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All the ideas for 'Logical Pluralism', 'What is Mathematical Truth?' and 'A Survey of Metaphysics'

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69 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Metaphysics is concerned with the fundamental structure of reality as a whole [Lowe]
     Full Idea: Metaphysics is concerned with the fundamental structure of reality as a whole.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.2)
     A reaction: I think it is vital to hang on to this big definition, focusing on ontology, and not retreat (like Kant) to the epistemological question of how humans happen to see reality, even if we are stuck with being humans.
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
Maybe such concepts as causation, identity and existence are primitive and irreducible [Lowe]
     Full Idea: It may well be that after all our attempts at analysis, we have to accept the notions of causality, identity and existence as being primitive and irreducible.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.191)
     A reaction: They may be irreducible, but it seems possible that the relationships between them might be revealed (as between Platonic Forms). To exist is to have identity and causal powers?
1. Philosophy / G. Scientific Philosophy / 2. Positivism
If all that exists is what is being measured, what about the people and instruments doing the measuring? [Lowe]
     Full Idea: If we think, in a positivistic spirit, that only measurements and observations exist, this is strikingly naïve. The scientists and their instruments can't be composed merely of measurements.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.234)
     A reaction: A strong rebuff to crude positivism and 'operationalism'. Such mistakes are the usual confusion of epistemology and ontology.
2. Reason / B. Laws of Thought / 6. Ockham's Razor
It is more extravagant, in general, to revise one's logic than to augment one's ontology [Lowe]
     Full Idea: It is more extravagant, in general, to revise one's logic than to augment one's ontology.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.219)
     A reaction: Meaning there are stronger principles of thought which can trump Ockham's Razor. A few more entities won't hurt. Sound right.
3. Truth / A. Truth Problems / 1. Truth
Some truths have true negations [Beall/Restall]
     Full Idea: Dialetheism is the view that some truths have true negations.
     From: JC Beall / G Restall (Logical Pluralism [2006], 7.4)
     A reaction: The important thing to remember is that they are truths. Thus 'Are you feeling happy?' might be answered 'Yes and no'.
3. Truth / B. Truthmakers / 5. What Makes Truths / b. Objects make truths
A truthmaker is an object which entails a sentence [Beall/Restall]
     Full Idea: The truthmaker thesis is that an object is a truthmaker for a sentence if and only if its existence entails the sentence.
     From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.3)
     A reaction: The use of the word 'object' here is even odder than usual, and invites many questions. And the 'only if' seems peculiar, since all sorts of things can make a sentence true. 'There is someone in the house' for example.
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
(∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall]
     Full Idea: The inference of 'distribution' (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically. It is straightforward to construct a 'stage' at which the LHS is true but the RHS is not.
     From: JC Beall / G Restall (Logical Pluralism [2006], 6.1.2)
     A reaction: This seems to parallel the iterative notion in set theory, that you must construct your hierarchy. All part of the general 'constructivist' approach to things. Is some kind of mad platonism the only alternative?
4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
Excluded middle must be true for some situation, not for all situations [Beall/Restall]
     Full Idea: Relevant logic endorses excluded middle, ..but says instances of the law may fail. Bv¬B is true in every situation that settles the matter of B. It is necessary that there is some such situation.
     From: JC Beall / G Restall (Logical Pluralism [2006], 5.2)
     A reaction: See next idea for the unusual view of necessity on which this rests. It seems easier to assert something about all situations than just about 'some' situation.
It's 'relevantly' valid if all those situations make it true [Beall/Restall]
     Full Idea: The argument from P to A is 'relevantly' valid if and only if, for every situation in which each premise in P is true, so is A.
     From: JC Beall / G Restall (Logical Pluralism [2006], 5.2)
     A reaction: I like the idea that proper inference should have an element of relevance to it. A falsehood may allow all sorts of things, without actually implying them. 'Situations' sound promising here.
Relevant logic does not abandon classical logic [Beall/Restall]
     Full Idea: We have not abandoned classical logic in our acceptance of relevant logic.
     From: JC Beall / G Restall (Logical Pluralism [2006], 5.4)
     A reaction: It appears that classical logic is straightforwardly accepted, but there is a difference of opinion over when it is applicable.
Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall]
     Full Idea: Relevant consequence says the conclusion of a relevantly invalid argument is not 'carried in' the premises - it does not follow from the premises.
     From: JC Beall / G Restall (Logical Pluralism [2006], 5.3.3)
     A reaction: I find this appealing. It need not invalidate classical logic. It is just a tougher criterion which is introduced when you want to do 'proper' reasoning, instead of just playing games with formal systems.
