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All the ideas for 'On the Question of Absolute Undecidability', 'Virtues of the Mind' and 'The Tarskian Turn'

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86 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Unlike knowledge, wisdom cannot be misused [Zagzebski]
     Full Idea: A distinctive mark of wisdom is that it cannot be misused, whereas knowledge surely can be misused.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], I 1.2)
     A reaction: She will argue, with Aristotle, that this is because wisdom (and maybe 'true' knowledge) must include 'phronesis' (practical wisdom), which is the key to all the virtues, intellectual and moral. This idea is striking, and obviously correct.
1. Philosophy / A. Wisdom / 2. Wise People
Wisdom is the property of a person, not of their cognitive state [Zagzebski, by Whitcomb]
     Full Idea: Zagzebski takes wisdom as literally properties of persons, not persons' cognitive states.
     From: report of Linda Trinkaus Zagzebski (Virtues of the Mind [1996], p.59-60) by Dennis Whitcomb - Wisdom 'Twofold'
     A reaction: Not sure about this. Zagzebski uses this idea to endorse epistemic virtue. But knowledge and ignorance are properties of persons too. There can be, though, a precise mental state involved in knowledge, but not in wisdom.
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy is the most general intellectual discipline [Horsten]
     Full Idea: Philosophy is the most general intellectual discipline.
     From: Leon Horsten (The Tarskian Turn [2011], 05.1)
     A reaction: Very simple, but exactly how I see the subject. It is continuous with the sciences, and tries to give an account of nature, but operating at an extreme level of generality. It must respect the findings of science, but offer bold interpretations.
2. Reason / D. Definition / 2. Aims of Definition
Precision is only one of the virtues of a good definition [Zagzebski]
     Full Idea: Precision is but one virtue of a definition, one that must be balanced against simplicity, elegance, conciseness, theoretical illumination, and practical usefulness.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 2.1)
     A reaction: Illumination looks like the dream virtue for a good definition. Otherwise it is just ticked as accurate and stowed away. 'True justified belief' is a very illuminating definition of knowledge - if it is right. But it's not very precise.
A definition should allow the defined term to be eliminated [Horsten]
     Full Idea: A definition allows a defined term to be eliminated in every context in which it appears.
     From: Leon Horsten (The Tarskian Turn [2011], 04.2)
     A reaction: To do that, a definition had better be incredibly comprehensive, so that no nice nuance of the original term is thrown out.
2. Reason / E. Argument / 1. Argument
Objection by counterexample is weak, because it only reveals inaccuracies in one theory [Zagzebski]
     Full Idea: Objection by counterexample is the weakest sort of attack a theory can undergo. Even when the objection succeeds, it shows only that a theory fails to achieve complete accuracy. It does not distinguish among the various rival theories.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 2.1)
     A reaction: Typically counterexamples are used to refute universal generalisations (i.e. by 'falsification'), but canny theorists avoid those, or slip in a qualifying clause. Counterexamples are good for exploring a theory's coverage.
3. Truth / A. Truth Problems / 1. Truth
Semantic theories of truth seek models; axiomatic (syntactic) theories seek logical principles [Horsten]
     Full Idea: There are semantical theories of truth, concerned with models for languages containing the truth predicate, and axiomatic (or syntactic) theories, interested in basic logical principles governing the concept of truth.
     From: Leon Horsten (The Tarskian Turn [2011], 01.1)
     A reaction: This is the map of contemporary debates, which seem now to have given up talking about 'correspondence', 'coherence' etc.
Truth is a property, because the truth predicate has an extension [Horsten]
     Full Idea: I take truth to be a property because the truth predicate has an extension - the collection of all true sentences - and this collection does not (unlike the 'extension' of 'exists') consist of everything, or even of all sentences.
     From: Leon Horsten (The Tarskian Turn [2011], 01.1)
     A reaction: He concedes that it may be an 'uninteresting' property. My problem is always that I am unconvinced that truth is tied to sentences. I can make perfect sense of animal thoughts being right or wrong. Extension of mental propositions?
3. Truth / A. Truth Problems / 2. Defining Truth
Truth has no 'nature', but we should try to describe its behaviour in inferences [Horsten]
     Full Idea: We should not aim at describing the nature of truth because there is no such thing. Rather, we should aim at describing the inferential behaviour of truth.
     From: Leon Horsten (The Tarskian Turn [2011], 10.2.3)
3. Truth / A. Truth Problems / 5. Truth Bearers
Propositions have sentence-like structures, so it matters little which bears the truth [Horsten]
     Full Idea: It makes little difference, at least in extensional contexts, whether the truth bearers are propositions or sentences (or assertions). Even if the bearers are propositions rather than sentences, propositions are structured rather like sentences.
