes that we can know (some) mind-independent mathematical truths through knowing about sets, and that we can obtain knowledge of sets through experience.
     From: report of Penelope Maddy (Realism in Mathematics [1990]) by Carrie Jenkins - Grounding Concepts 6.5
     A reaction: Maddy has since backed off from this, and now tries to merely defend 'objectivity' about sets (2011:114). My amateurish view is that she is overrating the importance of sets, which merely model mathematics. Look at category theory.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy]
     Full Idea: Crudely, the scientist posits only those entities without which she cannot account for observations, while the set theorist posits as many entities as she can, short of inconsistency.
     From: Penelope Maddy (Naturalism in Mathematics [1997], II.5)
Maybe applications of continuum mathematics are all idealisations [Maddy]
     Full Idea: It could turn out that all applications of continuum mathematics in natural sciences are actually instances of idealisation.
     From: Penelope Maddy (Naturalism in Mathematics [1997], II.6)
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
     Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics.
     From: Penelope Maddy (Defending the Axioms [2011], 2.3)
     A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor.
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy]
     Full Idea: Number words are not like normal adjectives. For example, number words don't occur in 'is (are)...' contexts except artificially, and they must appear before all other adjectives, and so on.
     From: Penelope Maddy (Sets and Numbers [1981], IV)
     A reaction: [She is citing Benacerraf's arguments]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy]
     Full Idea: Recent commentators have noted that Frege's versions of the basic propositions of arithmetic can be derived from Hume's Principle alone, that the fatal Law V is only needed to derive Hume's Principle itself from the definition of number.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1)
     A reaction: Crispin Wright is the famous exponent of this modern view. Apparently Charles Parsons (1965) first floated the idea.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy]
     Full Idea: The case of atoms makes it clear that the indispensable appearance of an entity in our best scientific theory is not generally enough to convince scientists that it is real.
     From: Penelope Maddy (Naturalism in Mathematics [1997], II.6)
     A reaction: She refers to the period between Dalton and Einstein, when theories were full of atoms, but there was strong reluctance to actually say that they existed, until the direct evidence was incontrovertable. Nice point.
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]
     Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles.
     From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro'
     A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture?
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy]
     Full Idea: In science we treat the earth's surface as flat, we assume the ocean to be infinitely deep, we use continuous functions for what we know to be quantised, and we take liquids to be continuous despite atomic theory.
     From: Penelope Maddy (Naturalism in Mathematics [1997], II.6)
     A reaction: If fussy people like scientists do this all the time, how much more so must the confused multitude be doing the same thing all day?
16. Persons / E. Rejecting the Self / 2. Self as Social Construct
The 'Kantian' self steps back from commitment to its social situation [Kymlicka]
     Full Idea: The 'Kantian' view of the self strongly defends the view that the self is prior to its socially given roles and relationships, and is free only if it is capable of holding these features of its social situation at a distance, and judging them by reason.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 6.3)
     A reaction: There is no correct answer here, because I am capable of Kantian distancing, and also capable of submersing myself in the social constructions around me. If society fosters rebellion (1810s, 1960s) then we become more Kantian.
22. Metaethics / C. The Good / 1. Goodness / c. Right and good
Teleological theories give the good priority over concern for people [Kymlicka]
     Full Idea: Teleological theories take concern for the good (e.g. freedom or utility) as fundamental, and concern for people as derivative.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.4.a.ii)
     A reaction: There's a nice fundamental question with which to begin a discussion of value: which matters most - abstract values, or individual people? Placing a collective of people first (Stalinism?) seems to fall between them.
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
Maybe the particularist moral thought of women is better than the impartial public thinking of men [Kymlicka]
     Full Idea: There is a significant strand of contemporary feminism which argues that we should take seriously women's different morality. ...The particularistic thought women employ is a better morality than the impartial thought men employ in the public sphere.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 7.3)
     A reaction: I had taken Particularism to be an offshoot of virtue theory, as promulgated by Jonathan Dancy. Evidently the influence of feminism is strong. Personally I think the world would be a better place if it was run by women.
23. Ethics / E. Utilitarianism / 1. Utilitarianism
One view says start with equality, and infer equal weight to interests, and hence maximum utility [Kymlicka]
     Full Idea: The first main argument for utilitarianism is that people matter equally, and hence each person's interests should be given equal weight, and hence morally right acts will maximise utility.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.4.a)
     A reaction: The point is that this starts from the aim of equality, and infers maximum utility as its consequence. Equality has a primitive value. Whenever you dig down to a primitive value in a theory, I just find myself puzzled. What can justify basic equality?