A doesn't imply A - that would be circular [Beall/Restall]
     Full Idea: We could reject the inference from A to itself (on grounds of circularity).
     From: JC Beall / G Restall (Logical Pluralism [2006], 8)
     A reaction: [Martin-Meyer System] 'It's raining today'. 'Are you implying that it is raining today?' 'No, I'm SAYING it's raining today'. Logicians don't seem to understand the word 'implication'. Logic should capture how we reason. Nice proposal.
Relevant logic may reject transitivity [Beall/Restall]
     Full Idea: Some relevant logics reject transitivity, but we defend the classical view.
     From: JC Beall / G Restall (Logical Pluralism [2006], 8)
     A reaction: [they cite Neil Tennant for this view] To reject transitivity (A?B ? B?C ? A?C) certainly seems a long way from classical logic. But in everyday inference Tennant's idea seems good. The first premise may be irrelevant to the final conclusion.
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall]
     Full Idea: A logic is 'free' to the degree it refrains from existential import of its singular and general terms. Classical logic must have non-empty domain, and each name must denote in the domain.
     From: JC Beall / G Restall (Logical Pluralism [2006], 7.1)
     A reaction: My intuition is that logic should have no ontology at all, so I like the sound of 'free' logic. We can't say 'Pegasus does not exist', and then reason about Pegasus just like any other horse.
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall]
     Full Idea: Nowadays we think of the consequence relation itself as the primary subject of logic, and view logical truths as degenerate instances of this relation. Logical truths follow from any set of assumptions, or from no assumptions at all.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.2)
     A reaction: This seems exactly right; the alternative is the study of necessities, but that may not involve logic.
Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall]
     Full Idea: According to the Peripatetics (Aristotelians), only syllogistic laws stated in variables belong to logic, and not their applications to concrete terms.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.5)
     A reaction: [from Lukasiewicz] Seems wrong. I take it there are logical relations between concrete things, and the variables are merely used to describe these relations. Variables lack the internal powers to drive logical necessities. Variables lack essence!
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
The view of logic as knowing a body of truths looks out-of-date [Beall/Restall]
     Full Idea: Through much of the 20th century the conception of logic was inherited from Frege and Russell, as knowledge of a body of logical truths, as arithmetic or geometry was a knowledge of truths. This is odd, and a historical anomaly.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.2)
     A reaction: Interesting. I have always taken this idea to be false. I presume logic has minimal subject matter and truths, and preferably none at all.
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall]
     Full Idea: Logic does not study formal languages for their own sake, which is formal grammar. Logic evaluates arguments, and primarily considers formal languages as interpreted.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.1)
     A reaction: Hodges seems to think logic just studies formal languages. The current idea strikes me as a much more sensible view.
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
The model theory of classical predicate logic is mathematics [Beall/Restall]
     Full Idea: The model theory of classical predicate logic is mathematics if anything is.
     From: JC Beall / G Restall (Logical Pluralism [2006], 4.2.1)
     A reaction: This is an interesting contrast to the claim of logicism, that mathematics reduces to logic. This idea explains why students of logic are surprised to find themselves involved in mathematics.
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
There are several different consequence relations [Beall/Restall]
     Full Idea: We are pluralists about logical consequence because we take there to be a number of different consequence relations, each reflecting different precisifications of the pre-theoretic notion of deductive logical consequence.
     From: JC Beall / G Restall (Logical Pluralism [2006], 8)
     A reaction: I don't see how you avoid the slippery slope that leads to daft logical rules like Prior's 'tonk' (from which you can infer anything you like). I say that nature imposes logical conquence on us - but don't ask me to prove it.
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
A sentence follows from others if they always model it [Beall/Restall]
     Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X.
     From: JC Beall / G Restall (Logical Pluralism [2006], 3.2)
     A reaction: This why the symbol |= is often referred to as 'models'.
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall]
     Full Idea: If mathematical truth reduces to logical truth then it is important what counts as logically true, …but if logicism is not a going concern, then the body of purely logical truths will be less interesting.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.2)
     A reaction: Logicism would only be one motivation for pursuing logical truths. Maybe my new 'Necessitism' will derive the Peano Axioms from broad necessary truths, rather than from logic.
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
An infinite series of tasks can't be completed because it has no last member [Lowe]
     Full Idea: It appears to be impossible to complete an infinite series of tasks, since such a series has, by definition, no last member.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.290)
     A reaction: This pinpoints the problem. So are there infinite tasks in a paradox of subdivision like the Achilles?