     From: Leon Horsten (The Tarskian Turn [2011], 02.4)
     A reaction: The 'extensional' context means you are only talking about the things that are referred to, and not about the way this is expressed. I prefer propositions, but this is an interesting point.
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
Modern correspondence is said to be with the facts, not with true propositions [Horsten]
     Full Idea: Modern correspondence theorists no longer take things to correspond to true propositions; they consider facts to be the truthmakers of propositions.
     From: Leon Horsten (The Tarskian Turn [2011], 02.1)
     A reaction: If we then define facts as the way certain things are, independently from our thinking about it, at least we seem to be avoiding circularity. Not much point in correspondence accounts if you are not a robust realist (like me). [14,000th idea, 23/4/12!]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
The correspondence 'theory' is too vague - about both 'correspondence' and 'facts' [Horsten]
     Full Idea: The principle difficulty of the correspondence theory of truth is its vagueness. It is too vague to be called a theory until more information is given about what is meant by the terms 'correspondence' and 'fact'. Facts can involve a heavy ontology.
     From: Leon Horsten (The Tarskian Turn [2011], 02.1)
     A reaction: I see nothing here to make me give up my commitment to the correspondence view of truth, though it sounds as if I will have to give up the word 'theory' in that context. Truth is so obviously about thought fitting reality that there is nothing to discuss.
3. Truth / D. Coherence Truth / 2. Coherence Truth Critique
The coherence theory allows multiple coherent wholes, which could contradict one another [Horsten]
     Full Idea: The coherence theory seems too liberal. It seems there can be more than one systematic whole which, while being internally coherent, contradict each other, and thus cannot all be true. Coherence is a necessary but not sufficient condition for truth.
     From: Leon Horsten (The Tarskian Turn [2011], 02.1)
     A reaction: This is a modern post-Tarski axiomatic truth theorist making very short work indeed of the coherence theory of truth. I take Horsten to be correct.
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
The pragmatic theory of truth is relative; useful for group A can be useless for group B [Horsten]
     Full Idea: The pragmatic theory is unsatisfactory because usefulness is a relative notion. One theory can be useful to group A while being thoroughly impractical for group B. This would make the theory both truth and false.
     From: Leon Horsten (The Tarskian Turn [2011], 02.1)
     A reaction: This objection, along with the obvious fact that certain falsehoods can be very useful, would seem to rule pragmatism out as a theory of truth. It is, in fact, an abandonment of truth.
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Tarski's hierarchy lacks uniform truth, and depends on contingent factors [Horsten]
     Full Idea: According to the Tarskian hierarchical conception, truth is not a uniform notion. ...Also Kripke has emphasised that the level of a token of the truth predicate can depend on contingent factors, such as what else has been said by a speaker.
     From: Leon Horsten (The Tarskian Turn [2011], 04.5)
Tarski Bi-conditional: if you'll assert φ you'll assert φ-is-true - and also vice versa [Horsten]
     Full Idea: The axiom schema 'Sentence "phi;" is true iff φ' is the (unrestricted) Tarski-Biconditional, and is motivated by the thought that if you are willing to assume or outright assert that φ, you will assert that φ is true - and also vice versa.
     From: Leon Horsten (The Tarskian Turn [2011], 02.2)
     A reaction: Very helpful! Most people are just bewildered by the Tarski bi-conditional ('"Snow is white"...), but this formulation nicely shows its minimal character while showing that it really does say something. It says what truths and truth-claims commit you to.
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
Semantic theories have a regress problem in describing truth in the languages for the models [Horsten]
     Full Idea: Semantic theories give a class of models with a truth predicate, ...but Tarski taught us that this needs a more encompassing framework than its language...so how is the semantics of the framework expressed? The model route has a regress.
     From: Leon Horsten (The Tarskian Turn [2011], 02.3)
     A reaction: [compressed] So this regress problem, of endless theories of truth going up the hierarchy, is Horsten's main reason for opting for axiomatic theories, which he then tries to strengthen, so that they are not quite so deflated.
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Axiomatic approaches avoid limiting definitions to avoid the truth predicate, and limited sizes of models [Horsten]
     Full Idea: An adequate definition of truth can only be given for the fragment of our language that does not contain the truth predicate. A model can never encompass the whole of the domain of discourse of our language. The axiomatic approach avoids these problems.
     From: Leon Horsten (The Tarskian Turn [2011], 10.1)
Axiomatic approaches to truth avoid the regress problem of semantic theories [Horsten]
     Full Idea: The axiomatic approach to truth does not suffer from the regress problem.
