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All the ideas for 'Classical Cosmology (frags)', 'Introduction to the Theory of Logic' and 'Truthmakers'

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39 ideas

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 / 1. Set Theory
Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo]
     Full Idea: We can define a set by 'enumeration' (by listing the items, within curly brackets), or by 'abstraction' (by specifying the elements as instances of a property), pretending that they form a determinate totality. The latter is written {x | x is P}.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3)
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo]
     Full Idea: The 'Cartesian Product' of two sets, written A x B, is the relation which pairs every element of A with every element of B. So A x B = { | x ∈ A and y ∈ B}.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6)
A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo]
     Full Idea: A binary relation in a set is a 'partial ordering' just in case it is reflexive, antisymmetric and transitive.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Determinacy: an object is either in a set, or it isn't [Zalabardo]
     Full Idea: Principle of Determinacy: For every object a and every set S, either a is an element of S or a is not an element of S.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.2)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
Specification: Determinate totals of objects always make a set [Zalabardo]
     Full Idea: Principle of Specification: Whenever we can specify a determinate totality of objects, we shall say that there is a set whose elements are precisely the objects that we have specified.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3)
     A reaction: Compare the Axiom of Specification. Zalabardo says we may wish to consider sets of which we cannot specify the members.
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
A first-order 'sentence' is a formula with no free variables [Zalabardo]
     Full Idea: A formula of a first-order language is a 'sentence' just in case it has no free variables.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.2)
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo]
     Full Idea: A propositional logic sentence is a 'logical consequence' of a set of sentences (written Γ |= φ) if for every admissible truth-assignment all the sentences in the set Γ are true, then φ is true.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4)
     A reaction: The definition is similar for predicate logic.
Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo]
     Full Idea: A formula is the 'logical consequence' of a set of formulas (Γ |= φ) if for every structure in the language and every variable interpretation of the structure, if all the formulas within the set are true and the formula itself is true.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5)
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 / b. Basic connectives
Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo]
     Full Idea: In propositional logic, any set containing ¬ and at least one of ∧, ∨ and → is expressively complete.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.8)
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.
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo]
     Full Idea: The semantic pattern of a first-order language is the ways in which truth values depend on which individuals instantiate the properties and relations which figure in them. ..So we pair a truth value with each combination of individuals, sets etc.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.3)
     A reaction: So truth reduces to a combination of 'instantiations', which is rather like 'satisfaction'.
We can do semantics by looking at given propositions, or by building new ones [Zalabardo]
     Full Idea: We can look at semantics from the point of view of how truth values are determined by instantiations of properties and relations, or by asking how we can build, using the resources of the language, a proposition corresponding to a given semantic pattern.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6)
     A reaction: The second version of semantics is model theory.
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo]
     Full Idea: A truth assignment is a function from propositions to the set {T,F}. We will think of T and F as the truth values true and false, but for our purposes all we need to assume about the identity of these objects is that they are different from each other.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4)
     A reaction: Note that T and F are 'objects'. This remark is important in understanding modern logical semantics. T and F can be equated to 1 and 0 in the language of a computer. They just mean as much as you want them to mean.
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
'Logically true' (|= φ) is true for every truth-assignment [Zalabardo]
     Full Idea: A propositional logic sentence is 'logically true', written |= φ, if it is true for every admissible truth-assignment.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4)
Logically true sentences are true in all structures [Zalabardo]
     Full Idea: In first-order languages, logically true sentences are true in all structures.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5)
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo]
     Full Idea: A propositional logic set of sentences Γ is 'satisfiable' if there is at least one admissible truth-assignment that makes all of its sentences true.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4)
Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo]
     Full Idea: A set of formulas of a first-order language is 'satisfiable' if there is a structure and a variable interpretation in that structure such that all the formulas of the set are true.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5)
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo]
     Full Idea: A structure is a model of a sentence if the sentence is true in the model; a structure is a model of a set of sentences if they are all true in the structure.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6)
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
If a set is defined by induction, then proof by induction can be applied to it [Zalabardo]
     Full Idea: Defining a set by induction enables us to use the method of proof by induction to establish that all the elements of the set have a certain property.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.3)
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.
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.
27. Natural Reality / E. Cosmology / 1. Cosmology
Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG]
     Full Idea: The four major disputes in classical cosmology were whether the cosmos is 'open' or 'closed', whether it is explained mechanistically or teleologically, whether it is alive or mere matter, and whether or not it has a beginning.
     From: report of T.M. Robinson (Classical Cosmology (frags) [1997]) by PG - Db (ideas)
     A reaction: A nice summary. The standard modern view is closed, mechanistic, inanimate and non-eternal. But philosophers can ask deeper questions than physicists, and I say we are entitled to speculate when the evidence runs out.