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51 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
Keep premises as weak as possible, to avoid controversial difficulties [Nussbaum]
     Full Idea: One should always choose the weakest premises from which one's conclusion follows, rather than saddling the theory with thicker or more controversial premises.
     From: Martha Nussbaum (Creating Capabilities [2011], 8)
     A reaction: I like this because it connects the rather vague Ockham's Razor to the logical concept of Thinning. The key point is that a thinner set of premises that prove something will be more persuasive, because critics may reject premises instead of conclusion.
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess]
     Full Idea: Fand P as 'will' and 'was', G as 'always going to be', H as 'always has been', all tenses reduce to 14 cases: the past series, each implying the next, FH,H,PH,HP,P,GP, and the future series PG,G,FG,GF,F,HF, plus GH=HG implying all, FP=PF which all imply.
     From: John P. Burgess (Philosophical Logic [2009], 2.8)
     A reaction: I have tried to translate the fourteen into English, but am not quite confident enough to publish them here. I leave it as an exercise for the reader.
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The temporal Barcan formulas fix what exists, which seems absurd [Burgess]
     Full Idea: In temporal logic, if the converse Barcan formula holds then nothing goes out of existence, and the direct Barcan formula holds if nothing ever comes into existence. These results highlight the intuitive absurdity of the Barcan formulas.
     From: John P. Burgess (Philosophical Logic [2009], 2.9)
     A reaction: This is my reaction to the modal cases as well - the absurdity of thinking that no actually nonexistent thing might possibly have existed, or that the actual existents might not have existed. Williamson seems to be the biggest friend of the formulas.
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Is classical logic a part of intuitionist logic, or vice versa? [Burgess]
     Full Idea: From one point of view intuitionistic logic is a part of classical logic, missing one axiom, from another classical logic is a part of intuitionistic logic, missing two connectives, intuitionistic v and →
     From: John P. Burgess (Philosophical Logic [2009], 6.4)
It is still unsettled whether standard intuitionist logic is complete [Burgess]
     Full Idea: The question of the completeness of the full intuitionistic logic for its intended interpretation is not yet fully resolved.
     From: John P. Burgess (Philosophical Logic [2009], 6.9)
4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess]
     Full Idea: The relevantist logician's → is perhaps expressible by 'if A, then B, for that reason'.
     From: John P. Burgess (Philosophical Logic [2009], 5.8)
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
     Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation.
     From: Ian Rumfitt ("Yes" and "No" [2000], II)
     A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts.
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess]
     Full Idea: Among the more technically oriented a 'logic' no longer means a theory about which forms of argument are valid, but rather means any formalism, regardless of its applications, that resembles original logic enough to be studied by similar methods.
     From: John P. Burgess (Philosophical Logic [2009], Pref)
     A reaction: There doesn't seem to be any great intellectual obligation to be 'technical'. As far as pure logic is concerned, I am very drawn to the computer approach, since I take that to be the original dream of Aristotle and Leibniz - impersonal precision.
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Classical logic neglects the non-mathematical, such as temporality or modality [Burgess]
     Full Idea: There are topics of great philosophical interest that classical logic neglects because they are not important to mathematics. …These include distinctions of past, present and future, or of necessary, actual and possible.
     From: John P. Burgess (Philosophical Logic [2009], 1.1)
The Cut Rule expresses the classical idea that entailment is transitive [Burgess]
     Full Idea: The Cut rule (from A|-B and B|-C, infer A|-C) directly expresses the classical doctrine that entailment is transitive.
     From: John P. Burgess (Philosophical Logic [2009], 5.3)
Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess]
     Full Idea: Classical logic neglects counterfactual conditionals for the same reason it neglects temporal and modal distinctions, namely, that they play no serious role in mathematics.
     From: John P. Burgess (Philosophical Logic [2009], 4.1)
     A reaction: Science obviously needs counterfactuals, and metaphysics needs modality. Maybe so-called 'classical' logic will be renamed 'basic mathematical logic'. Philosophy will become a lot clearer when that happens.
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
Philosophical logic is a branch of logic, and is now centred in computer science [Burgess]
     Full Idea: Philosophical logic is a branch of logic, a technical subject. …Its centre of gravity today lies in theoretical computer science.