     From: Leon Horsten (The Tarskian Turn [2011], 02.3)
     A reaction: See Idea 15345 for the regress problem. The difficulty then seems to be that axiomatic approaches lack expressive power, so the hunt is on for a set of axioms which will do a decent job. Fun work, if you can cope with it.
An axiomatic theory needs to be of maximal strength, while being natural and sound [Horsten]
     Full Idea: The challenge is to find the arithmetically strongest axiomatical truth theory that is both natural and truth-theoretically sound.
     From: Leon Horsten (The Tarskian Turn [2011], 07.7)
'Reflexive' truth theories allow iterations (it is T that it is T that p) [Horsten]
     Full Idea: A theory of truth is 'reflexive' if it allows us to prove truth-iterations ("It is true that it is true that so-and-so").
     From: Leon Horsten (The Tarskian Turn [2011], 01.4)
A good theory of truth must be compositional (as well as deriving biconditionals) [Horsten]
     Full Idea: Deriving many Tarski-biconditionals is not a sufficient condition for being a good theory of truth. A good theory of truth must in addition do justice to the compositional nature of truth.
     From: Leon Horsten (The Tarskian Turn [2011], 06.1)
The Naďve Theory takes the bi-conditionals as axioms, but it is inconsistent, and allows the Liar [Horsten]
     Full Idea: The Naďve Theory of Truth collects all the Tarski bi-conditionals of a language and takes them as axioms. But no consistent theory extending Peano arithmetic can prove all of them. It is inconsistent, and even formalises the liar paradox.
     From: Leon Horsten (The Tarskian Turn [2011], 03.5.2)
     A reaction: [compressed] This looks to me like the account of truth that Davidson was working with, since he just seemed to be compiling bi-conditionals for tricky cases. (Wrong! He championed the Compositional Theory, Horsten p.71)
Axiomatic theories take truth as primitive, and propose some laws of truth as axioms [Horsten]
     Full Idea: In the axiomatic approach we take the truth predicate to express an irreducible, primitive notion. The meaning of the truth predicate is partially explicated by proposing certain laws of truth as basic principles, as axioms.
     From: Leon Horsten (The Tarskian Turn [2011], 04.2)
     A reaction: Judging by Horsten's book, this is a rather fruitful line of enquiry, but it still seems like a bit of a defeat to take truth as 'primitive'. Presumably you could add some vague notion of correspondence as the background picture.
By adding truth to Peano Arithmetic we increase its power, so truth has mathematical content! [Horsten]
     Full Idea: It is surprising that just by adding to Peano Arithmetic principles concerning the notion of truth, we increase the mathematical strength of PA. So, contrary to expectations, the 'philosophical' notion of truth has real mathematical content.
     From: Leon Horsten (The Tarskian Turn [2011], 06.4)
     A reaction: Horsten invites us to be really boggled by this. All of this is in the Compositional Theory TC. It enables a proof of the consistency of arithmetic (but still won't escape Gödel's Second).
3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
Friedman-Sheard theory keeps classical logic and aims for maximum strength [Horsten]
     Full Idea: The Friedman-Sheard theory of truth holds onto classical logic and tries to construct a theory that is as strong as possible.
     From: Leon Horsten (The Tarskian Turn [2011], 01.4)
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength [Horsten]
     Full Idea: If we abandon classical logic in favour of truth-value gaps and try to strengthen the theory, this leads to the Kripke-Feferman theory of truth, and variants of it.
     From: Leon Horsten (The Tarskian Turn [2011], 01.4)
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Inferential deflationism says truth has no essence because no unrestricted logic governs the concept [Horsten]
     Full Idea: According to 'inferential deflationism', truth is a concept without a nature or an essence. This is betrayed by the fact that there are no unrestricted logical laws that govern the concept of truth.
     From: Leon Horsten (The Tarskian Turn [2011], 01.1)
Deflationism skips definitions and models, and offers just accounts of basic laws of truth [Horsten]
     Full Idea: Contemporary deflationism about truth does not attempt to define truth, and does not rely on models containing the truth predicate. Instead they are interpretations of axiomatic theories of truth, containing only basic laws of truth.
     From: Leon Horsten (The Tarskian Turn [2011], 02.3)
Deflationism concerns the nature and role of truth, but not its laws [Horsten]
     Full Idea: Deflationism is not a theory of the laws of truth. It is a view on the nature and role of the concept of truth.