A second view says start with maximising the good, implying aggregation, and hence equality [Kymlicka]
     Full Idea: The second main argument for utilitarianism defines the right in terms of maximising the good, which leads to the utilitarian aggregation standard, which as a mere consequence treats people's interests equally.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.4.b)
     A reaction: This takes maximum good as a primitive, and arrives at equality as the way to achieve it. So which is more morally fundamental, a maximum of goodness, or human equality? Kymlicka says this idea is too impersonal.
Utilitarianism is not a decision-procedure; choice of the best procedure is an open question [Kymlicka]
     Full Idea: Utilitarianism is essentially a 'standard of rightness', not a 'decision-procedure'. ...It is an open question whether we should employ a utilitarian decision-procedure - indeed, this question itself is to be answered by examining its consequences.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.3.b)
     A reaction: The point is that the aim is to maximise happiness, and you might do that by just maximising baked bean consumption, and not even thinking about happiness. This idea is labelled 'indirect utilitarianism'. Happiness does seem to be a by-product.
24. Political Theory / A. Basis of a State / 2. Population / a. Human population
To maximise utility should we double the population, even if life somewhat deteriorates? [Kymlicka]
     Full Idea: Morally, should we double the population, even if it means reducing each person's welfare by almost half (since that will still increase overall utility)?
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.4.b)
     A reaction: [He cites Derek Parfit for this] The key word is 'almost', which ensures a small increase in overall utility. I think this is a particularly good objection to utilitarianism, which aims to maximise an abstraction called 'utility'.
24. Political Theory / A. Basis of a State / 4. Original Position / c. Difference principle
The difference principles says we must subsidise the costs of other people's choices [Kymlicka]
     Full Idea: The difference principle does not make any distinction between chosen and unchosen inequalities, ....but the difference principle requires that some people subsidise the costs of other people's choices.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 3.3.b.2)
     A reaction: We do this in education, allowing people to study things in which we can see little point. We subsidise public ceremonies which strike us as ridiculous.
24. Political Theory / B. Nature of a State / 2. State Legitimacy / a. Sovereignty
Liberal state legitimacy is based on a belief in justice, not in some conception of the good life [Kymlicka]
     Full Idea: For liberals the basis of state legitimacy is a shared sense of justice, not a shared conception of the good.
     From: Will Kymlicka (Community [1993], 'legitimacy')
     A reaction: For a liberal state to work, the citizens have to roughly believe in the core values of liberalism, which are primarily freedom and equality (and hence justice).
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Social contract theories are usually rejected because there never was such a contract [Kymlicka]
     Full Idea: Social contract theories have all been subjected to the same criticism - that there never was such a state of nature, or such a contract. Hence neither citizens nor government are bound by it. Contracts only create obligations if they are actually agreed.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 3.3)
     A reaction: Even if they have been agreed in the past, why should subsequent generations be bound to them? Modern Germans aren't bound by their grandparents' oaths of allegiance to fascism.
24. Political Theory / B. Nature of a State / 4. Citizenship
Some liberals thinks checks and balances are enough, without virtuous citizens [Kymlicka]
     Full Idea: Many classical liberals believed that a liberal democracy could function effectively even in the absence of an especially virtuous citizenry, by creating checks and balances. …One set of private interests would check another set of private interests.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7)
     A reaction: This seems to be the view of those who think a completely free market will evolve into a flourishing and just society. There is a basic debate about the importance of the character of the citizens in any polity. Marxists say they are entangled.
Good citizens need civic virtues of loyalty, independence, diligence, respect, etc. [Kymlicka]
     Full Idea: Galston says responsible citizenship requires four types of civic virtue: general (law-abiding, loyal), social (independent, open-minded), economic (diligent, restrained, adaptable), and political (respect, sensible, judgement, engagement).
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7)
     A reaction: [Galston's 'Liberal Purposes' 1991] (compressed) This immediately seems to be asking too much, especially for those who know little, or are short of money.
