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All the ideas for 'works', 'Mathematics without Foundations' and 'Truthmakers'

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28 ideas

1. Philosophy / G. Scientific Philosophy / 1. Aims of Science
Realism is the only philosophy of science that doesn't make the success of science a miracle [Putnam]
     Full Idea: Realism….is the only philosophy science which does not make the success of science a miracle.
     From: Hilary Putnam (works [1980]), quoted by Alexander Bird - Philosophy of Science Ch.4
     A reaction: This was from his earlier work; he became more pragmatist and anti-realist later. Personally I approve of the remark. The philosophy of science must certainly offer an explanation for its success. Truth seems the obvious explanation.
3. Truth / A. Truth Problems / 2. Defining Truth
We might define truth as arising from the truth-maker relation [MacBride]
     Full Idea: We might define truth using the truth-maker relation, albeit in a roundabout way, according to the pattern of saying 'S is true' is equivalent to 'there is something which makes S true'.
     From: Fraser MacBride (Truthmakers [2013], 3.3)
     A reaction: [MacBride gives it more algebraically, but I prefer English!] You would need to explain 'truth-making' without reference to truth. Horwich objects, reasonably, that ordinary people grasp 'truth' much more clearly than 'truth-making'. Bad idea, I think.
3. Truth / B. Truthmakers / 1. For Truthmakers
Phenomenalists, behaviourists and presentists can't supply credible truth-makers [MacBride]
     Full Idea: For Martin the fatal error of phenomenalists was their inability to supply credible truth-makers for truths about unobserved objects; the same error afflicted Ryle's behaviourism, ...and Prior's Presentism (for past-tensed and future-tensed truths).
     From: Fraser MacBride (Truthmakers [2013], 3.1)
     A reaction: This seems to be the original motivation for the modern rise of the truthmaker idea. Personally I find 'Napoleon won at Austerlitz' is a perfectly good past-tensed truthmaker which is compatible with presentism. Truth-making is an excellent challenge.
3. Truth / B. Truthmakers / 2. Truthmaker Relation
If truthmaking is classical entailment, then anything whatsoever makes a necessary truth [MacBride]
     Full Idea: If a truthmaker entails its truth, this threatens to over-generate truth-makers for necessary truths - at least if the entailment is classical. It's a feature of this notion that anything whatsoever entails a given necessary truth.
     From: Fraser MacBride (Truthmakers [2013], 1.1)
     A reaction: This is a good reason to think that the truth-making relation does not consist of logical entailment.
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
'Maximalism' says every truth has an actual truthmaker [MacBride]
     Full Idea: The principle of 'maximalism' is that for every truth, then there must be something in the world that makes it true.
     From: Fraser MacBride (Truthmakers [2013], 2.1)
     A reaction: That seems to mean that no truths can be uttered about anything which is not in the world. If I say 'pigs might have flown', that isn't about the modal profile of actual pigs, it is about what might have resulted from that profile.
Maximalism follows Russell, and optimalism (no negative or universal truthmakers) follows Wittgenstein [MacBride]
     Full Idea: If maximalism is intellectual heir to Russell's logical atomism, then 'optimalism' (the denial that universal and negative statements need truth-makers) is heir to Wittgenstein's version, where only atomic propositions represent states of affairs.
     From: Fraser MacBride (Truthmakers [2013], 2.2)
     A reaction: Wittgenstein's idea is that you can use the logical connectives to construct all the other universal and negative facts. 'Optimalism' restricts truthmaking to atomic statements.
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
The main idea of truth-making is that what a proposition is about is what matters [MacBride]
     Full Idea: According the Lewis, the kernel of truth in truth-making is the idea that propositions have a subject matter. They are about things, so whether they are true or false depends on how those things stand.
     From: Fraser MacBride (Truthmakers [2013], 2.4.1)
     A reaction: [Lewis 'Things Qua Truth-makers' 2003] That sounds like the first step in the story, rather than the 'kernel' of the truth-making approach.
3. Truth / B. Truthmakers / 6. Making Negative Truths
There are different types of truthmakers for different types of negative truth [MacBride]
     Full Idea: We recognise that what makes it true that there is no oil in this engine is different from what makes it true that there are no dodos left.
     From: Fraser MacBride (Truthmakers [2013], 2.1.4.1)
     A reaction: This looks like a local particular negation up against a universal negation. I'm not sure there is a big difference between 'my dodo's gone missing' (like my oil), and 'all the dodos have gone permanently missing'.
There aren't enough positive states out there to support all the negative truths [MacBride]
     Full Idea: It's not obvious that there are enough positive states out there to underwrite all the negative truths. Even though it may be true that this liquid is odourless this needn't be because there's something further about it that excludes its being odourless.