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / d. The Preface paradox
Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall]
     Full Idea: The Paradox of the Preface is an apology, that you are committed to each proposition in the book, but admit that collectively they probably contain a mistake. There is a contradiction, of affirming and denying the conjunction of propositions.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.4)
     A reaction: This seems similar to the Lottery Paradox - its inverse perhaps. Affirm all and then deny one, or deny all and then affirm one?
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
It might be argued that mathematics does not, or should not, aim at truth [Lowe]
     Full Idea: It might be argued that mathematics does not, or should not, aim at truth.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.375)
     A reaction: Intriguing. Sounds wrong to me. At least maths seems to need the idea of the 'correct' answer. If, however, maths is a huge pattern, there is no correctness, just the pattern. We can be wrong, but maths can't be wrong. Ah, I see…!
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects [Lowe]
     Full Idea: The Peano postulates imply an infinity of numbers, but there are probably not infinitely many concrete objects in existence, so natural numbers must be abstract objects.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.375)
     A reaction: Presumably they are abstract objects even if they aren't universals. 'Abstract' is an essential term in our ontological vocabulary to cover such cases. Perhaps possible concrete objects are infinite.
7. Existence / A. Nature of Existence / 4. Abstract Existence
Nominalists deny abstract objects, because we can have no reason to believe in their existence [Lowe]
     Full Idea: Nominalists tend to deny the existence of abstract objects since, given their purported nature (non-causal), we can have no reason to believe in their existence.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.372)
     A reaction: A good point. Aristotle worried about the causal inadequacy of the Forms. My mind can conceive of a 'thing' with no causal powers, just sitting there.
7. Existence / B. Change in Existence / 1. Nature of Change
Change can be of composition (the component parts), or quality (properties), or substance [Lowe]
     Full Idea: There seem to be three kinds of change: compositional change (of component parts), qualitative change (of properties), or substantial change (when underlying essence begins or ceases).
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.59)
     A reaction: Notice this gives 'components' a more prominent ontological status than usual. Is this computer a component of my study?
Four theories of qualitative change are 'a is F now', or 'a is F-at-t', or 'a-at-t is F', or 'a is-at-t F' [Lowe, by PG]
     Full Idea: Qualitative change is seen as either (i) 'Presentism' - 'a is F now', or (ii) 'relational properties' - 'a is F-at-t', or (iii) 'temporal parts' - 'a-at-t is F', or (iv) 'adverbial' - 'a is-a-t F'.
     From: report of E.J. Lowe (A Survey of Metaphysics [2002], p.44) by PG - Db (ideas)
     A reaction: The traditional view would let a stay the same over time, and change its property (ii). Lewis favours (iii). My suspicion is that thinking collapses if you abandon the tradtional view.
7. Existence / B. Change in Existence / 4. Events / a. Nature of events
Numerically distinct events of the same kind (like two battles) can coincide in space and time [Lowe]
     Full Idea: Numerically distinct events of the same kind (like two battles) can plausible coincide in space and time.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.225)
     A reaction: This is certainly discouraging for anyone who wanted to make events ontologically basic. Physicalist need to be able to individuate events in a reductive way.
7. Existence / B. Change in Existence / 4. Events / b. Events as primitive
Maybe modern physics requires an event-ontology, rather than a thing-ontology [Lowe]
     Full Idea: It is sometimes said that modern physics requires us to espouse an event-ontology, rather than a thing-ontology.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.233)
     A reaction: It has to be a mistake to build our philosophical ontology on current physics, because even the physicists say they don't understand the latter very well.
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
Maybe an event is the exemplification of a property at a time [Lowe]
     Full Idea: Maybe an event is the exemplification of a property at a time.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.229)
     A reaction: What exactly would 'exemplify' mean here? This probably turns out to be circular when you attempt to explain what a property is.
Events are changes in the properties of or relations between things [Lowe]
     Full Idea: My own preference is for a conception of events which reduces them to changes in the properties of or relations between things.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.245)
     A reaction: Changes of property and changes of relations are two very different things. Is a 'near miss' an event? If so, is any movement an event? If movement is relative, then so are events.
7. Existence / E. Categories / 3. Proposed Categories
The main categories of existence are either universal and particular, or abstract and concrete [Lowe]
     Full Idea: Some metaphysicians think the fundamental categories of existence are universals and particulars, while other prefer the division between abstract and concrete.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.15)
     A reaction: Interestingly, in trying to choose between these, it is tempting to think about the capacities of the brain. Which is the cart and which is the horse?