Liberals accept that people need society, but Aristotelians must show that they need political activity [Kymlicka]
     Full Idea: To defend Aristotelian republicanism it is not enough to show that individual require society - liberals do not deny this. They must also show that individuals need to be politically active.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7)
     A reaction: Interesting. People are not just inactive because they have been rendered powerless. In any group of people there are some who are keen to have a voice, or lead, and others who are largely happy to follow.
Minimal liberal citizenship needs common civility, as well as mere non-interference [Kymlicka]
     Full Idea: Minimal citizenship is often seen as simply requiring non-interference with others, but that ignores a basic requirement of liberal citizenship, which is the social virtue of 'civility' or 'decency'.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7)
     A reaction: He makes the point that the minimal requirement has to be given up when there is a crisis, which needs much more involvement. This largely describes modern Britain, prior to the Brexit rift.
Modern non-discrimination obliges modern citizens to treat each other as equals [Kymlicka]
     Full Idea: The extension of non-discrimination from government to civil society …involves a radical extension of the obligations of liberal citizenship. The obligation to treat people as equal citizens now applies to everyday decisions.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7)
     A reaction: This is very difficult for an older generation who felt their 'entitlement' as leading citizens, or who routinely favoured their local traditional community. But they just have to 'get over it'!
The right wing sees citizenship in terms of responsibility to earn a living, rather than rights [Kymlicka]
     Full Idea: According to the New Right, to promote active citizenship-for-all or entitlements, we must focus instead on people's responsibility to earn a living.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7)
     A reaction: Every creature has to earn a living, but one method is to successfully sponge off others. A cushy job is a sort of sponging. An excessively well paid job is a sort of sponging. Citizenship must involve responsibilities of some sort.
24. Political Theory / B. Nature of a State / 5. Culture
Liberals say state intervention in culture restricts people's autonomy [Kymlicka]
     Full Idea: According to liberal theory, a state which intervenes in the cultural market place to encourage any particular way of life restricts people's autonomy.
     From: Will Kymlicka (Community [1993], 'social')
     A reaction: The communitarian idea is that the state should intervene, in order to foster the best aspects of communal culture. The dangers are obvious, and can be seen in any totalitarian state. A gentle hand on the tiller, perhaps? Increase the options?
24. Political Theory / D. Ideologies / 4. Social Utilitarianism
Utilitarianism is no longer a distinctive political position [Kymlicka]
     Full Idea: Modern utilitarianism, despite its radical heritage, no longer defines a distinctive political position.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.6)
     A reaction: This is his final sentence on the topic. I suppose utilitarianism exists as a moral theory at too high a level of generality to count as a political theory.
The quest of the general good is partly undermined by people's past entitlements [Kymlicka]
     Full Idea: The existence of past entitlements on the part of particular people partially pre-empts, or constrains, the utilitarian quest to maximise the general good.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.3.a)
     A reaction: In other words, there is never a clean slate in politics (except in some hideously violent revolution). You might be able to justify to someone a withdrawal of their past entitlements. E.g. confiscating a stolen painting that was bought in ignorance.
We shouldn't endorse preferences which reject equality, and show prejudice and selfishness [Kymlicka]
     Full Idea: Equality should enter into the very formation of our preferences. ....Prejudiced and selfish preferences should be excluded from the start, for they already reflect a failure to show equal consideration.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.5.b)
     A reaction: This is meant to block utilitarian summing of preferences like racism, but it feels like a rather desperate attempt to get righteous liberal values in at the beginning, where they can't be questioned. How can you justify equal respect and treatment?
Using utilitarian principles to make decisions encourages cold detachment from people [Kymlicka]
     Full Idea: Acting directly on utilitarian grounds is counter-productive, for it encourages a contingent and detached attitude towards what should be whole-hearted personal and political commitments.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.7)
     A reaction: I've always seen this as an objection to utilitarianism, but I now see that it is only an objection to the decision procedure. We should be warm-hearted and committed, in the knowledge that this will increase benefits to all. Hm. A bit schizoid.
Utilitarianism is irrational if it tells you to trade in your rights and resources just for benefits [Kymlicka]
     Full Idea: Utilitarianism is an irrational choice, for it is rational to ensure your basic rights and resources are protected, even if you thereby lessen your chance of receiving benefits above and beyond the basic goods that you seek to protect.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 3.3)
     A reaction: [He's discussing Rawls] Utilitarians would obviously respond to this by saying that the rights and resources are needed to protect future benefits, so it would be short-termism to trade them in now.