     From: Fraser MacBride (Truthmakers [2013], 2.1.4.1)
     A reaction: What is the ontological status of all these hypothetical truths? What is the truthmaker for 'a trillion trillion negative truths exist'? What is the status of 'this is not not-red'?
3. Truth / B. Truthmakers / 8. Making General Truths
Optimalists say that negative and universal are true 'by default' from the positive truths [MacBride]
     Full Idea: Optimalists say that negative truths are 'true by default' (having the opposite truth value of p), and universal truths are too. Universal truths are equivalent to negative existential truths, which are true by default.
     From: Fraser MacBride (Truthmakers [2013], 2.2)
     A reaction: The background idea is Wittgenstein's, that if p is false, then not-p is true by default, without anyone having to assert the negation. This strikes me as a very promising approach to truthmaking. See Simons 2008.
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
Does 'this sentence has no truth-maker' have a truth-maker? Reductio suggests it can't have [MacBride]
     Full Idea: If the sentence 'This sentence has no truth-maker' has a truth-maker, then it must be true. But then what it says must be the case, so it has no truth-maker. Hence by reductio the sentence has no truth-maker.
     From: Fraser MacBride (Truthmakers [2013], 2.1.1)
     A reaction: [Argument proposed by Peter Milne 2005] Rodriguez-Pereyra replies that the sentence is meaningless, so that it can't possibly be true. The Liar sentence is also said to be meaningless. The argument opposes Maximalism.
Even idealists could accept truthmakers, as mind-dependent [MacBride]
     Full Idea: Even an idealist could accept that there are truth-makers whilst thinking of them as mind-dependent entities.
     From: Fraser MacBride (Truthmakers [2013], 3.1)
     A reaction: This undercuts anyone (me, perhaps?) who was hoping to prop up their robust realism with an angry demand to be shown the truthmakers.
Maybe 'makes true' is not an active verb, but just a formal connective like 'because'? [MacBride]
     Full Idea: Maybe the truth-maker panegyrists have misconstrued the logical form of 'makes true'. They have taken it to be a verb like 'x hits y', when really it is akin to the connective '→' or 'because'.
     From: Fraser MacBride (Truthmakers [2013], 3.7)
     A reaction: [He cites Melia 2005] This isn't any sort of refutation of truth-making, but an offer of how to think of the phenomenon if you reject the big principle. I like truth-making, but resist the 'makes' that brings unthought propositions into existence.
Truthmaker talk of 'something' making sentences true, which presupposes objectual quantification [MacBride]
     Full Idea: When supporters of truth-making talk of 'something' which makes a sentence true, they make the assumption that it is an objectual quantifier in name position.
     From: Fraser MacBride (Truthmakers [2013], 3.8)
     A reaction: We might say, more concisely, that they are 'reifying' the something. This makes it sound as if Armstrong and Bigelow have made a mistake, but that are simply asserting that this particular quantification is indeed objectual.
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
We understand some statements about all sets [Putnam]
     Full Idea: We seem to understand some statements about all sets (e.g. 'for every set x and every set y, there is a set z which is the union of x and y').
     From: Hilary Putnam (Mathematics without Foundations [1967], p.308)
     A reaction: His example is the Axiom of Choice. Presumably this is why the collection of all sets must be referred to as a 'class', since we can talk about it, but cannot define it.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Connectives link sentences without linking their meanings [MacBride]
     Full Idea: The 'connectives' are expressions that link sentences but without expressing a relation that holds between the states of affairs, facts or tropes that these sentences denote.
     From: Fraser MacBride (Truthmakers [2013], 3.7)
     A reaction: MacBride notes that these contrast with ordinary verbs, which do express meaningful relations.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
'A is F' may not be positive ('is dead'), and 'A is not-F' may not be negative ('is not blind') [MacBride]
     Full Idea: Statements of the form 'a is F' aren't invariably positive ('a is dead'), and nor are statements of the form 'a isn't F' ('a isn't blind') always negative.
     From: Fraser MacBride (Truthmakers [2013], 2.1.4)
     A reaction: The point is that the negation may be implicit in the predicate. There are many ways to affirm or deny something, other than by use of the standard syntax.
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
I do not believe mathematics either has or needs 'foundations' [Putnam]
     Full Idea: I do not believe mathematics either has or needs 'foundations'.
     From: Hilary Putnam (Mathematics without Foundations [1967])
     A reaction: Agreed that mathematics can function well without foundations (given that the enterprise got started with no thought for such things), the ontology of the subject still strikes me as a major question, though maybe not for mathematicians.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
     Full Idea: I believe that under certain circumstances revisions in the axioms of arithmetic, or even of the propositional calculus (e.g. the adoption of a modular logic as a way out of the difficulties in quantum mechanics), is fully conceivable.
