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All the ideas for 'Realism in Mathematics', 'What is Justified Belief?' and 'Truth (2nd edn)'

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20 ideas

3. Truth / A. Truth Problems / 1. Truth
The function of the truth predicate? Understanding 'true'? Meaning of 'true'? The concept of truth? A theory of truth? [Horwich]
     Full Idea: We must distinguish the function of the truth predicate, what it is to understand 'true', the meaning of 'true', grasping the concept of truth, and a theory of truth itself.
     From: Paul Horwich (Truth (2nd edn) [1990], Ch.2.8)
     A reaction: It makes you feel tired to think about it. Presumably every other philosophical analysis has to do this many jobs. Clearly Horwich wants to propose one account which will do all five jobs. Personally I don't believe these five are really distinct.
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Some correspondence theories concern facts; others are built up through reference and satisfaction [Horwich]
     Full Idea: One correspondence theory (e.g. early Wittgenstein) concerns representations and facts; alternatively (Tarski, Davidson) the category of fact is eschewed, and the truth of sentences or propositions is built out of relations of reference and satisfaction.
     From: Paul Horwich (Truth (2nd edn) [1990], Ch.7.35)
     A reaction: A helpful distinction. Clearly the notion of a 'fact' is an elusive one ("how many facts are there in this room?"), so it seems quite promising to say that the parts of the sentence correspond, rather than the whole thing.
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
The common-sense theory of correspondence has never been worked out satisfactorily [Horwich]
     Full Idea: The common-sense notion that truth is a kind of 'correspondence with the facts' has never been worked out to anyone's satisfaction.
     From: Paul Horwich (Truth (2nd edn) [1990], Ch.1)
     A reaction: I've put this in to criticise it. Philosophy can't work by rejecting theories which can't be 'worked out', and accepting theories (like Tarski's) because they can be 'worked out'. All our theories will end up minimal, and defiant of common sense.
3. Truth / H. Deflationary Truth / 1. Redundant Truth
The redundancy theory cannot explain inferences from 'what x said is true' and 'x said p', to p [Horwich]
     Full Idea: The redundancy theory is unable to account for the inference from "Oscar's claim is true" and "Oscar's claim is that snow is white" to "the proposition 'that snow is white' is true", and hence to "snow is white".
     From: Paul Horwich (Truth (2nd edn) [1990], Ch.2.9)
     A reaction: Earlier objections appealed to the fact that the word 'true' seemed to have a use in ordinary speech, but this seems a much stronger one. In general, showing the role of a term in making inferences pins it down better than ordinary speech does.
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Truth is a useful concept for unarticulated propositions and generalisations about them [Horwich]
     Full Idea: All uses of the truth predicate are explained by the hypothesis that its entire raison d'ętre is to help us say things about unarticulated propositions, and in particular to express generalisations about them.
     From: Paul Horwich (Truth (2nd edn) [1990], Concl)
     A reaction: This certain is a very deflationary notion of truth. Articulated propositions are considered to stand on their own two feet, without need of 'is true'. He makes truth sound like a language game, though. Personally I prefer to mention reality.
No deflationary conception of truth does justice to the fact that we aim for truth [Horwich]
     Full Idea: It has been suggested that no deflationary conception of truth could do justice to the fact that we aim for the truth.
     From: Paul Horwich (Truth (2nd edn) [1990], Ch.2.11)
     A reaction: (He mentions Dummett and Wright). People don't only aim for it - they become very idealistic about it, and sometimes die for it. Personally I think that any study of truth should use as its example police investigations, not philosophical analysis.
Horwich's deflationary view is novel, because it relies on propositions rather than sentences [Horwich, by Davidson]
     Full Idea: Horwich's brave and striking move is to make the primary bearers of truth propositions - not exactly a new idea in itself, but new in the context of a serious attempt to defend deflationism.
     From: report of Paul Horwich (Truth (2nd edn) [1990]) by Donald Davidson - The Folly of Trying to Define Truth p.30
     A reaction: Davidson rejects propositions because they can't be individuated, but I totally accept propositions. I'm puzzled why this would produce a deflationist theory, since I think it points to a much more robust view.
The deflationary picture says believing a theory true is a trivial step after believing the theory [Horwich]
     Full Idea: According to the deflationary picture, believing that a theory is true is a trivial step beyond believing the theory.
     From: Paul Horwich (Truth (2nd edn) [1990], Ch.2.17)
     A reaction: What has gone wrong with this picture is that you cannot (it seems to me) give a decent account of belief without mentioning truth. To believe a proposition is to hold it true. Hume's emotional account (Idea 2208) makes belief bewildering.
