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All the ideas for 'Function and Concept', 'Completeness of Axioms of Logic' and 'Truthmakers, Realism and Ontology'

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28 ideas

3. Truth / B. Truthmakers / 2. Truthmaker Relation
Moral realism doesn't seem to entail the existence of any things [Cameron]
     Full Idea: Moral realism isn't realism about things, and it seems strange to suggest that moral realism is existence entailing in the way that realism about unobservable is.
     From: Ross P. Cameron (Truthmakers, Realism and Ontology [2008], 'Realism')
     A reaction: Cameron is questioning whether a realist has to believe in truthmakers. It seems to me that his doubts are because he insists that truthmaking is committed to the existence of 'things'. I assume any moral realism must supervene on nature.
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
Surely if some propositions are grounded in existence, they all are? [Cameron]
     Full Idea: What possible reason could one have for thinking of some propositions that they need to be grounded in what there is that doesn't apply to all propositions?
     From: Ross P. Cameron (Truthmakers, Realism and Ontology [2008], 'Max and Nec')
     A reaction: Well, if truthmaking said that all truths are grounded, then some could be grounded in what there is, and others in how it is, or maybe even how it isn't (if you get a decent account of negative truths).
3. Truth / B. Truthmakers / 4. Truthmaker Necessitarianism
Orthodox Truthmaker applies to all propositions, and necessitates their truth [Cameron]
     Full Idea: Orthodox truthmaker theory (Armstrong's) entails Maximalism (that every true proposition has at least one truthmaker), and Necessitarianism (that the existence of a truthmaker necessitates the truth of its proposition).
     From: Ross P. Cameron (Truthmakers, Realism and Ontology [2008], 'Max and Nec')
     A reaction: I think I accept both of these. If you say only some truths have truthmakers, the other truths are then baffling. And how could a truthmaker fail in its job? But that doesn't necessitate the existence of the proposition.
God fixes all the truths of the world by fixing what exists [Cameron]
     Full Idea: The truthmaker thought is that explanation only bottoms out at existence facts; for God to give a complete plan of the world He needs only make an inventory of what is to exist.
     From: Ross P. Cameron (Truthmakers, Realism and Ontology [2008], 'Max and Nec')
     A reaction: He is defending Necessitarianism about truthmaking. I'm struggling with this. An inventory of the contents of my house doesn't begin to fix all the truths that arise from them. Why is Cameron so resistent to 'how' things are being part of the truthmaking?
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
What the proposition says may not be its truthmaker [Cameron]
     Full Idea: The explanation of the truth of the proposition [p] doesn't stop at it being the case that p, so it's false to claim that whenever a proposition is true it's true in virtue of the world being as the proposition says it is. The features often lie deeper.
     From: Ross P. Cameron (Truthmakers, Realism and Ontology [2008], 'Grounding')
     A reaction: [He is opposing Jennifer Hornsby 2005] Cameron offers 'the average family has 2.4 children' as a counterexample' (since no one actually has 2.4 children). That seems compelling. Second example: 'the rose is beautiful'.
Rather than what exists, some claim that the truthmakers are ways of existence, dispositions, modalities etc [Cameron]
     Full Idea: Rivals to the truthmaker claim that facts about what there is are the truthmakers, there are theories that add facts about how the things are, or add dispositional facts, or modal facts, or haecceitistic facts, or maybe moral facts.
     From: Ross P. Cameron (Truthmakers, Realism and Ontology [2008], 'Grounding')
     A reaction: [compressed] He seems to think his version has a monopoly on truthmaking, but I don't see why these other theories shouldn't count as truthmaking. The truthmaker for 'live grenades are dangerous' is not just the existence of grenades.
Truthmaking doesn't require realism, because we can be anti-realist about truthmakers [Cameron]
     Full Idea: It's definitely not sufficient to be a realist that one be a truthmaker theorist, since one can simply be anti-realist about the truthmakers.
     From: Ross P. Cameron (Truthmakers, Realism and Ontology [2008], 'Realism')
     A reaction: It is not quite clear how unreal truth makers could actually MAKE propositions true, rather than just being correlated with them.
3. Truth / B. Truthmakers / 6. Making Negative Truths
Without truthmakers, negative truths must be ungrounded [Cameron]
     Full Idea: If negative truths don't have truthmakers then make no mistake: they are ungrounded.
     From: Ross P. Cameron (Truthmakers, Realism and Ontology [2008], 'Max and Nec')
     A reaction: What would be the grounding for truths which expressed the necessary preconditions for all existence? Could 'nothing whatever exists' ever be a truth?
