Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'Formal and Transcendental Logic' and 'Necessity, Essence and Individuation'

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34 ideas

1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
Metaphysics is clarifying how we speak and think (and possibly improving it) [Sidelle]
     Full Idea: Metaphysics, for the conventionalist, is not a matter of trying to see deeply into the structure of mind-independent reality, but of trying to clarify the way we actually speak and think, and perhaps negotiating ways of doing this to our best advantage.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.1)
     A reaction: Note that he is still allowing space for 'revisionary' as well as for 'descriptive' metaphysics. I can't wholly accept this, as I really do think we can have some deep insights into reality, but Sidelle is articulating a large part of the truth.
2. Reason / E. Argument / 7. Thought Experiments
We seem to base necessities on thought experiments and imagination [Sidelle]
     Full Idea: Judgments of necessity seem always to be based on thought experiments and appeals to what we can imagine.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.1)
     A reaction: That is, the denial of this thing seems inconceivable. I would say that they are also based on coherence. The idea that we can think without imagination is nonsense.
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
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 / C. Ontology of Logic / 1. Ontology of Logic
Logicians presuppose a world, and ignore logic/world connections, so their logic is impure [Husserl, by Velarde-Mayol]
     Full Idea: Husserl maintained that because most logicians have not studied the connection between logic and the world, logic did not achieve its status of purity. Even more, their logic implicitly presupposed a world.
     From: report of Edmund Husserl (Formal and Transcendental Logic [1929]) by Victor Velarde-Mayol - On Husserl 4.5.1
     A reaction: The point here is that the bracketing of phenomenology, to reach an understanding with no presuppositions, is impossible if you don't realise what your are presupposing. I think the logic/world relationship is badly neglected, thanks to Frege.
Phenomenology grounds logic in subjective experience [Husserl, by Velarde-Mayol]
     Full Idea: The phenomenological logic grounds logical notions in subjective acts of experience.
     From: report of Edmund Husserl (Formal and Transcendental Logic [1929], p.183) by Victor Velarde-Mayol - On Husserl 4.5.1
     A reaction: I'll approach this with great caution, but this is a line of thought that appeals to me. The core assumptions of logic do not arise ex nihilo.
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
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
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.
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Pure mathematics is the relations between all possible objects, and is thus formal ontology [Husserl, by Velarde-Mayol]
     Full Idea: Pure mathematics is the science of the relations between any object whatever (relation of whole to part, relation of equality, property, unity etc.). In this sense, pure mathematics is seen by Husserl as formal ontology.
     From: report of Edmund Husserl (Formal and Transcendental Logic [1929]) by Victor Velarde-Mayol - On Husserl 4.5.2
     A reaction: I would expect most modern analytic philosophers to agree with this. Modern mathematics (e.g. category theory) seems to have moved beyond this stage, but I still like this idea.
7. Existence / A. Nature of Existence / 1. Nature of Existence
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 / C. Powers and Dispositions / 6. Dispositions / d. Dispositions as occurrent
There doesn't seem to be anything in the actual world that can determine modal facts [Sidelle]
     Full Idea: Metaphysically, nothing in the actual world seems to be a candidate for determining what is necessarily the case.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.4)
     A reaction: I file this under 'Dispositions' to show what is at stake in the debate about dispositional and categorical properties. I take a commitment to dispositions to be a commitment to modal facts about the actual world.
9. Objects / D. Essence of Objects / 2. Types of Essence
Causal reference presupposes essentialism if it refers to modally extended entities [Sidelle]
     Full Idea: Even if the causal theory of reference proper does not presuppose essentialism, it does presuppose essentialism if it is to be an account of reference to modally extended entities.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.6)
9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
Clearly, essential predications express necessary properties [Sidelle]
     Full Idea: It is clear, of course, that if there are true essential predications, then they express necessary properties.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.2)
     A reaction: I would certainly want to ask whether essences have to be analysed as properties, and also (more boldly) whether there might not be contingent essences.
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
Being a deepest explanatory feature is an actual, not a modal property [Sidelle]
     Full Idea: The property of being a deepest explanatory feature is a nonmodal property: it's an actual property.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.4)
     A reaction: I don't accept the existence of properties of the form 'being-F'. The possibility of securing a door may be the deepest explanatory feature of a lock. [To be fair to Sidelle, see context - just for once!] Dispositions are actual.
9. Objects / D. Essence of Objects / 15. Against Essentialism
That the essence of water is its microstructure is a convention, not a discovery [Sidelle]
     Full Idea: The necessity to water of whatever is found out to be the water's microstructure is given by convention, and is not something which is discovered.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.2)
     A reaction: A powerful point. It shows the authority of science that we accept the microstructure as the essence. The essences of statues and people are definitely not their microstructures. One H2O molecule isn't water. Why not? Macro-properties count too!
9. Objects / F. Identity among Objects / 3. Relative Identity
We aren't clear about 'same stuff as this', so a principle of individuation is needed to identify it [Sidelle]
     Full Idea: Independent of conventions, no definite sense can be given to the notion of 'the same stuff as this'. So reference-fixing must include some principle of individuation to determine the aspects of sameness for the identity referred to.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.6)
     A reaction: Is he really saying that we don't understand 'same stuff as this'? Surely animals can manage that, and they are not famous for their conventions. Sidelle has fallen into the sortalist trap, I think.
10. Modality / A. Necessity / 4. De re / De dicto modality
Evaluation of de dicto modalities does not depend on the identity of its objects [Sidelle]
     Full Idea: In the evaluation of de dicto modal statements, whether some possible state of affairs is relevant to its truth does not depend on the identity of its objects, as in 'Necessarily, the President of the USA is male'.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.3)
     A reaction: This is a more clear-cut and easy to grasp criterion than most that are on offer.