     From: Hilary Putnam (Mathematics without Foundations [1967], p.303)
     A reaction: One can change the axioms of a system without necessarily changing the system (by swapping an axiom and a theorem). Especially if platonism is true, since the eternal objects reside calmly above our attempts to axiomatise them!
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Maybe mathematics is empirical in that we could try to change it [Putnam]
     Full Idea: Mathematics might be 'empirical' in the sense that one is allowed to try to put alternatives into the field.
     From: Hilary Putnam (Mathematics without Foundations [1967], p.303)
     A reaction: He admits that change is highly unlikely. It take hardcore Millian arithmetic to be only changeable if pebbles start behaving very differently with regard to their quantities, which appears to be almost inconceivable.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Science requires more than consistency of mathematics [Putnam]
     Full Idea: Science demands much more of a mathematical theory than that it should merely be consistent, as the example of the various alternative systems of geometry dramatizes.
     From: Hilary Putnam (Mathematics without Foundations [1967])
     A reaction: Well said. I don't agree with Putnam's Indispensability claims, but if an apparent system of numbers or lines has no application to the world then I don't consider it to be mathematics. It is a new game, like chess.
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Maybe it only exists if it is a truthmaker (rather than the value of a variable)? [MacBride]
     Full Idea: 'To be is to be a truth-maker' has been proposed as a replacement the standard conception of ontological commitment, that to be is to be the value of a variable.
     From: Fraser MacBride (Truthmakers [2013], 2.1.4.2)
     A reaction: [He cites Ross Cameron 2008] Unconvincing. What does it mean to say that some remote unexperienced bit of the universe 'makes truths'? How many truths? Where do these truths reside when they aren't doing anything useful?
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
Different types of 'grounding' seem to have no more than a family resemblance relation [MacBride]
     Full Idea: The concept of 'grounding' appears to cry out for treatment as a family resemblance concept, a concept whose instances have no more in common than different games do.
     From: Fraser MacBride (Truthmakers [2013], 1.6)
     A reaction: I like the word 'determinations', though MacBride's point my also apply to that. I take causation to be one species of determination, and truth-making to be another. They form a real family, with no adoptees.
Which has priority - 'grounding' or 'truth-making'? [MacBride]
     Full Idea: Some philosophers define 'grounding' in terms of 'truth-making', rather than the other way around.
     From: Fraser MacBride (Truthmakers [2013], 1.6)
     A reaction: [Cameron exemplifies the first, and Schaffer the second] I would have thought that grounding was in the world, but truth-making required the introduction of propositions about the world by minds, so grounding is prior. Schaffer is right.
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
Russell allows some complex facts, but Wittgenstein only allows atomic facts [MacBride]
     Full Idea: The logical atomism of Russell admitted some logically complex facts but not others - in contrast to Wittgenstein's version which admitted only atomic facts.
     From: Fraser MacBride (Truthmakers [2013], 2.1.3)
     A reaction: For truthmakers, it looks as if the Wittgenstein version might do a better job (e.g. with negative truths). I quite like the Russell approach, where complex facts underwrite the logical connectives. Disjunctive, negative, conjunctive, hypothetical facts.
7. Existence / D. Theories of Reality / 4. Anti-realism
You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam]
     Full Idea: Surely the mere fact that we may never know whether the continuum hypothesis is true or false is by itself just no reason to think that it doesn't have a truth value!
     From: Hilary Putnam (Mathematics without Foundations [1967])
     A reaction: This is Putnam in 1967. Things changed later. Personally I am with the younger man all they way, but I reserve the right to totally change my mind.
Putnam says anti-realism is a bad explanation of accurate predictions [Putnam, by Okasha]
     Full Idea: Putnam's 'no miracle' argument says that being an anti-realist is akin to believing in miracles (because of the accurate predictons). …It is a plausibility argument - an inference to the best explanation.
     From: report of Hilary Putnam (works [1980]) by Samir Okasha - Philosophy of Science: Very Short Intro (2nd ed) 4
     A reaction: [not sure of ref] Putnam later backs off from this argument, but my personal realism rests on best explanation. Does anyone want to prefer an inferior explanation? The objection is that successful theories can turn out to be false. Phlogiston, ether.
10. Modality / A. Necessity / 6. Logical Necessity
Wittgenstein's plan to show there is only logical necessity failed, because of colours [MacBride]
     Full Idea: It is almost universally acknowledged that Wittgenstein's plan to show all necessity is logical necessity ended in failure - indeed foundered upon the very problem of explaining colour incompatibilities.
     From: Fraser MacBride (Truthmakers [2013], 2.1.4.1)
     A reaction: I'm not sure whether you can 'show' that colour incompatibility is some sort of necessity, though intuitively it seems so. I'm thinking that 'necessity' is a unitary concept, with a wide variety of sources generating it.