Combining Texts

All the ideas for 'Substance and Individuation in Leibniz', 'A Completeness Theorem in Modal Logic' and 'How to Make our Ideas Clear'

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20 ideas

3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
Truth is the opinion fated to be ultimately agreed by all investigators [Peirce]
     Full Idea: The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real.
     From: Charles Sanders Peirce (How to Make our Ideas Clear [1878], p.38)
     A reaction: At least this affirms that truth is an ideal about which we dream, and is not confined merely to what we can actually know. But it rules out anything beyond the reach of all investigation, which seems a misconception of truth. What could angels know?
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman]
     Full Idea: At the age of 19 Saul Kripke published a completeness proof of propositional modal logic.
     From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Feferman / Feferman - Alfred Tarski: life and logic Int V
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg]
     Full Idea: Kripke gave a possible worlds semantics to a whole range of modal logics, and S4 and S5 turned out to be both sound and complete with this semantics. Hence more systems could be designed. S1-S3 failed in soundness, leading to 'impossible worlds'.
     From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Marcus Rossberg - First-order Logic, 2nd-order, Completeness §4
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The variable domain approach to quantified modal logic invalidates the Barcan Formula [Kripke, by Simchen]
     Full Idea: Kripke's variable domain approach to quantified modal logic famously invalidates the Barcan Formula.
     From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Ori Simchen - The Barcan Formula and Metaphysics §3
     A reaction: [p.9 and p.16] In a single combined domain all the possibilia must be present, but with variable domains objects in remote domains may not exist in your local domain. BF is committed to those possible objects.
The Barcan formulas fail in models with varying domains [Kripke, by Williamson]
     Full Idea: Kripke showed that the Barcan formula ∀x□A⊃□∀xA and its converse fail in models which require varying domains.
     From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Timothy Williamson - Truthmakers and Converse Barcan Formula §1
     A reaction: I think this is why I reject the Barcan formulas for metaphysics - because the domain of metaphysics should be seen as varying, since some objects are possible in some contexts and not in others. Hmm…
8. Modes of Existence / A. Relations / 1. Nature of Relations
Scholastics treat relations as two separate predicates of the relata [Cover/O'Leary-Hawthorne]
     Full Idea: The scholastics treated it as a step in the right explanatory direction to analyze a relational statement of the form 'aRb' into two subject-predicate statements, attributing different relational predicates to a and to b.
     From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 2.2.1)
     A reaction: The only alternative seems to be Russell's view of relations as pure universals, having a life of their own, quite apart from their relata. Or you could take them as properties of space, time (and powers?), external to the relata?
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
If you individuate things by their origin, you still have to individuate the origins themselves [Cover/O'Leary-Hawthorne]
     Full Idea: If we go for the necessity-of-origins view, A and B are different if the origin of A is different from the origin of B. But one is left with the further question 'When is the origin of A distinct from the origin of B?'
     From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.4.1)
     A reaction: There may be an answer to this, in a regress of origins that support one another, but in the end the objection is obviously good. You can't begin to refer to an 'origin' if you can't identify anything in the first place.
Numerical difference is a symmetrical notion, unlike proper individuation [Cover/O'Leary-Hawthorne]
     Full Idea: Scholastics distinguished criteria of numerical difference from questions of individuation proper, since numerical difference is a symmetrical notion.
     From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.4.1)
     A reaction: This apparently old-fashioned point appears to be conclusively correct. Modern thinkers, though, aren't comfortable with proper individuation, because they don't believe in concepts like 'essence' and 'substance' that are needed for the job.
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
Haecceity as property, or as colourless thisness, or as singleton set [Cover/O'Leary-Hawthorne]
     Full Idea: There is a contemporary property construal of haecceities, ...and a Scotistic construal as primitive, 'colourless' thisnesses which, unlike singleton-set haecceities, are aimed to do some explanatory work.
     From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.4.4)
     A reaction: [He associates the contemporary account with David Kaplan] I suppose I would say that individuation is done by properties, but not by some single property, so I take it that I don't believe in haecceities at all. What individuates a haecceity?
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
Maybe 'substance' is more of a mass-noun than a count-noun [Cover/O'Leary-Hawthorne]
     Full Idea: We could think of 'substance' on the model of a mass noun, rather than a count noun.
     From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.3)
     A reaction: They offer this to help Leibniz out of a mess, but I think he would be appalled. The proposal seems close to 'prime matter' in Aristotle, which never quite does the job required of it. The idea is nice, though, and should be taken seriously.
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
We can ask for the nature of substance, about type of substance, and about individual substances [Cover/O'Leary-Hawthorne]
     Full Idea: In the 'blueprint' approach to substance, we confront at least three questions: What is it for a thing to be an individual substance? What is it for a thing to be the kind of substance that it is? What is it to be that very individual substance?
     From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 1.1.1)