     From: Leon Horsten (The Tarskian Turn [2011], 05 Intro)
This deflationary account says truth has a role in generality, and in inference [Horsten]
     Full Idea: On the conception of deflationism developed in this book, the prime positive role of the truth predicate is to serve as a device for expressing generalities, and an inferential tool.
     From: Leon Horsten (The Tarskian Turn [2011], 07.5)
Deflationism says truth isn't a topic on its own - it just concerns what is true [Horsten]
     Full Idea: Deflationism says the theory of truth does not have a substantial domain of its own. The domain of the theory of truth consists of the bearers of truth.
     From: Leon Horsten (The Tarskian Turn [2011], 05.1)
     A reaction: The immediate thought is that truth also concerns falsehoods, which would be inexplicable without it. If physics just concerns the physical, does that mean that physics lacks its own 'domain'? Generalising about the truths is a topic.
Deflation: instead of asserting a sentence, we can treat it as an object with the truth-property [Horsten]
     Full Idea: The Deflationary view just says that instead of asserting a sentence, we can turn the sentence into an object and assert that this object has the property of truth.
     From: Leon Horsten (The Tarskian Turn [2011], 05.2.2)
     A reaction: That seems to leave a big question hanging, which concerns the nature of the property that is being attributed to this object. Quine 1970:10-13 says it is just a 'device'. Surely you can rest content with that as an account of truth?
4. Formal Logic / E. Nonclassical Logics / 1. Nonclassical Logics
Nonclassical may accept T/F but deny applicability, or it may deny just T or F as well [Horsten]
     Full Idea: Some nonclassical logic stays close to classical, assuming two mutually exclusive truth values T and F, but some sentences fail to have one. Others have further truth values such as 'half truth', or dialethists allow some T and F at the same time.
     From: Leon Horsten (The Tarskian Turn [2011], 01.2)
     A reaction: I take that to say that the first lot accept bivalence but reject excluded middle (allowing 'truth value gaps'), while the second lot reject both. Bivalence gives the values available, and excluded middle says what has them.
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
     Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro)
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
     Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1)
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Doubt is thrown on classical logic by the way it so easily produces the liar paradox [Horsten]
     Full Idea: Aside from logic, so little is needed to generate the liar paradox that one wonders whether the laws of classical logic are unrestrictedly valid after all. (Many theories of truth have therefore been formulated in nonclassical logic.)
     From: Leon Horsten (The Tarskian Turn [2011], 01.2)
     A reaction: Kripke uses Strong Kleene logic for his theory. The implication is that debates discussed by Horsten actually have the status of classical logic at stake, as well as the nature of truth.
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms [Horsten]
     Full Idea: The Deduction Theorem says ψ is derivable in classical predicate logic from ψ iff the sentence φ→ψ is a theorem of classical logic. Hence inferring φ to ψ is truth-preserving iff the axiom scheme φ→ψ is provable.
     From: Leon Horsten (The Tarskian Turn [2011], 02.2)
     A reaction: Horsten offers this to show that the Tarski bi-conditionals can themselves be justified, and not just the rule of inference involved. Apparently you can only derive something if you first announce that you have the ability to derive it. Odd.
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten]
     Full Idea: A theory is 'non-conservative' if it allows us to prove mathematical facts that go beyond what the background mathematical theory can prove on its own.
     From: Leon Horsten (The Tarskian Turn [2011], 01.4)
     A reaction: This is an instance of the relationship with mathematics being used as the test case for explorations of logic. It is a standard research method, because it is so precise, but should not be mistaken for the last word about a theory.
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F) [Horsten]
     Full Idea: It is easier to imagine what it is like for a sentence to lack a truth value than what it is like for a sentence to be both truth and false. So I am grudgingly willing to entertain the possibility that certain sentences (like the Liar) lack a truth value.
     From: Leon Horsten (The Tarskian Turn [2011], 02.5)
     A reaction: Fans of truth value gluts are dialethists like Graham Priest. I'm with Horsten on this one. But in what way can a sentence be meaningful if it lacks a truth-value? He mentions unfulfilled presuppositions and indicative conditionals as gappy.
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
Satisfaction is a primitive notion, and very liable to semantical paradoxes [Horsten]
     Full Idea: Satisfaction is a more primitive notion than truth, and it is even more susceptible to semantical paradoxes than the truth predicate.
     From: Leon Horsten (The Tarskian Turn [2011], 06.3)
     A reaction: The Liar is the best known paradox here. Tarski bases his account of truth on this primitive notion, so Horsten is pointing out the difficulties.
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
     Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3)
The first incompleteness theorem means that consistency does not entail soundness [Horsten]
     Full Idea: It is a lesson of the first incompleteness theorem that consistency does not entail soundness. If we add the negation of the gödel sentence for PA as an extra axiom to PA, the result is consistent. This negation is false, so the theory is unsound.