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
Modern democratic theory focuses on talk, not votes, because we need consensus or compromise [Kymlicka]
     Full Idea: Modern discussion has shifted from 'vote-centric' (or 'aggregative') to 'talk-centric' democracy. The vote-centric model has no mechanism for developing a consensus, or shaping public opinion, or even formulating an honourable compromise.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7)
     A reaction: I'm struck by the fact that a person's preferences betweent these two is a reflection of character, or basic attitudes to morality. Some people think democratically about their relationships, and others very obviously don't.
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
In a liberal democracy all subjects of authority have a right to determine the authority [Kymlicka]
     Full Idea: A liberal-democratic system is one in which those people who are subject to political authority have a right to participate in determining that authority.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.4)
     A reaction: This applies to immigrants. The most anti-democratic move in recent democracies is the strategy of trying to make it more difficult to vote, perhaps by demanding identification documents, or creating huge queues.
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
Modern liberalism has added personal privacy to our personal social lives [Kymlicka]
     Full Idea: Modern liberalism is concerned not only to protect the private sphere of social life, but also to carve out a realm within the private sphere where individuals can have privacy.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 7.2.b)
     A reaction: Interestingly, he associates this development with the romantic movement, which designated social interaction as public and political, creating a need for true privacy. Privacy is the blessing and blight of the modern world.
We have become attached to private life because that has become greatly enriched [Kymlicka]
     Full Idea: Our attachment to private life, I believe, is the result not (or not only) of the impoverishment of public life, but the enrichment of private life.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7)
     A reaction: Interesting. Perhaps a sentiment expected more from a university lecturer than from a poorly-paid labourer. Does he mean watching innumerable TV shows instead of having sing-songs in the local pub? Increased leisure is indisputable.
24. Political Theory / D. Ideologies / 6. Liberalism / d. Liberal freedom
Liberalism tends to give priority to basic liberties [Kymlicka]
     Full Idea: One way of differentiating liberalism is that it gives priority to the basic liberties.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 3.1.b)
     A reaction: [He is citing Rawls for this] This is not the same as extreme libertarianism, which makes liberty the only priority. The issue would be over which liberties count as 'basic'. Taxation would be a good test case.
24. Political Theory / D. Ideologies / 6. Liberalism / e. Liberal community
Liberals are not too individualistic, because people recognise and value social relations [Kymlicka]
     Full Idea: It is alleged that liberals fail to recognise that people are naturally social or communal. …But liberals believe that people form and join social relations in which they come to understand and pursue the good.
     From: Will Kymlicka (Liberal Individualism and Liberal Neutrality [1989], Conc)
     A reaction: This is particulary aimed at communitarians, who see liberalism as based on a distorted concept of people as isolated beings. Personally I am beginning to shift my views from Aristotelian communitarianism to modern liberalism, so I like this idea.
Modern liberals see a community as simply a society which respects freedom and equality [Kymlicka]
     Full Idea: Most contemporary liberal philosophers have little to say about the ideal of community. …It is often seen as derivative of liberty and equality - a society lives up to the ideal of community if its members are treated as free and equal persons.
     From: Will Kymlicka (Community [1993], 'Intro')
     A reaction: He cites Rawls as an example. This is the central idea which was attacked by modern communitarians. A collection of scattered self-seeking isolated individuals doesn't seem to amount to a healthy communal life. Maybe community needs further rights?
Liberals must avoid an official culture, as well as an official religion [Kymlicka]
     Full Idea: Just as liberalism precludes the establishment of an official religion, so too there cannot be official cultures that have preferred status.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.3)
     A reaction: This becomes tricky in schools, where the old way of teaching national literature and particular types of music has been eroded in modern times. But once wide diversity is allowed there is no single story which can be taught.
Liberals need more than freedom; they must build a nation, through a language and institutions [Kymlicka]
     Full Idea: Liberals need to replace the idea of 'benign neglect', and recognise the central role of nation-building in a democracy. …This means promoting a common language, and equal access to institutions operating in that language.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.3)
     A reaction: 'Benign neglect' is non-interference with citizens' lives. Obviously the institutions include education, but is a state health service implied? Can equal access by guaranteed to private institutions?