     From: John P. Burgess (Philosophical Logic [2009], Pref)
     A reaction: He firmly distinguishes it from 'philosophy of logic', but doesn't spell it out. I take it that philosophical logic concerns metaprinciples which compare logical systems, and suggest new lines of research. Philosophy of logic seems more like metaphysics.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
     Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table.
     From: Ian Rumfitt ("Yes" and "No" [2000])
     A reaction: This is the standard view which Rumfitt sets out to challenge.
Formalising arguments favours lots of connectives; proving things favours having very few [Burgess]
     Full Idea: When formalising arguments it is convenient to have as many connectives as possible available.; but when proving results about formulas it is convenient to have as few as possible.
     From: John P. Burgess (Philosophical Logic [2009], 1.4)
     A reaction: Illuminating. The fact that you can whittle classical logic down to two (or even fewer!) connectives warms the heart of technicians, but makes connection to real life much more difficult. Hence a bunch of extras get added.
The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
     Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious.
     From: Ian Rumfitt ("Yes" and "No" [2000], III)
     A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess]
     Full Idea: Gricean implicature theory might suggest that a disjunction is never assertable when a disjunct is (though actually the disjunction might be 'pertinent') - but the procedure is indispensable in mathematical practice.
     From: John P. Burgess (Philosophical Logic [2009], 5.2)
     A reaction: He gives an example of a proof in maths which needs it, and an unusual conversational occasion where it makes sense.
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
All occurrences of variables in atomic formulas are free [Burgess]
     Full Idea: All occurrences of variables in atomic formulas are free.
     From: John P. Burgess (Philosophical Logic [2009], 1.7)
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
The denotation of a definite description is flexible, rather than rigid [Burgess]
     Full Idea: By contrast to rigidly designating proper names, …the denotation of definite descriptions is (in general) not rigid but flexible.
     From: John P. Burgess (Philosophical Logic [2009], 2.9)
     A reaction: This modern way of putting it greatly clarifies why Russell was interested in the type of reference involved in definite descriptions. Obviously some descriptions (such as 'the only person who could ever have…') might be rigid.
5. Theory of Logic / H. Proof Systems / 1. Proof Systems
'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess]
     Full Idea: There are atomic formulas, and formulas built from the connectives, and that is all. We show that all formulas have some property, first for the atomics, then the others. This proof is 'induction on complexity'; we also use 'recursion on complexity'.
     From: John P. Burgess (Philosophical Logic [2009], 1.4)
     A reaction: That is: 'induction on complexity' builds a proof from atomics, via connectives; 'recursion on complexity' breaks down to the atomics, also via the connectives. You prove something by showing it is rooted in simple truths.
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess]
     Full Idea: It might be wondered how one could have any kind of proof procedure at all if transitivity of entailment is disallowed, but the sequent calculus can get around the difficulty.
     From: John P. Burgess (Philosophical Logic [2009], 5.3)
     A reaction: He gives examples where transitivity of entailment (so that you can build endless chains of deductions) might fail. This is the point of the 'cut free' version of sequent calculus, since the cut rule allows transitivity.
We can build one expanding sequence, instead of a chain of deductions [Burgess]
     Full Idea: Instead of demonstrations which are either axioms, or follow from axioms by rules, we can have one ever-growing sequence of formulas of the form 'Axioms |- ______', where the blank is filled by Axioms, then Lemmas, then Theorems, then Corollaries.
     From: John P. Burgess (Philosophical Logic [2009], 5.3)
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess]
     Full Idea: The valid formulas of classical sentential logic are called 'tautologically valid', or simply 'tautologies'; with other logics 'tautologies' are formulas that are substitution instances of valid formulas of classical sentential logic.
     From: John P. Burgess (Philosophical Logic [2009], 1.5)
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess]
     Full Idea: Validity (truth by virtue of logical form alone) and demonstrability (provability by virtue of logical form alone) have correlative notions of logical possibility, 'satisfiability' and 'consistency', which come apart in some logics.
     From: John P. Burgess (Philosophical Logic [2009], 3.3)
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models leave out meaning, and just focus on truth values [Burgess]
     Full Idea: Models generally deliberately leave out meaning, retaining only what is important for the determination of truth values.