     From: Leon Horsten (The Tarskian Turn [2011], 04.3)
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated [Horsten]
     Full Idea: The Strengthened Liar sentence says 'this sentence is not true in any context'. It is not hard to figure out that there is no context in which the sentence can be coherently evaluated.
     From: Leon Horsten (The Tarskian Turn [2011], 04.6)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable [Horsten]
     Full Idea: The number of English expressions is denumerably infinite. But Cantor's theorem can be used to show that there are nondenumerably many real numbers. So not every real number has a (simple or complex name in English).
     From: Leon Horsten (The Tarskian Turn [2011], 06.3)
     A reaction: This really bothers me. Are we supposed to be committed to the existence of entities which are beyond our powers of naming? How precise must naming be? If I say 'pick a random real number', might that potentially name all of them?
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
     Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable).
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4)
     A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
     Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem].
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1)
     A reaction: Each expansion brings a limitation, but then you can expand again.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
     Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
ZFC showed that the concept of set is mathematical, not logical, because of its existence claims [Horsten]
     Full Idea: One of the strengths of ZFC is that it shows that the concept of set is a mathematical concept. Many originally took it to be a logical concept. But ZFC makes mind-boggling existence claims, which should not follow if it was a logical concept.
     From: Leon Horsten (The Tarskian Turn [2011], 05.2.3)
     A reaction: This suggests that set theory is not just a way of expressing mathematics (see Benacerraf 1965), but that some aspect of mathematics has been revealed by it - maybe even its essential nature.
Set theory is substantial over first-order arithmetic, because it enables new proofs [Horsten]
     Full Idea: The nonconservativeness of set theory over first-order arithmetic has done much to establish set theory as a substantial theory indeed.
     From: Leon Horsten (The Tarskian Turn [2011], 07.5)
     A reaction: Horsten goes on to point out the price paid, which is the whole new ontology which has to be added to the arithmetic. Who cares? It's all fictions anyway!
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Predicativism says mathematical definitions must not include the thing being defined [Horsten]
     Full Idea: Predicativism has it that a mathematical object (such as a set of numbers) cannot be defined by quantifying over a collection that includes that same mathematical object. To do so would be a violation of the vicious circle principle.
     From: Leon Horsten (The Tarskian Turn [2011], 07.7)
     A reaction: In other words, when you define an object you are obliged to predicate something new, and not just recycle the stuff you already have.
7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
We may believe in atomic facts, but surely not complex disjunctive ones? [Horsten]
     Full Idea: While positive and perhaps even negative atomic facts may be unproblematic, it seems excessive to commit oneself to the existence of logically complex facts such as disjunctive facts.
     From: Leon Horsten (The Tarskian Turn [2011], 02.1)
     A reaction: Presumably it is hard to deny that very complex statements involving massive disjunctions can be true or false. But why does commitment to real facts have to involve a huge ontology? The ontology is just the ingredients of the fact, isn't it?
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
In the supervaluationist account, disjunctions are not determined by their disjuncts [Horsten]
     Full Idea: If 'Britain is large' and 'Italy is large' lack truth values, then so must 'Britain or Italy is large' - so on the supervaluationist account the truth value of a disjunction is not determined by the truth values of its disjuncts.
     From: Leon Horsten (The Tarskian Turn [2011], 06.2)
     A reaction: Compare Idea 15362 to get the full picture here.
If 'Italy is large' lacks truth, so must 'Italy is not large'; but classical logic says it's large or it isn't [Horsten]
     Full Idea: If 'Italy is a large country' lacks a truth value, then so too, presumably, does 'Italy is not a large country'. But 'Italy is or is not a large country' is true, on the supervaluationist account, because it is a truth of classical propositional logic.
     From: Leon Horsten (The Tarskian Turn [2011], 06.2)
     A reaction: See also Idea 15363. He cites Fine 1975.
11. Knowledge Aims / A. Knowledge / 2. Understanding
Modern epistemology is too atomistic, and neglects understanding [Zagzebski]
     Full Idea: There are complaints that contemporary epistemology is too atomistic, and that the value of understanding has been neglected.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], I 2)
     A reaction: This is because of the excessive influence of logic in contemporary analytic philosophy, which has to reduce knowledge to K(Fa), rather than placing it in a human context.
Epistemology is excessively atomic, by focusing on justification instead of understanding [Zagzebski]
     Full Idea: The present obsession with justification and the neglect of understanding has resulted in a feature of epistemology already criticised by several epistemologists: its atomism.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 2.2)
     A reaction: All analytic philosophy has become excessively atomic, because it relies too heavily on logic for its grounding and rigour. There are other sorts of rigour, such as AI, peer review, programming. Or rigour is an idle dream.