10. Modality / C. Sources of Modality / 3. Necessity by Convention
Necessary a posteriori is conventional for necessity and nonmodal for a posteriority [Sidelle, by Sider]
     Full Idea: Sidelle defends conventionalism against a posteriori necessities by 'factoring' a necessary a posteriori truth into an analytic component and a nonmodal component. The modal force then comes from the analytic part, and the a posteriority from the other.
     From: report of Alan Sidelle (Necessity, Essence and Individuation [1989]) by Theodore Sider - Writing the Book of the World 12.8
     A reaction: [I note that Sidelle refers, it seems, to the nonmodal component as a 'deep explanatory feature', which is exactly what I take an essence to be].
To know empirical necessities, we need empirical facts, plus conventions about which are necessary [Sidelle]
     Full Idea: What we need to know, in order to know what is empirically necessary, is some empirical fact plus our conventions that tell us which truths are necessary given which empirical facts.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.4)
     A reaction: I take this attack on a posteriori necessities to be the most persuasive part of Sidelle's case, but you can't just put all of our truths down to convention. There are stabilities in the world, as well as in our conventions.
10. Modality / D. Knowledge of Modality / 3. A Posteriori Necessary
The necessary a posteriori is statements either of identity or of essence [Sidelle]
     Full Idea: The necessary a posteriori crudely divides into two groups - (synthetic) identity statements (between rigid designators), and statements of essential properties. The latter is either statements of property identity, or of the essences of natural kinds.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.2)
     A reaction: He cites Kripke's examples (Hesperus,Cicero,Truman,water,gold), and divides them into the two groups. Helpful.
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
Empiricism explores necessities and concept-limits by imagining negations of truths [Sidelle]
     Full Idea: In the traditional empiricist picture, we go about modal enquiry by trying to see whether we can imagine a situation in which it would be correct to assert the negation of a proposed necessary truth. Thus we can find out the limits of our concepts.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.1)
Contradictoriness limits what is possible and what is imaginable [Sidelle]
     Full Idea: Contradictoriness is the boundary both of what is possible and also of what is imaginable.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.4)
     A reaction: Of course we may see contradictions where there are none, and fail to grasp real hidden contradictions, so the two do not coincide in the practice. I think I would say it is 'a' boundary, not 'the' boundary.
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
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.
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
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
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.
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
The individuals and kinds involved in modality are also a matter of convention [Sidelle]
     Full Idea: It is not merely the modal facts that result from our conventions, but the individuals and kinds that are modally involved.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.3)
     A reaction: I am beginning to find Sidelle's views very sympathetic - going over to the Dark Side, I'm afraid. But conventions won't work at all if they don't correspond closely to reality.
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
A thing doesn't need transworld identity prior to rigid reference - that could be a convention of the reference [Sidelle]
     Full Idea: For a term to be rigid, it is said there must be real transworld identity prior to our use of the rigid term, ..but this may only be because we have conventional principles for individuating across worlds. 'Let's call him Fred' - perhaps explicitly rigid.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.3)
     A reaction: This seems right. An example might be a comic book character, who retains a perfect identity in all the comics, with no scars, weight change, or ageing.
'Dthat' operates to make a singular term into a rigid term [Sidelle]
     Full Idea: 'Dthat' is Kaplan's indexical operator; it operates on a given singular term, φ, and makes it into a rigid designator of whatever φ designates in the original context.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.6 n11)
     A reaction: I like this idea a lot, because it strikes me that referring to something rigidly is a clear step beyond referring to it in actuality. I refer to 'whoever turns up each week', but that is hardly rigid. The germ of 2-D semantics is here.
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
A priori knowledge is entirely of analytic truths [Sidelle]
     Full Idea: The a priori method yields a priori knowledge, and the objects of this knowledge are not facts about the world, but analytic truths.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.1)
     A reaction: Are we not allowed any insights at all into how the world must be, independent of how we happen to conceptualise it?
18. Thought / C. Content / 5. Twin Earth
That water is essentially H2O in some way concerns how we use 'water' [Sidelle]
     Full Idea: If water is essentially H2O, this is going to have something to do with our intentions in using 'water'.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.1)
     A reaction: This very simple point looks to be correct, and raises very important questions about the whole Twin Earth thing. When new discoveries are made, words shift their meanings. We're not quite sure what 'jade' means any more.
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
Causal reference seems to get directly at the object, thus leaving its nature open [Sidelle]
     Full Idea: The causal theory of reference appears to give us a way to get at an object while leaving it undetermined what its essence or necessary features might be.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.1)
     A reaction: This pinpoints why the direct/causal theory of reference seems to open the doors to scientific essentialism. Sidelle, of course, opposes the whole programme.
19. Language / B. Reference / 5. Speaker's Reference
Because some entities overlap, reference must have analytic individuation principles [Sidelle]
     Full Idea: The phenomenon of overlapping entities requires that if our reference is to be determinate (as determinate as it is), then there must be analytic principles of individuation.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.5)
     A reaction: His point is that there is something inescapably conventional about the way in which our reference works. It isn't just some bald realist baptism.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
Can anything in science reveal the necessity of what it discovers? [Sidelle]
     Full Idea: Is there anything in the procedures of scientists that could reveal to them that water is necessarily H2O or that gold necessarily has atomic number 79.
     From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.4)
     A reaction: This is Leibniz's is view, that empirical evidence can never reveal necessities. Given that we know some necessities, you have an argument for rationalism.