     From: John P. Burgess (Philosophical Logic [2009], 2.2)
     A reaction: This is the key point to hang on to, if you are to avoid confusing mathematical models with models of things in the real world.
We only need to study mathematical models, since all other models are isomorphic to these [Burgess]
     Full Idea: In practice there is no need to consider any but mathematical models, models whose universes consist of mathematical objects, since every model is isomorphic to one of these.
     From: John P. Burgess (Philosophical Logic [2009], 1.8)
     A reaction: The crucial link is the technique of Gödel Numbering, which can translate any verbal formula into numerical form. He adds that, because of the Löwenheim-Skolem theorem only subsets of the natural numbers need be considered.
We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess]
     Full Idea: The aim in setting up a model theory is that the technical notion of truth in all models should agree with the intuitive notion of truth in all instances. A model is supposed to represent everything about an instance that matters for its truth.
     From: John P. Burgess (Philosophical Logic [2009], 3.2)
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess]
     Full Idea: It is a common view that the liar sentence ('This very sentence is not true') is an instance of a truth-value gap (neither true nor false), but some dialethists cite it as an example of a truth-value glut (both true and false).
     From: John P. Burgess (Philosophical Logic [2009], 5.7)
     A reaction: The defence of the glut view must be that it is true, then it is false, then it is true... Could it manage both at once?
10. Modality / A. Necessity / 4. De re / De dicto modality
De re modality seems to apply to objects a concept intended for sentences [Burgess]
     Full Idea: There is a problem over 'de re' modality (as contrasted with 'de dicto'), as in ∃x□x. What is meant by '"it is analytic that Px" is satisfied by a', given that analyticity is a notion that in the first instance applies to complete sentences?
     From: John P. Burgess (Philosophical Logic [2009], 3.9)
     A reaction: This is Burgess's summary of one of Quine's original objections. The issue may be a distinction between whether the sentence is analytic, and what makes it analytic. The necessity of bachelors being unmarried makes that sentence analytic.
10. Modality / A. Necessity / 6. Logical Necessity
General consensus is S5 for logical modality of validity, and S4 for proof [Burgess]
     Full Idea: To the extent that there is any conventional wisdom about the question, it is that S5 is correct for alethic logical modality, and S4 correct for apodictic logical modality.
     From: John P. Burgess (Philosophical Logic [2009], 3.8)
     A reaction: In classical logic these coincide, so presumably one should use the minimum system to do the job, which is S4 (?).
Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess]
     Full Idea: Logical necessity is a genus with two species. For classical logic the truth-related notion of validity and the proof-related notion of demonstrability, coincide - but they are distinct concept. In some logics they come apart, in intension and extension.
     From: John P. Burgess (Philosophical Logic [2009], 3.3)
     A reaction: They coincide in classical logic because it is sound and complete. This strikes me as the correct approach to logical necessity, tying it to the actual nature of logic, rather than some handwavy notion of just 'true in all possible worlds'.
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess]
     Full Idea: Three main theories of the truth of indicative conditionals are Materialism (the conditions are the same as for the material conditional), Idealism (identifying assertability with truth-value), and Nihilism (no truth, just assertability).
     From: John P. Burgess (Philosophical Logic [2009], 4.3)
It is doubtful whether the negation of a conditional has any clear meaning [Burgess]
     Full Idea: It is contentious whether conditionals have negations, and whether 'it is not the case that if A,B' has any clear meaning.
     From: John P. Burgess (Philosophical Logic [2009], 4.9)
     A reaction: This seems to be connected to Lewis's proof that a probability conditional cannot be reduced to a single proposition. If a conditional only applies to A-worlds, it is not surprising that its meaning gets lost when it leaves that world.
19. Language / F. Communication / 3. Denial
We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
     Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A.
     From: Ian Rumfitt ("Yes" and "No" [2000], IV)
     A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role).
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
Storytelling is never neutral; some features of the world must be emphasised [Nussbaum]
     Full Idea: Storytelling is never neutral; the narrator always directs attention to some features of the world rather than others.
     From: Martha Nussbaum (Creating Capabilities [2011], 1)
     A reaction: The audience would be a bit stupid if it insisted on neutrality.