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
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 / E. Structures of Logic / 1. Logical Form
Logical form is the aspects of meaning that determine logical entailments [Horwich]
     Full Idea: The logical forms of the sentences in a language are those aspects of their meanings that determine the relations of deductive entailment holding amongst them.
     From: Paul Horwich (Truth (2nd edn) [1990], Ch.6.30)
     A reaction: A helpful definition. Not all sentences, therefore, need to have a 'logical form'. Is the logical form the same as the underlying proposition. The two must converge, given that propositions lack the ambiguity that is often found in sentences.
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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.
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.
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
A belief can be justified when the person has forgotten the evidence for it [Goldman]
     Full Idea: A characteristic case in which a belief is justified though the cognizer doesn't know that it's justified is where the original evidence for the belief has long since been forgotten.
     From: Alvin I. Goldman (What is Justified Belief? [1976], II)
     A reaction: This is a central problem for any very literal version of internalism. The fully rationalist view (to which I incline) will be that the cognizer must make a balanced assessment of whether they once had the evidence. Were my teachers any good?
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
If justified beliefs are well-formed beliefs, then animals and young children have them [Goldman]
     Full Idea: If one shares my view that justified belief is, at least roughly, well-formed belief, surely animals and young children can have justified beliefs.
     From: Alvin I. Goldman (What is Justified Belief? [1976], III)
     A reaction: I take this to be a key hallmark of the externalist view of knowledge. Personally I think we should tell the animals that they have got true beliefs, but that they aren't bright enough to aspire to 'knowledge'. Be grateful for what you've got.
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Justification depends on the reliability of its cause, where reliable processes tend to produce truth [Goldman]
     Full Idea: The justificational status of a belief is a function of the reliability of the processes that cause it, where (provisionally) reliability consists in the tendency of a process to produce beliefs that are true rather than false.
     From: Alvin I. Goldman (What is Justified Belief? [1976], II)
     A reaction: Goldman's original first statement of reliabilism, now the favourite version of externalism. The obvious immediate problem is when a normally very reliable process goes wrong. Wise people still get it wrong, or right for the wrong reasons.
16. Persons / C. Self-Awareness / 1. Introspection
Introspection is really retrospection; my pain is justified by a brief causal history [Goldman]
     Full Idea: Introspection should be regarded as a form of retrospection. Thus, a justified belief that I am 'now' in pain gets its justificational status from a relevant, though brief, causal history.
     From: Alvin I. Goldman (What is Justified Belief? [1976], II)
     A reaction: He cites Hobbes and Ryle as having held this view. See Idea 6668. I am unclear why the history must be 'causal'. I may not know the cause of the pain. I may not believe an event which causes a proposition, or I may form a false belief from it.
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
We could know the truth-conditions of a foreign sentence without knowing its meaning [Horwich]
     Full Idea: Someone who does not understand German and is told 'Schnee ist weiss' is true if frozen H2O is white, does not understand the German sentence, even though he knows the truth-conditions.
     From: Paul Horwich (Truth (2nd edn) [1990], Ch.5.22 n1)
     A reaction: This sounds like a powerful objection to Davidson's well-known claim that meaning is truth-conditions. Horwich likes the idea that meaning is use, but I think a similar objection arises - you can use a sentence well without knowing its meaning.
19. Language / D. Propositions / 1. Propositions
There are Fregean de dicto propositions, and Russellian de re propositions, or a mixture [Horwich]
     Full Idea: There are pure, Fregean, abstract, de dicto propositions, in which a compositional structure is filled only with senses; there are pure, Russellian, concrete, de re propositions, which are filled with referents; and there are mixed propositions.
     From: Paul Horwich (Truth (2nd edn) [1990], Ch.6.31)
     A reaction: Once Frege has distinguished sense from reference, this distinction of propositions is likely to follow. The current debate over the internalist and externalist accounts of concepts seems to continue the debate. A mixed strategy sounds good.
19. Language / F. Communication / 6. Interpreting Language / b. Indeterminate translation
Right translation is a mapping of languages which preserves basic patterns of usage [Horwich]
     Full Idea: The right translation between words of two languages is the mapping that preserves basic patterns of usage - where usage is characterised non-semantically, in terms of circumstances of application, assertibility conditions and inferential role.
     From: Paul Horwich (Truth (2nd edn) [1990], Ch.6.32)
     A reaction: It still strikes me that if you ask why a piece of language is used in a certain way, you find yourself facing something deeper about meaning than mere usage. Horwich cites Wittgenstein and Quine in his support. Could a machine pass his test?