3. Truth / B. Truthmakers / 11. Truthmaking and Correspondence
I support the correspondence theory because I believe in truthmakers [Cameron]
     Full Idea: I tend to think that the fundamental reason we can have the correspondence theory of truth is that truthmaker theory is correct.
     From: Ross P. Cameron (Truthmakers, Realism and Ontology [2008], 'Max and Nec')
     A reaction: [This responds to Fumerton 2006, who gives the opposite view] Cameron gives himself the classic problem of spelling out the correspondence relation (perhaps as 'congruence'). I like truthmaking, but I'm unsure about correspondence.
Maybe truthmaking and correspondence stand together, and are interdefinable [Cameron]
     Full Idea: One view says truthmaker theory stands or falls with the correspondence theory of truth, because the truthmaker for p is just the portion of reality that p corresponds to: truthmaker and correspondence can be conversely defined.
     From: Ross P. Cameron (Truthmakers, Realism and Ontology [2008], 'Max and Nec')
     A reaction: The normal view, which I prefer, is that correspondence is a particular theory of truthmaking, invoking a precise 'correspondence' relation. Hence abolishing correspondence would not abolish truthmaking, if you had a rival account.
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt]
     Full Idea: Frege rejected the traditional categories as importing psychological and linguistic impurities into logic.
     From: report of Gottlob Frege (Function and Concept [1891]) by Ian Rumfitt - The Boundary Stones of Thought 1.2
     A reaction: Resisting such impurities is the main motivation for making logic entirely symbolic, but it doesn't follow that the traditional categories have to be dropped.
4. Formal Logic / C. Predicate Calculus PC / 3. Completeness of PC
Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki]
     Full Idea: Gödel proved the completeness of first order predicate logic in his doctoral dissertation of 1930.
     From: report of Kurt Gödel (Completeness of Axioms of Logic [1930]) by Michal Walicki - Introduction to Mathematical Logic History E.2.2
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
First-level functions have objects as arguments; second-level functions take functions as arguments [Frege]
     Full Idea: Just as functions are fundamentally different from objects, so also functions whose arguments are and must be functions are fundamentally different from functions whose arguments are objects. The latter are first-level, the former second-level, functions.
     From: Gottlob Frege (Function and Concept [1891], p.38)
     A reaction: In 1884 he called it 'second-order'. This is the standard distinction between first- and second-order logic. The first quantifies over objects, the second over intensional entities such as properties and propositions.
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
Relations are functions with two arguments [Frege]
     Full Idea: Functions of one argument are concepts; functions of two arguments are relations.
     From: Gottlob Frege (Function and Concept [1891], p.39)
     A reaction: Nowadays we would say 'two or more'. Another interesting move in the aim of analytic philosophy to reduce the puzzling features of the world to mathematical logic. There is, of course, rather more to some relations than being two-argument functions.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege]
     Full Idea: I am of the opinion that arithmetic is a further development of logic, which leads to the requirement that the symbolic language of arithmetic must be expanded into a logical symbolism.
     From: Gottlob Frege (Function and Concept [1891], p.30)
     A reaction: This may the the one key idea at the heart of modern analytic philosophy (even though logicism may be a total mistake!). Logic and arithmetical foundations become the master of ontology, instead of the servant. The jury is out on the whole enterprise.
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Frege takes the existence of horses to be part of their concept [Frege, by Sommers]
     Full Idea: Frege regarded the existence of horses as a property of the concept 'horse'.
     From: report of Gottlob Frege (Function and Concept [1891]) by Fred Sommers - Intellectual Autobiography 'Realism'
7. Existence / D. Theories of Reality / 2. Realism
Realism says a discourse is true or false, and some of it is true [Cameron]
     Full Idea: Realism about a discourse is 1) to think that the sentences are, when construed literally, literally true or false, and 2) to think that some of the sentences of the discourse are non-vacuously true.
     From: Ross P. Cameron (Truthmakers, Realism and Ontology [2008], 'Realism')
     A reaction: [Cameron adds 'non-vacuously' to an idea of Sayre-McCord 199 p.5] This is realism based on what is 'true', without specifying 'commitments', so I like it. Cameron says it makes mathematical postulationists into realists. He likes 'mind-independent'.
Realism says truths rest on mind-independent reality; truthmaking theories are about which features [Cameron]
     Full Idea: All that is necessary for realism, I claim, is that truth is grounded in mind-independent features of fundamental reality. Truthmaker theory comes into play because it is a theory about what those features are (…so it isn't a commitment to realism).