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
Particularism gives no guidance for the future [Nussbaum]
     Full Idea: Situation ethics offers no guidance for the future.
     From: Martha Nussbaum (Creating Capabilities [2011], 8)
     A reaction: Not sure if Situation Ethics is the same as Particularism. Jonathan Danby famously champions the latter.
23. Ethics / C. Virtue Theory / 3. Virtues / f. Compassion
Compassion is unreliable, because it favours people close to us [Nussbaum]
     Full Idea: Daniel Batson's important research has shown us that compassion is not reliable on its own, because it can easily give priority to people close to the self.
     From: Martha Nussbaum (Creating Capabilities [2011], 8)
     A reaction: In Britain animal charities receive vastly more money than children's charities, presumably for this very reason. Kittens - you've got to hate them.
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Social contracts assume equal powers among the participants [Nussbaum]
     Full Idea: All contract theories, including Rawls's, assume a rough equality of physical and mental power among the participants.
     From: Martha Nussbaum (Creating Capabilities [2011], 4)
24. Political Theory / D. Ideologies / 4. Social Utilitarianism
We shouldn't focus on actual preferences, which may be distorted by injustices [Nussbaum]
     Full Idea: When society puts things out of reach for people, they typically learn not to want those things. ..By defining the social goal in terms of satisfaction of actual preferences, utilitarian approaches often reinforce the status quo, which may be very unjust.
     From: Martha Nussbaum (Creating Capabilities [2011], 3)
     A reaction: Maximising happiness is potentially very paternalistic, whereas preference satisfaction is not, which aligns utilitarianism better with liberalism. It is notorious that slaves can be contented with their slavery, and battered wives can remain loyal.
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
Liberalism does not need a comprehensive account of value [Nussbaum]
     Full Idea: The role of political liberalism in my theory requires me to prescind from offering any comprehensive account of value.
     From: Martha Nussbaum (Creating Capabilities [2011], 2)
     A reaction: Obviously liberalism has values, but they are the minimum ones of freedom and respect. Liberals have to tolerate some fairly ugly and miserable societies. Can liberals intervene in family life?
24. Political Theory / D. Ideologies / 12. Feminism
Women are often treated like children, and not respected for their choices [Nussbaum]
     Full Idea: Women are often treated as passive dependents, creatures to be cared for (or not), rather than as independent human beings deserving respect for their choices. In other words they are often infantilized.
     From: Martha Nussbaum (Creating Capabilities [2011], 3)
     A reaction: Her prime example is from India, but you see the same thing in more subtle forms in the UK, especially among older people, and especially in art galleries.
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
Negative liberty is incoherent; all liberties, to do and to be, require the prevention of interference [Nussbaum]
     Full Idea: The very idea of 'negative liberty' ...is an incoherent idea: all liberties are positive, meaning liberties to do or to be something, which all require the inhibition of interference by others.
     From: Martha Nussbaum (Creating Capabilities [2011], 3)
     A reaction: This rejects Isaiah Berlin's well-known claim that negative liberties are good, but positive liberties are far too dangerous.
25. Social Practice / A. Freedoms / 6. Political freedom
Political freedom is an incoherent project, because some freedoms limit other freedoms [Nussbaum]
     Full Idea: It is unclear whether the idea of promoting freedom is even a coherent political project. Some freedoms limit others. The freedom of rich people to make large donations to political campaigns can limit the equal worth of the right to vote.
     From: Martha Nussbaum (Creating Capabilities [2011], 4)
     A reaction: It is not just American right-wingers who over-emphasise 'freedom'. French philosophy seems to be riddled with the same thing.
25. Social Practice / C. Rights / 1. Basis of Rights
Political and civil rights are not separate from economic and social rights [Nussbaum]
     Full Idea: My approach rejects the distinction, common in the human rights movement, between 'first-generation rights' (political and civil) and 'second-generation rights' (economic and social). The second group are preconditions of the first group.
     From: Martha Nussbaum (Creating Capabilities [2011], 3)
     A reaction: [last sentence compressed] This sounds like the sort of point Marx argued for. Nowadays it is feminists who make this point most strongly.