24. Political Theory / D. Ideologies / 6. Liberalism / f. Multiculturalism
Some individuals can gain citizenship as part of a group, rather than as mere individuals [Kymlicka]
     Full Idea: On the view of 'differentiated citizenship', members of certain groups would be incorporated into the community, not only as individuals, but also through the group, and their rights would depend in part on their group membership.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8)
     A reaction: This is obviously a strategy to enable marginalised individuals to be fully included in society. The downside is that individuals gain their social identity through a label, rather than through themselves, which pure liberals dislike. 'Identity politics'.
The status hierarchy is independent of the economic hierarchy [Kymlicka]
     Full Idea: The evidence suggests that (contrary to the Marxist view) the status hierarchy is not reducible to the economic hierarchy.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8)
     A reaction: Kymlicka is particularly thinking of racism, which lowers the status of certain groups, even if they are economically successful. I console myself for my modest economic status by getting lots of education.
Some multiculturalists defended the rights of cohesive minorities against liberal individualism [Kymlicka]
     Full Idea: Defending multiculturalism initially involved endorsing the communitarian critique of liberalism, and viewed minority rights as defending cohesive minority groups against the encroachment of liberal individualism.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.1)
     A reaction: Liberal individualists have to accept these criticisms from Marxists, communitarians and multiculturalists. The lone individual has no group that guarantees support, and individuals (especially the young) can easily sink.
'Culturalist' liberals say that even liberal individuals may need minority rights [Kymlicka]
     Full Idea: The 'liberal culturalist' position is that minorities which share basic liberal principles nonetheless need minority rights.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.2)
     A reaction: Disabled liberals are an obvious example. This strikes me as a promising version of liberalism, which accepts the criticisms of extreme individualism.
Multiculturalism may entail men dominating women in minority groups [Kymlicka]
     Full Idea: Many feminists express concern that multiculturalism in practice typically means giving male members of the group the power to control the women in the group.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.2)
     A reaction: The way the young are treated might also be a problem. The underlying question is whether the minority group is more or less civilised than the central state. Liberalism always fights for the rights of the least powerful.
Liberals must prefer minority right which are freedoms, not restrictions [Kymlicka]
     Full Idea: Liberal defenders of multiculturalism must distinguish 'bad' minority rights which are restrictions from 'good' minority rights which supplement individual rights.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.2)
     A reaction: Presumably no sensible liberal wants to remove all restrictions, so deeper values must be invoked to justify the mode of approved minority rights. A list of human goods seems needed.
Why shouldn't national minorities have their own right to nation-build? [Kymlicka]
     Full Idea: Why should national minorities not have the same powers of nation-building as the majority?
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.4)
     A reaction: A 'national minority' is marked by a different language, or a different religion, or both. No one doubts the majority's right to nation-build. Some further principle would be needed to deny that right to a minority. Maybe the minority was there first?
Multiculturalism is liberal if it challenges inequality, conservative if it emphasises common good [Kymlicka]
     Full Idea: Liberal multiculturalism challenges status inequalities while preserving individual freedom. …Conservative multiculturalism replaces liberal principles with a communitarian politics of the common good, at least at the local or group level.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.6)
     A reaction: [compressed] This sounds a bit simplistic. Recent emphasis on 'the common good', in the face of white supremacists etc., seems admirable, but surely challenging inequalities promotes the common good? Minority cultures are often conservative.
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
Marxists say liberalism is unjust, because it allows exploitation in the sale of labour [Kymlicka]
     Full Idea: The fundamental flaw of liberal justice, Marxists claim, is that it licences the continuation of the worker by the capitalist, since it licences the buying and selling labour.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 5.2.a)
     A reaction: I can't see that all sale of labour is exploitation, if (for example) the wage paid was extremely high (maybe even higher than the employer's wage, which is possible). So exploitation involves something more.
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Community can focus on class or citizenship or ethnicity or culture [Kymlicka]
     Full Idea: In recent centuries the ideal of community has taken many forms, from class solidarity or shared citizenship to a common ethnic descent or cultural identity.
     From: Will Kymlicka (Community [1993], 'Intro')
     A reaction: Language and religion are not explicitly mentioned, but must be implied. Supporting a major sports team is also worth mentioning.
The 'Kantian' view of the self misses the way it is embedded or situated in society [Kymlicka]
     Full Idea: Communitarians believe that the 'Kantian' view of the self is false, because it ignores the fact that the self is 'embedded' or 'situated' in existing social practices, so that we cannot always stand back and opt out of them.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 6.3)
     A reaction: [Hegel and Charles Taylor 1979 seem to be the sources for this] I have several times been told that I am so typical of the culture I arose in that it is almost comical. This was quite disconcerting, but I got used to it, and now I love it.