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
Trope theory says blueness is a real feature of objects, but not the same as an identical blue found elsewhere [Lowe]
     Full Idea: The trope theorist holds that the blueness of a blue chair really exists as much as the chair, but is not identified with the blueness of anything else, even if it resembles it exactly.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.361)
     A reaction: You are left with explaining how 'resemblance' works if you cannot spot some 'thing' in common. It is an inviting idea, though, because it avoids the ontological baggage of universals.
Maybe a cushion is just a bundle of tropes, such as roundness, blueness and softness [Lowe]
     Full Idea: The trope theorist says that a cushion is just a 'bundle' of tropes, such as roundness, blueness and softness.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.362)
     A reaction: Certainly if you dispense with the idea of substance (which is clearly bad science even if it is good metaphysics), something like this is what remains of a cushion, though it sounds more epistemological than ontological. Only philosophers care about this
Tropes seem to be abstract entities, because they can't exist alone, but must come in bundles [Lowe]
     Full Idea: Tropes seem to be abstract entities because, unlike concrete entities, they are ontologically dependent; ..there are no 'free' tropes, and they must always be bundled with other appropriate tropes to exist.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.367)
     A reaction: Only a Platonist would think that a universal property could 'exist alone'. I presume Aristotle thought universals were real, though bound up with substances.
8. Modes of Existence / D. Universals / 1. Universals
The category of universals can be sub-divided into properties and relations [Lowe]
     Full Idea: One might want to divide the category of 'universals' into two sub-categories of properties and relations.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.15)
     A reaction: This means a Platonic form like 'horse' ends up as a cluster of properties and relations. Is a substance not also a universal?
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
Nominalists believe that only particulars exist [Lowe]
     Full Idea: Nominalists believe that only particulars exist.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.352)
     A reaction: A neat definition. Hence they deny universals. I suspect that nominalism is incoherent. Rational thought seems easy to create with universals, impossible with just particulars. Robotics is nominalist, which is why it will fail.
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
'Is non-self-exemplifying' is a predicate which cannot denote a property (as it would be a contradiction) [Lowe]
     Full Idea: Not every meaningful predicate expresses an existing property; thus 'is non-self-exemplifying' cannot refer to a property, because the property would contradict the predicate.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.100)
     A reaction: Needs thought. The example is based on Russell's so-called Barber's Paradox. If it can't be a property, can it be a predicate?
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
If 'blueness' is a set of particulars, there is danger of circularity, or using universals, in identifying the set [Lowe]
     Full Idea: If sets are particulars, a nominalist may say that 'blueness' is a set of particulars, but which set? If the particulars 'are blue' this threatens circularity - though resemblance is usually appealed to to avoid this.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.355)
     A reaction: This supports my suspicion that nominalism is superficially attractive and 'scientific', but when you dig deep into it the theory won't get off the ground without universals.
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
Conventionalists see the world as an amorphous lump without identities, but are we part of the lump? [Lowe]
     Full Idea: For the conventionalist the world is doomed to merge into an amorphous lump with no real individuality or differentiation, ..but we can hardly make our own identity in the world in the way we are supposed to conventionally create identity for objects.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.113)
     A reaction: Very nice argument! We need to 'cut nature at the joints' (Plato), and one joint is screamingly obvious - that between observer and world. You could try denying this, but it would be a bizarre view.
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Statues can't survive much change to their shape, unlike lumps of bronze, which must retain material [Lowe]
     Full Idea: A statue is a kind of object which cannot survive much change to its shape, unlike a lump of bronze, which cannot survive any change to its material composition.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.70)
     A reaction: Also the statue could survive being hollowed out, changing its material composition. Hence a statue is not just a lump of bronze, but we knew that.
9. Objects / E. Objects over Time / 9. Ship of Theseus
If old parts are stored and then appropriated, they are no longer part of the original (which is the renovated ship). [Lowe]
     Full Idea: The parts of a ship in a warehouse belong to no ship at all, ..and once they are appropriated by another ship they cease to be parts of the original, ..so it seems that the renovated ship (not the reconstruction) is identified with the original.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.31)
     A reaction: The parts in the warehouse could belong to the original (they might even labelled), but assigning them to a new ship does indeed look like a crucial break in the continuity.
If 5% replacement preserves a ship, we can replace 4% and 4% again, and still retain the ship [Lowe]
     Full Idea: If we say that up to 5% of a ship's parts can be replaced without the ship ceasing to exist, we could replace 4% and then 4% again, and it would retain its identity, if identity is transitive.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.26)
     A reaction: One suspected that all attempts at precision with the ship of Theseus were doomed, but this nicely demonstrates it.