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
Truth is valuable, but someone knowing the truth is more valuable [Zagzebski]
     Full Idea: Of course we value the truth, but the value we place on knowledge is more than the value of the truth we thereby acquire. …It also involves a valuabe relation between the knower and the truth.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 1)
     A reaction: Hard to assess this. I take truth to be a successful relationship between a mind and a fact. Knowledge needs something extra, to avoid lucky true beliefs. Does a truth acquire greater and greater value as more people come to know it? Doubtful.
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
Some claim that indicative conditionals are believed by people, even though they are not actually held true [Horsten]
     Full Idea: In the debate about doxastic attitudes towards indicative conditional sentences, one finds philosophers who claim that conditionals can be believed even though they have no truth value (and thus are not true).
     From: Leon Horsten (The Tarskian Turn [2011], 09.3)
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
Some beliefs are fairly voluntary, and others are not at all so [Zagzebski]
     Full Idea: My position is that beliefs, like acts, arrange themselves on a continuum of degrees of voluntariness, ranging from quite a bit to none at all.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], I 4.2)
     A reaction: I'm sure we have no idea how we came to hold many of our beliefs, and if we see a cat, nothing seems to intervene between the seeing and the believing. But if you adopt a religion, believing its full creed is a big subsequent effort.
11. Knowledge Aims / A. Knowledge / 5. Aiming at Truth
Knowledge either aims at a quantity of truths, or a quality of understanding of truths [Zagzebski]
     Full Idea: Getting knowledge can be a matter either of reaching more truths or of gaining understanding of truths already believed. So it may be a way of increasing either the quality of true belief (cognitive contact with reality) or the quantity.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 2.1)
     A reaction: I'm not sure how one would increase understanding of currently believed truths if it didn't involve adding some new truths to the collection. There is only the discovery of connections or structures, but those are new facts.
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem
For internalists Gettier situations are where internally it is fine, but there is an external mishap [Zagzebski]
     Full Idea: In internalist theories the grounds for justification are accessible to the believer, and Gettier problems arise when there is nothing wrong with the internally accessible aspects of the situation, but there is a mishap inaccessible to the believer.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 3.1)
     A reaction: I'm sure we could construct an internal mishap which the believer was unaware of, such as two confusions of the meanings of words cancelling one another out.
Gettier problems are always possible if justification and truth are not closely linked [Zagzebski]
     Full Idea: As long as the concept of knowledge closely connects the justification component and the truth component but permits some degree of independence between them, justified true belief will never be sufficient for knowledge.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 3.1)
     A reaction: Out of context this sounds like an advertisement for externalism. Or maybe it just says we have to live with Gettier threats. Zagzebski has other strategies.
We avoid the Gettier problem if the support for the belief entails its truth [Zagzebski]
     Full Idea: The way to avoid the Gettier problem is to define knowledge in such a way that truth is entailed by the other component(s) of the definition.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 3.1)
     A reaction: Thus she defines virtuous justification as being successful, as virtues tend to be. This smacks of cheating. Surely we can be defeated in a virtuous way? If the truth is entailed then of course Gettier can be sent packing.
Gettier cases arise when good luck cancels out bad luck [Zagzebski]
     Full Idea: The procedure for generating Gettier cases involves 'double luck': an instance of good luck cancels out an instance of bad luck.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 3.2)
     A reaction: You can end up with the right answer in arithmetic if you make two mistakes rather than one. I'm picturing a life of one blundering error after another, which to an outsider seems to be going serenely well.
13. Knowledge Criteria / B. Internal Justification / 1. Epistemic virtues
Intellectual virtues are forms of moral virtue [Zagzebski]
     Full Idea: I argue that intellectual virtues are forms of moral virtue.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II Intro)
     A reaction: This contrasts with Sosa, who seems to think intellectual virtues are just the most efficient ways of reaching the truth. I like Zabzebski's approach a lot, though we are in a very small minority. I love her book. We have epistemic and moral duties.
A reliable process is no use without the virtues to make use of them [Zagzebski]
     Full Idea: It is not enough that a process is reliable; a person will not reliably use such a process without certain virtues.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 4.1.2)
     A reaction: This is a point against Sosa's reliabilist account of virtues. Of course, all theories of epistemic justification (or of morality) will fail if people can't be bothered to implement them.