Communitarians say we should pay more attention to our history [Kymlicka]
     Full Idea: Communitarians like to say that political theory should pay more attention to the history of each culture.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 6.4.c)
     A reaction: I like this. Kylicka says communitarians tend not to do this, partly because history might reveal an unpleasant basis for present society (such as English country house life benefiting from slavery). The ignorance of history among politicians appals me.
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
Communitarianism struggles with excluded marginalised groups [Kymlicka]
     Full Idea: The problem of the exclusion of historically marginalised groups is endemic to the communitarian project.
     From: Will Kymlicka (Community [1993], 'legitimacy')
     A reaction: Put simply, old-fashioned styles of community are probably impossible in large modern states, some with rather arbitrary borders.
Communitarian states only encourage fairly orthodox ideas of the good life [Kymlicka]
     Full Idea: A communitarian state can and should encourage people to adopt conceptions of the good that conform to the community's way of life, while discouraging conceptions of the good that conflict with it.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 6.2)
     A reaction: This is the conservative aspect of communitarianism which many people (notably liberals) find uncongenial. This conservatism is implicit in Aristotle's account of virtue. I have become more conservative to accommodate it.
Feminism has shown that social roles are far from fixed (as communitarians tend to see them) [Kymlicka]
     Full Idea: Communitarians say that some of our social roles must be regarded as fixed when planning our lives, …but the women's movement has shown how deeply entrenched social roles can be questioned and rejected.
     From: Will Kymlicka (Community [1993], 'Embedded')
     A reaction: True, but parents walking out on young children also shows that. The ideal must be some sort of balance.
Participation aids the quest for the good life, but why should that be a state activity? [Kymlicka]
     Full Idea: Communitarians rarely distinguish between collective activities and political activities. Shared participation aids intelligent decisions about the good life, but why should that be organised through the state, rather than by free individuals?
     From: Will Kymlicka (Community [1993], 'need')
     A reaction: Kylicka points out later that local groups can be very unintelligent or prejudiced. Modern media have changed that picture, because participation can be with geographically remote people.
25. Social Practice / A. Freedoms / 1. Slavery
If everyone owned himself, that would prevent slavery [Kymlicka]
     Full Idea: The best way to prevent enslavement of one person to another is to give each person ownership over himself.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 4.2.c)
     A reaction: [The idea comes from Nozick, but Kymlicka is assessing how it should be understood] The best way to block any social evil like slavery is to make it unthinkable. Legislation is second best. Presumably I could sell myself into slavery (like Faust)?
25. Social Practice / A. Freedoms / 4. Free market
Libertarians like the free market, but they also think that the free market is just [Kymlicka]
     Full Idea: Not everyone who favours the free market is a libertarian, for they do not all share the libertarian view that the free market is inherently just.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 4.1.a)
     A reaction: Illuminating. It would appear that exploitation is possible within a strictly free market, so it seems unlikely that free markets are inherently just (unless you don't acknowledge that 'exploitation' is wrong).
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
The most valuable liberties to us need not be the ones with the most freedom [Kymlicka]
     Full Idea: Different liberties promote different interests for many different reasons, and there is no reason to assume that the liberties which are most valuable to us are the ones with the most freedom.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.4.a.iii)
     A reaction: As I grow older I come more and more to think that freedom is overvalued. But have you tried the other thing? We complacently take huge freedoms for granted. Be passionate about fundamental freedoms, and relaxed about the rest.
25. Social Practice / A. Freedoms / 6. Political freedom
Ancient freedom was free participation in politics, not private independence of life [Kymlicka]
     Full Idea: The liberty of the ancients was their active participation in the exercise of political power, not the peaceful enjoyment of personal independence.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 7.2.a)
     A reaction: Interesting. It takes a feat of imagination to grasp a world where the desire for freedom to sit at home and compile a database of philosophical ideas never even crossed anyone's mind.
