Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'Abstract Objects: a Case Study' and 'Truthmakers, Realism and Ontology'

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19 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.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
     Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
     From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
     Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10)
     A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity.
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
     Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08)
     A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo]
     Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01)
We are thought to know concreta a posteriori, and many abstracta a priori [Yablo]
     Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02)
7. Existence / D. Theories of Reality / 2. Realism
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.
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'.
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?