Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'Substance and Individuation in Leibniz' and 'The Varieties of Reference'

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26 ideas

5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
18739 Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
     Full Idea: Three periods can be distinguished in philosophical logic: the syntactic stage, from Russell's definite descriptions to the 1950s, the dominance of possible world semantics from the 50s to 80s, and a current widening of the subject.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 1)
     A reaction: [compressed] I've read elsewhere that the arrival of Tarski's account of truth in 1933, taking things beyond the syntactic, was also a landmark.
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18741 Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
     Full Idea: Logical formalization forces the investigator to make the central philosophical concepts precise. It can also show how some philosophical concepts and objects can be defined in terms of others.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2)
     A reaction: This is the main rationale of the highly formal and mathematical approach to such things. The downside is when you impose 'precision' on language that was never intended to be precise.
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
18744 Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
     Full Idea: A (logical) model is a set with functions and relations defined on it that specify the denotation of the non-logical vocabulary. A series of recursive clauses explicate how truth values of complex sentences are compositionally determined from the parts.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: See the ideas on 'Functions in logic' and 'Relations in logic' (in the alphabetical list) to expand this important idea.
7. Existence / A. Nature of Existence / 1. Nature of Existence
18740 If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
     Full Idea: If there is indeed no property of existence that is expressed by the word 'exist', then it makes no sense to ask for its essence.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2)
     A reaction: As far as I can tell, this was exactly Aristotle's conclusion, so he skirted round the question of 'being qua being', and focused on the nature of objects instead. Grand continental talk of 'Being' doesn't sound very interesting.
8. Modes of Existence / A. Relations / 1. Nature of Relations
13076 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
13102 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.
13103 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
13104 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
13100 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
13068 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
13069 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
13072 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.
17080 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
13101 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 / 1. Possible Worlds / a. Possible worlds
18745 A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
     Full Idea: A Tarskian model can in a sense be seen as a model of a possible state of affairs.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: I include this remark to show how possible worlds semantics built on the arrival of model theory.
18747 The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew]
     Full Idea: The notion of a possible worlds model was extended (resulting in the concept of a 'spheres model') in order to obtain a satisfactory logical treatment of counterfactual conditional sentences.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4)
     A reaction: Thus we add 'centred' worlds, and an 'actual' world, to the loose original model. It is important to remember when we discuss 'close' worlds that we are then committed to these presuppositions.
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
18748 Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
     Full Idea: The idea of 'impossible worlds' was introduced into epistemic logic.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4)
     A reaction: Nathan Salmon seems interested in their role in metaphysics (presumably in relation to Meinongian impossible objects, like circular squares, which must necessarily be circular).
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
18746 Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
     Full Idea: Each possible worlds model contains a set of possible worlds. For this reason, possible worlds semantics is often charged with smuggling in heavy metaphysical commitments.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: To a beginner it looks very odd that you should try to explain possibility by constructing a model of it in terms of 'possible' worlds.
18750 Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]
     Full Idea: When the possible worlds semantics were further extended to model notions of knowledge and of moral obligation, the application was beginning to look distinctly forced and artificial.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 5)
     A reaction: They accept lots of successes in modelling necessity and time.
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
13081 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!
12. Knowledge Sources / B. Perception / 6. Inference in Perception
12580 Experiences have no conceptual content [Evans, by Greco]
     Full Idea: In Evans's work experiences are conceived of as not having a conceptual content at all.
     From: report of Gareth Evans (The Varieties of Reference [1980]) by John Greco - Justification is not Internal
     A reaction: I presume it is this view which provoked McDowell's contrary view in 'Mind and World'. I say this is a job for neuroscience, and I struggle to see what philosophical questions hang on the outcome. I think I side with Evans.
7643 We have far fewer colour concepts than we have discriminations of colour [Evans]
     Full Idea: Do we really understand the proposal that we have as many colour concepts as there are shades colour that we can sensibly discriminate?
     From: Gareth Evans (The Varieties of Reference [1980], 7.5)
     A reaction: This is the argument (rejected by McDowell) that experience cannot be conceptual because experience is too rich. We should not confuse lack of concepts with lack of words. I may have a concept of a colour between two shades, but no word for it.
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
13071 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.
18. Thought / C. Content / 1. Content
23794 Some representational states, like perception, may be nonconceptual [Evans, by Schulte]
     Full Idea: Evans introduced the idea that there are some representational states, for example perceptual experiences, which have content that is nonconceptual.
     From: report of Gareth Evans (The Varieties of Reference [1980]) by Peter Schulte - Mental Content 3.4
     A reaction: McDowell famously disagree, and whether all experience is inherently conceptualised is a main debate from that period. Hard to see how it could be settled, but I incline to McDowell, because minimal perception hardly counts as 'experience'.
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
16366 The Generality Constraint says if you can think a predicate you can apply it to anything [Evans]
     Full Idea: If a subject can be credited with the thought that a is F, then he must have the conceptual resources for entertaining the thought that a is G, for every property of being G of which he has conception. This condition I call the 'Generality Constraint'.
     From: Gareth Evans (The Varieties of Reference [1980], p.104), quoted by François Recanati - Mental Files 5.3
     A reaction: Recanati endorses the Constraint in his account of mental files. Apparently if I can entertain the thought of a circle being round, I can also entertain the thought of it being square, so I am not too sure about this one.
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
12575 Concepts have a 'Generality Constraint', that we must know how predicates apply to them [Evans, by Peacocke]
     Full Idea: Evans's 'Generality Constraint' says that if a thinker is capable of attitudes to the content Fa and possesses the singular concept b, then he is capable of having attitudes to the content Fb.
     From: report of Gareth Evans (The Varieties of Reference [1980], 4.3) by Christopher Peacocke - A Study of Concepts 1.1
     A reaction: So having an attitude becomes the test of whether one possesses a concept. I suppose if one says 'You know you've got a concept when you are capable of thinking about it', that is much the same thing. Sounds fine.