25. Social Practice / B. Equalities / 2. Political equality
Equal opportunities seems fair, because your fate is from your choices, not your circumstances [Kymlicka]
     Full Idea: The ideology of equal opportunity seems fair to many people in our society because it ensures that people's fate is determined by their choices, rather than their circumstances.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 3.2)
     A reaction: Is it that we surmise that people have 'free will', and then engineer a situation where it can be exercised? Is it that the rest of us don't want to feel guilty when someone else's life goes awry (because it was 'their fault')?
Equal opportunity arbitrarily worries about social circumstances, but ignores talents [Kymlicka]
     Full Idea: The prevailing view [of equal opportunity] only recognises differences in social circumstances, while ignoring differences in natural talents (or treating them as if they were a choice). This is an arbitrary limit on the theory's central intuition.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 3.2)
     A reaction: Of course we (society) can do a lot about your social circumstances, but very little about your talents, other than to develop them or thwart them. Talented children need more than mere 'opportunity'.
25. Social Practice / B. Equalities / 3. Legal equality
Marxists say justice is unneeded in the truly good community [Kymlicka]
     Full Idea: Marxists believe that justice, far from being the first virtue of social institutions, is something that the truly good community has no need for.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 5.1)
     A reaction: This seems to imply that in the truly good community there are nothing but truly good individuals, which is taking social determinism to its limits. Are all the citizens of a bad community inherently bad?
25. Social Practice / C. Rights / 1. Basis of Rights
The Lockean view of freedom depends on whether you had a right to what is restricted [Kymlicka]
     Full Idea: The Lockean camp defines freedom in terms of the exercise of our rights. Whether or not a restriction decreases our freedom depends on whether or not we had a right to do the restricted thing.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.4.a.iii)
     A reaction: My first instinct is to be sympathetic to this, since a detached and general notion of 'freedom' strikes me as suspect. He offers the rival 'Spenserian' view of freedom as just having the choice.
Rights are a part of nation-building, to build a common national identity and culture [Kymlicka]
     Full Idea: Extending citizenship to include common social rights was a tool of nation-building, intended in part to construct and consolidate a sense of common national identity and culture.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8)
     A reaction: Kymlicka explains a lot of politics and society in terms of the desire of governments to 'build' their nation. You have to make people who are essentially powerless feel that they are at least in some way involved, and benefiting.
Rights derived from group membership are opposed to the idea of state citizenship [Kymlicka]
     Full Idea: The organisation of society on the basis of rights or claims that derive from group membership is sharply opposed to the concept of society based on citizenship.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8)
     A reaction: [from John Porter 1987] Does this imply that you might have rights as part of a group which you don't have as a state citizen? Positive discrimination, for example. Differential rights sounds like potential trouble.
25. Social Practice / D. Justice / 1. Basis of justice
Justice corrects social faults, but also expresses respect to individuals as ends [Kymlicka]
     Full Idea: Justice is more than a remedial virtue. It does remedy defects in social co-ordination, ...but it also expresses the respect individuals are owed as ends in themselves, not as mean's to someone's good, or even to the common good.
     From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 5.1)
     A reaction: That is, I take it, that justice operates at two different levels in our theoretical social thinking.
Communitarians see justice as primarily a community matter, rather than a principle [Kymlicka]
     Full Idea: Communitarians believe either that community replaces the need for principles of justice, or that the community is either the source of such principles or should play a greater role in deciding their content.
     From: Will Kymlicka (Community [1993], 'Intro')
     A reaction: [compressed] The idea that a racist or chauvinist or puritanical or insular community should decide justice for all its members sounds horrible. It drives you to liberal individualism, just thinking about it.
Justice resolves conflicts, but may also provoke them [Kymlicka]
     Full Idea: Justice can help mediate conflicts, but it also tends to creat conflicts, and to decrease the natural expression of sociability.
     From: Will Kymlicka (Community [1993], 'limits')
     A reaction: [He is discussing Michael Sandel on liberalism] Family life might not go well if all of its members continually demanded justice for themselves as individuals. Maybe our concept of justice is too individualistic? Do we need a sense of 'group' justice?
25. Social Practice / E. Policies / 3. Welfare provision
The welfare state helps to integrate the working classes into a national culture [Kymlicka]
     Full Idea: The development of the welfare state has been quite successful in integrating the working classes into national cultures throughout the Western democracies.
     From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8)
     A reaction: Hard-line capitalists tend to hate the welfare state, as unfair to high earners, but it not only makes workers feel involved, but also provides a healthier, happier, more knowledgeable work force for employers.