Intellectual and moral prejudice are the same vice (and there are other examples) [Zagzebski]
     Full Idea: Maybe the intellectual and the moral forms of prejudice are the same vice, and this may also be true of other traits with shared names, such as humility, autonomy, integrity, perseverance, courage and trustworthiness.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 3.1)
     A reaction: I find this claim very persuasive. The virtue of 'integrity' rather obviously embraces groups of both intellectually and morally desirable traits.
We can name at least thirteen intellectual vices [Zagzebski]
     Full Idea: Some examples of intellectual vices: pride, negligence, idleness, cowardice, conformity, carelessness, rigidity, prejudice, wishful thinking, closed-mindedness, insensitivity to detail, obtuseness (in seeing relevance), and lack of thoroughness.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 3.1)
     A reaction: There are thousands of vices for which we don't have names, like thinking about football when you should be doing metaphysics. The other way round is also a vice too, because football needs concentration. Discontent with your chair is bad too.
A justified belief emulates the understanding and beliefs of an intellectually virtuous person [Zagzebski]
     Full Idea: A justified belief is what a person who is motivated by intellectual virtue, and who has the understanding of his cognitive situation a virtuous person would have, might believe in like circumstances.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 6.1)
     A reaction: This is a whole-hearted definition of justification in terms of a theory of intellectual virtues. Presumably this would allow robots to have justified beliefs, if they managed to behave the way intellectually virtuous persons would behave.
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
Epistemic perfection for reliabilism is a truth-producing machine [Zagzebski]
     Full Idea: Just as a utility-calculating machine would be the ideal moral agent according to utilitarianism, a truth-producing machine would be the ideal epistemic agent according to reliabilism,
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], I 1.2)
     A reaction: Love this one! For consequentialists a successful robot is morally superior to an average human being. The reliabilist dream is just something that churns out truths. But what is the role of these truths in subsequent life?
16. Persons / C. Self-Awareness / 2. Knowing the Self
The self is known as much by its knowledge as by its action [Zagzebski]
     Full Idea: It seems to me that the concept of the self is constituted as much by what we know as by what we do.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 1)
     A reaction: People take pride in what they know, which indicates that it is of central importance to a person's nature. Hard to evaluate ideas such as this.
18. Thought / A. Modes of Thought / 3. Emotions / d. Emotional feeling
The feeling accompanying curiosity is neither pleasant nor painful [Zagzebski]
     Full Idea: Most feelings are experienced as pleasant or painful, but it is not evident that they all are; curiosity may be one that is not. [note: 'curiosity' may not be the name of a feeling, but a feeling typically accompanies it]
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 3.1)
     A reaction: If a machine generates a sliding scale from pain to pleasure, is there a neutral feeling at the midpoint, or does all feeling briefly vanish there? Not sure.
19. Language / C. Assigning Meanings / 1. Syntax
A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten]
     Full Idea: A notion of formal provability can be articulated in Peano arithmetic. ..This is surprisingly 'linguistic' rather than mathematical, but the key is in the Gödel coding. ..Hence we use Peano arithmetic as a theory of syntax.
     From: Leon Horsten (The Tarskian Turn [2011], 02.4)
     A reaction: This is the explanation of why issues in formal semantics end up being studied in systems based on formal arithmetic. And I had thought it was just because they were geeks who dream in numbers, and can't speak language properly...
20. Action / C. Motives for Action / 1. Acting on Desires
Motives involve desires, but also how the desires connect to our aims [Zagzebski]
     Full Idea: A motive does have an aspect of desire, but it includes something about why a state of affairs is desired, and that includes something about the way my emotions are tied to my aim.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 2.6)
     A reaction: It is standard usage that a 'motive' involves some movement towards achieving the desire, and not merely having the desire. I'd quite like to stand on top of Everest, but have absolutely no motivation to try to achieve it.
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
Modern moral theory concerns settling conflicts, rather than human fulfilment [Zagzebski]
     Full Idea: Modern ethics generally considers morality much less a system for fulfilling human nature than a set of principles for dealing with individuals in conflict.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 7)
     A reaction: Historically I associate this move with Hugo Grotius around 1620. He was a great legalist, and eudaimonist virtue ethics gradually turned into jurisprudence. The Enlightenment sought rules for resolving dilemmas. Liberalism makes fulfilment private.
22. Metaethics / C. The Good / 1. Goodness / i. Moral luck
Moral luck means our praise and blame may exceed our control or awareness [Zagzebski]
     Full Idea: Because of moral luck, the realm of the morally praiseworthy / blameworthy is not indisputably within one's voluntary control or accessible to one's consciousness.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], I 4.2)
     A reaction: [She particularly cites Thomas Nagel for this] It is a fact that we will be blamed (more strongly) when we have moral bad luck, but the question is whether we should be. It seems harsh, but you can't punish someone as if they had had bad luck.