     From: Ross P. Cameron (Truthmakers, Realism and Ontology [2008], 'Realism')
     A reaction: [He cites Michael Devitt for this approach] What is the word 'fundamental' doing here? Because the mind-dependent parts of reality are considered non-fundamental? The no-true-Scotsman-hates-whisky move? His truthmaking is committed to 'things'.
For realists it is analytic that truths are grounded in the world [Cameron]
     Full Idea: The analytic commitment of realism is that truths are grounded in the world.
     From: Ross P. Cameron (Truthmakers, Realism and Ontology [2008], 'Grounding')
     A reaction: Certain fifth-level truths might be a long way from the actual world, and deeply interfused with human concepts and theories. Negative truths must be fitted into this picture.
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege]
     Full Idea: Frege's theory of properties (which he calls 'concepts') yields too few properties, by identifying coextensive properties, and also too many, by letting every predicate express a property.
     From: comment on Gottlob Frege (Function and Concept [1891]) by DH Mellor / A Oliver - Introduction to 'Properties' §2
     A reaction: Seems right; one extension may have two properties (have heart/kidneys), two predicates might express the same property. 'Cutting nature at the joints' covers properties as well as objects.
9. Objects / A. Existence of Objects / 3. Objects in Thought
The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege]
     Full Idea: I regard a regular definition of 'object' as impossible, since it is too simple to admit of logical analysis. Briefly: an object is anything that is not a function, so that an expression for it does not contain any empty place.
     From: Gottlob Frege (Function and Concept [1891], p.32)
     A reaction: Here is the core of the programme for deriving our ontology from our logic and language, followed through by Russell and Quine. Once we extend objects beyond the physical, it becomes incredibly hard to individuate them.
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
We should reject distinct but indiscernible worlds [Cameron]
     Full Idea: I think we should reject distinct but indiscernible worlds.
     From: Ross P. Cameron (Truthmakers, Realism and Ontology [2008], 'Max and Nec')
     A reaction: An interesting passing remark. Presumably there would be unknowable truths about such worlds, which wouldn't bother a full-blooded realist. Indiscernible to whom? Me? Humanity? A divine mind?
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman]
     Full Idea: Concepts, for Frege, are the ontological counterparts of predicative expressions.
     From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2
     A reaction: That sounds awfully like what many philosophers call 'universals'. Frege, as a platonist (at least about numbers), I would take to be in sympathy with that. At least we can say that concepts seem to be properties.
An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale]
     Full Idea: Frege had a notorious difficulty over the concept 'horse', when he suggests that if we wish to assert something about a concept, we are obliged to proceed indirectly by speaking of an object that represents it.
     From: report of Gottlob Frege (Function and Concept [1891], Ch.2.II) by Bob Hale - Abstract Objects
     A reaction: This sounds like the thin end of a wedge. The great champion of objects is forced to accept them here as a façon de parler, when elsewhere they have ontological status.
A concept is a function whose value is always a truth-value [Frege]
     Full Idea: A concept in logic is closely connected with what we call a function. Indeed, we may say at once: a concept is a function whose value is always a truth-value. ..I give the name 'function' to what is meant by the 'unsaturated' part.
     From: Gottlob Frege (Function and Concept [1891], p.30)
     A reaction: So a function becomes a concept when the variable takes a value. Problems arise when the value is vague, or the truth-value is indeterminable.
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman]
     Full Idea: For Frege, concepts differ from objects in being inherently incomplete in nature.
     From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2
     A reaction: This is because they are 'unsaturated', needing a quantified variable to complete the sentence. This could be a pointer towards Quine's view of properties, as simply an intrinsic feature of predication about objects, with no separate identity.
19. Language / B. Reference / 5. Speaker's Reference
I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege]
     Full Idea: From sameness of meaning there does not follow sameness of thought expressed. A fact about the Morning Star may express something different from a fact about the Evening Star, as someone may regard one as true and the other false.
     From: Gottlob Frege (Function and Concept [1891], p.14)
     A reaction: This all gets clearer if we distinguish internalist and externalist theories of content. Why take sides on this? Why not just ask 'what is in the speaker's head?', 'what does the sentence mean in the community?', and 'what is the corresponding situation?'
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
The Ontological Argument fallaciously treats existence as a first-level concept [Frege]
     Full Idea: The ontological proof of God's existence suffers from the fallacy of treating existence as a first-level concept.
     From: Gottlob Frege (Function and Concept [1891], p.38 n)
     A reaction: [See Idea 8490 for first- and second-order functions] This is usually summarised as the idea that existence is a quantifier rather than a predicate.