25. Social Practice / D. Justice / 1. Basis of justice
Capabilities: Life, Health, Safety, Mental life, Love, Planning, Joining in, Nature, Play, Control [Nussbaum, by PG]
     Full Idea: Ten Capabilities: Life (decent), Health (reproduction, shelter), Safety, Mental life (with education), Love (relationships), Planning (with free beliefs), Joining in (and non-discrimination), Nature (relations to), Play, Control (politics and property).
     From: report of Martha Nussbaum (Creating Capabilities [2011], 2) by PG - Db (ideas)
     A reaction: She gives her crucial list in rather wordy form. To have impact it needs to be reduced to brief simple slogans.
Justice requires that the ten main capabilities of people are reasonably enabled [Nussbaum]
     Full Idea: The basic claim of my account of social justice is this: respect for human dignity requires that citizens be placed above an ample (specified) threshold of capability in all ten of the areas.
     From: Martha Nussbaum (Creating Capabilities [2011], 2)
     A reaction: [The capabilities are given, briefly, in Idea 21009] The one word that bothers me here is 'dignity'. It is very vague, and can, I think, be reduced to much clearer and more obvious concepts. A person lacks dignity when they vomit, in ordinary usage.
Capabilities are grounded in bare humanity and agency; qualifying as rational is not needed [Nussbaum]
     Full Idea: The capabilities approach grounds rights claims in bare human birth and minimal agency, not in rationality or any other specific property, something that permits it to recognise the equal human rights of people with cognitive disabilities.
     From: Martha Nussbaum (Creating Capabilities [2011], 3)
     A reaction: She says elsewhere that she also sees animals as included in the capabilities approach. This is a rejection of the Kantian grounds for rights (by a well-known Aristotelian).
Rights are not just barriers against state interference; governments must affirm capabilities of citizens [Nussbaum]
     Full Idea: A prominent idea, common in the U.S., sees rights as barriers against interfering state action. ...The Capabilities Approach, by contrast, insists that all entitlements involve an affirmative task for government, to actively support capabilities.
     From: Martha Nussbaum (Creating Capabilities [2011], 3)
     A reaction: This makes her approach very left wing, by U.S. standards, because it needs higher taxation and a degree of government paternalism. Her approach strikes me as an excellent agenda for a fairly interventionist European liberal party.
25. Social Practice / E. Policies / 2. Religion in Society
Any establishment belief system is incompatible with full respect for all citizens [Nussbaum]
     Full Idea: The idea of equal respect is difficult or impossible to render compatible with a religious establishment, even one that is benign and noncoercive. Any established church (or government secularism) denigrates nonbelievers, by stating they are an out-group.
     From: Martha Nussbaum (Creating Capabilities [2011], 4)
     A reaction: This sort of applies to membership of anything. She is sort of right, but there is no reason in principle why full respect should not be accorded to any out-group.
25. Social Practice / F. Life Issues / 6. Animal Rights
We should respect animals in the way that we respect the animal nature in humans [Nussbaum]
     Full Idea: If we show respect to our own animal natures, it is simply inconsistent, and a kind of vicious self-promoting of a sort to which Kantians are especially opposed, to refuse the same respect to our fellow creatures.
     From: Martha Nussbaum (Creating Capabilities [2011], 8)
     A reaction: Nussbaum says Kant is hopeless on animals, but Christine Korsgaard offers this Kantian approach that demands genuine respect for animals, even though they are not considered rational. Nussbaum says animals are agents. Did Kant respect our animality?
It may be no harm to kill an animal which cannot plan for its future [Nussbaum]
     Full Idea: The painless killing of an animal of a species that does not make plans extending into the future may not be a harm: this depends on how we think about the harm of death.
     From: Martha Nussbaum (Creating Capabilities [2011], 8)
     A reaction: Very old human beings may have no plans for the future. I, on the other hand, have got lots and lots of plans. Definitely. No one can specify the harm of death. How can it be distinguished from the harm of not being born?
The Capabilities Approach sees animals as agents, not just as having feelings [Nussbaum]
     Full Idea: The Capabilities Approach sees animals as agents, not as receptacles of pleasure or pain.
     From: Martha Nussbaum (Creating Capabilities [2011], 8)
     A reaction: This is in opposition to the utilitarian view. The key consequence is that animals can be victims of injustice, as well as of cruelty. Nice.