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
Nowadays we doubt the Greek view that the flourishing of individuals and communities are linked [Zagzebski]
     Full Idea: Modern moral philosophers have been considerably more skeptical than were the ancient Greeks about the close association between the flourishing of the individual and that of the community.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 2.2)
     A reaction: I presume this is not just a change in fashion, but a reflection of how different the two societies are. In a close community with almost no privacy, flourishing individuals are good citizens. In the isolations of modern liberalism they may be irrelevant.
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
Virtue theory is hopeless if there is no core of agreed universal virtues [Zagzebski]
     Full Idea: An analysis of virtue is hopeless unless we can assume that most of a selected list of traits count as virtues, in a way not strictly culture. ...These would include wisdom, courage, benevolence, justice, honesty, loyalty, integrity, and generosity.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 2.1)
     A reaction: This requirement needs there to be a single core to human nature, right across the species. If we are infinitely flexible (as existentialists imply) then the virtues will have matching flexibility, and so will be parochial and excessively relative.
A virtue must always have a corresponding vice [Zagzebski]
     Full Idea: It is important for the nature of virtue that it have a corresponding vice (or two, in the doctrine of the mean). Claustrophobia is not a vice not only because it is involuntary, but also because there is no corresponding virtue.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 2.3)
     A reaction: Presumably attaining a virtue is an achievement, so we would expect a label for failure in the same field of endeavour. The failure is not purely negative, because bad things ensue if the virtue is not present.
Eight marks distingush skills from virtues [Zagzebski, by PG]
     Full Idea: The difference between skills and virtues is that virtues must be enacted, are always desirable, can't be forgotten, and can be simulated, whereas skills are very specific, involve a technique, lack contraries, and lack intrinsic value.
     From: report of Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 2.4) by PG - Db (ideas)
     A reaction: [my summary of her II 2.4 discussion of the differences] She observes that Aristotle made insufficient effort to distinguish the two. It may be obscure to say that virtues go 'deeper' than skills, but we all know what is meant. 'Skills serve virtues'.
Virtues are deep acquired excellences of persons, which successfully attain desire ends [Zagzebski]
     Full Idea: A virtue can be defined as 'a deep and enduring acquired excellence of a person, involving a characteristic motivation to produce a certain desired end and reliable success in bringing about that end'.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 2.7)
     A reaction: She puts this in bold, and it is the culminating definition of a long discussion. It rather obviously fails to say anything about the nature of the end that is desired. Learning the telephone book off by heart seems to fit the definition.
Every moral virtue requires a degree of intelligence [Zagzebski]
     Full Idea: Being reasonably intelligent within a certain area of life is part of having almost any moral virtue.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 3.1)
     A reaction: The fact that this bars persons of very limited intelligence from acquiring the Aristotelian virtues is one of the attractions of the Christian enjoinder to merely achieve 'love'. Anyone can have a warm heart. So is virtue elitist?
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
Virtue theory can have lots of rules, as long as they are grounded in virtues and in facts [Zagzebski]
     Full Idea: A pure virtue theory can have as many rules as you like as long as they are understood as grounded in the virtuous motivations and understanding of the nonmoral facts that virtuous agents possess.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 6.1)
     A reaction: It is important, I think, to see that a virtue theorist does not have to be a particularist.
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
We need phronesis to coordinate our virtues [Zagzebski]
     Full Idea: We need phronesis (practical wisdom) to coordinate the various virtues into a single line of action or line of thought leading up to an act or to a belief.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 5.2)
     A reaction: If I have a conflicting virtue and vice in a single situation, something must make sure that the virtue dominates. That sounds more like Kant's 'good will' than like phronesis.
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
For the virtue of honesty you must be careful with the truth, and not just speak truly [Zagzebski]
     Full Idea: It is not sufficient for honesty that a person tells whatever she happens to believe is the truth. An honest person is careful with the truth.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 3.2)
     A reaction: Not sure about that. It matches what Aristotle says about courage, which also needs practical reason [phronesis]. But being sensitive and careful with truth seems to need other virtues. If total honesty is not a virtue, then is honesty a virtue at all?
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
The courage of an evil person is still a quality worth having [Zagzebski]
     Full Idea: In the case of a courageous Nazi soldier, my position is that a virtue is worth having even in those cases in which it makes a person worse overall.
     From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 2.2)
     A reaction: A brave claim, which seems right. If a nasty Nazi reforms, they will at least have one good quality which can be put to constructive use.