     A reaction: My working view is that the answer to the first question is that substance is essence, that the second question is overrated and parasitic on the third, and that the third is the key question, and also reduces to essence.
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
The general assumption is that substances cannot possibly be non-substances [Cover/O'Leary-Hawthorne]
     Full Idea: There is a widespread assumption, now and in the past, that substances are essentially substances: nothing is actually a substance but possibly a non-substance.
     From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 1.1.2)
     A reaction: It seems to me that they clearly mean, in this context, that substances are 'necessarily' substances, not that they are 'essentially' substances. I would just say that substances are essences, and leave the necessity question open.
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
Modern essences are sets of essential predicate-functions [Cover/O'Leary-Hawthorne]
     Full Idea: The modern view of essence is that the essence of a particular thing is given by the set of predicate-functions essential to it, and the essence of any kind is given by the set of predicate-functions essential to every possible member of that kind.
     From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 1.2.2)
     A reaction: Thus the modern view has elided the meanings of 'essential' and 'necessary' when talking of properties. They are said to be 'functions' from possible worlds to individuals. The old view (and mine) demands real essences, not necessary properties.
Modern essentialists express essence as functions from worlds to extensions for predicates [Cover/O'Leary-Hawthorne]
     Full Idea: The modern essentialist gives the same metaphysical treatment to every grammatical predicate - by associating a function from worlds to extensions for each.
     From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 2.2)
     A reaction: I take this to mean that essentialism is the view that if some predicate attaches to an object then that predicate is essential if there is an extension of that predicate in all possible worlds. In English, essential predicates are necessary predicates.
9. Objects / E. Objects over Time / 12. Origin as Essential
Necessity-of-origin won't distinguish ex nihilo creations, or things sharing an origin [Cover/O'Leary-Hawthorne]
     Full Idea: A necessity-of-origins approach cannot work to distinguish things that come into being genuinely ex nihilo, and cannot work to distinguish things sharing a single origin.
     From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.4.1)
     A reaction: Since I am deeply suspicious of essentiality or necessity of origin (and they are not, I presume, the same thing) I like these two. Twins have always bothered me with the second case (where order of birth seems irrelevant).
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
Even extreme modal realists might allow transworld identity for abstract objects [Cover/O'Leary-Hawthorne]
     Full Idea: It might be suggested that even the extreme modal realist can countenance transworld identity for abstract objects.
     From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 3.2.2 n46)
     A reaction: This may sound right for uncontroversial or well-defined abstracta such as numbers and circles, but even 'or' is ambiguous, and heaven knows what the transworld identity of 'democracy' is!
11. Knowledge Aims / A. Knowledge / 2. Understanding
Our whole conception of an object is its possible practical consequences [Peirce]
     Full Idea: Consider what effects, which might conceivably have practical bearings, we conceive the objects of our conceptions to have. Then, our conception of these effects is the whole of our conception of the object.
     From: Charles Sanders Peirce (How to Make our Ideas Clear [1878], EP i.132), quoted by Albert Atkin - Peirce 2 'early'
     A reaction: This is his 1878 version, which was fine-tuned later in life. He seems to have extended his principle to include possibilities, as well as the mere objects. That is, he moved beyond mere nominalism.
11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs
We are aware of beliefs, they appease our doubts, and they are rules of action, or habits [Peirce]
     Full Idea: A belief has just three properties: first, it is something that we are aware of; second, it appeases the irritation of doubt; and, third, it involves the establishment in our nature of a rule of action, or, say for short, a habit.
     From: Charles Sanders Peirce (How to Make our Ideas Clear [1878], p.28)
     A reaction: Peirce probably believed that Bismarck breathed oxygen, but was unaware of his belief, and no one ever dreamed of acting on such a belief, unless Bismarck was gasping for air.
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
We can go beyond mere causal explanations if we believe in an 'order of being' [Cover/O'Leary-Hawthorne]
     Full Idea: The philosopher comfortable with an 'order of being' has richer resources to make sense of the 'in virtue of' relation than that provided only by causal relations between states of affairs, positing in addition other sorts of explanatory relationships.
     From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 1.1.2)
     A reaction: This might best be characterised as 'ontological dependence', and could be seen as a non-causal but fundamental explanatory relationship, and not one that has to depend on a theistic world view.
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Non-positivist verificationism says only take a hypothesis seriously if it is scientifically based and testable [Ladyman/Ross on Peirce]
     Full Idea: With Peirce, we endorse a non-positivist version of verificationism - no hypothesis should be taken seriously if apparently beyond our capacity to investigate, and serious metaphysics must concern at least two plausible scientific hypotheses.
     From: comment on Charles Sanders Peirce (How to Make our Ideas Clear [1878]) by J Ladyman / D Ross - Every Thing Must Go 1.3
     A reaction: [compressed] They say this is NOT a theory about meaning, as 'The Big Bang was caused by Elvis' is perfectly meaningful. Verificationism always seems to rule out bold speculation. Don't say 'take string theory seriously', if we can't test it?