A renovation or a reconstruction of an original ship would be accepted, as long as the other one didn't exist [Lowe]
     Full Idea: If a ship is renovated without reconstruction of original parts, we happily identify the renovation with the original; if there was a reconstruction without the renovated version, we would identify the reconstruction with the original.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.27)
     A reaction: This really shakes our belief in identity as a natural rather than mental phenomenon. The existence of clones undermines our normal idea of personal identity.
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
Identity of Indiscernibles (same properties, same thing) ) is not Leibniz's Law (same thing, same properties) [Lowe]
     Full Idea: The Identity of Indiscernibles (no two objects can possess exactly the same properties) is not the same as Leibniz's Law (what is true of a thing is true of what is identical with that thing).
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.62)
     A reaction: Two things can't be the same because we can't discern the difference, which may be our inadequacy. But if they actually have identical properties, it is hard to see how they could be different. A universe with just two perfect spheres is couterexample.
10. Modality / A. Necessity / 3. Types of Necessity
Relevant necessity is always true for some situation (not all situations) [Beall/Restall]
     Full Idea: In relevant logic, the necessary truths are not those which are true in every situation; rather, they are those for which it is necessary that there is a situation making them true.
     From: JC Beall / G Restall (Logical Pluralism [2006], 5.2)
     A reaction: This seems to rest on the truthmaker view of such things, which I find quite attractive (despite Merricks's assault). Always ask what is making some truth necessary. This leads you to essences.
10. Modality / B. Possibility / 1. Possibility
It is impossible to reach a valid false conclusion from true premises, so reason itself depends on possibility [Lowe]
     Full Idea: Reasoning itself depends upon a grasp of possibilities, because a valid argument is one in which it is not possible for the conclusion to be false if the premises are true.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.11)
     A reaction: A very valuable corrective to my pessimistic view of philosophers' attempts to understand metaphysical necessity. But if we can only grasp natural necessity, then all reason is naturalistic.
Mathematics eliminates possibility, as being simultaneous actuality in sets [Putnam]
     Full Idea: Mathematics has got rid of possibility by simply assuming that, up to isomorphism anyway, all possibilities are simultaneous actual - actual, that is, in the universe of 'sets'.
     From: Hilary Putnam (What is Mathematical Truth? [1975], p.70), quoted by Stewart Shapiro - Philosophy of Mathematics 7.5
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
We might eliminate 'possible' and 'necessary' in favour of quantification over possible worlds [Lowe]
     Full Idea: It may be possible to eliminate the modal operators (in English, 'is possible' and 'is necessary') in favour of quantifier expressions with variables ranging over possible worlds.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.121)
     A reaction: Hence 'necessary' becomes 'exists/is true in all possible worlds'. Deep problems, but at least we must show that referring to 'possible' worlds isn't a circular explanation of 'is possible'.
14. Science / A. Basis of Science / 6. Falsification
Unfalsifiability may be a failure in an empirical theory, but it is a virtue in metaphysics [Lowe]
     Full Idea: Although unfalsifiability is probably a defect in scientific hypothesis, because it is deprived of empirical content, it seems rather to be a virtue in a metaphysical hypothesis.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.241)
     A reaction: Presumably nothing could ever be found to count against a necessary truth. A nice point. 'Find me an instance where 2+2 is not 4'.
14. Science / D. Explanation / 1. Explanation / d. Explaining people
The behaviour of persons and social groups seems to need rational rather than causal explanation [Lowe]
     Full Idea: There are some entities which exist in time and space (such as persons or social groups) of which the behaviour seems to be subject to rational rather than merely causal explanation.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.2)
     A reaction: This begs of the question of whether 'rational' can be reduced to causal. We can't manage causal explanations of the very complex, so we use broad-brush second-best explanations?
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
Judgement is always predicating a property of a subject [Beall/Restall]
     Full Idea: All judgement, for Kant, is essentially the predication of some property to some subject.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.5)
     A reaction: Presumably the denial of a predicate could be a judgement, or the affirmation of ambiguous predicates?
18. Thought / E. Abstraction / 5. Abstracta by Negation
The centre of mass of the solar system is a non-causal abstract object, despite having a location [Lowe]
     Full Idea: The centre of mass of the solar system seems to lack causal powers, and so is an abstract object, even though it has a location and movement.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.368)
     A reaction: Nice example, with rich ramifications. Abstraction is deeply tied into our understanding of the physical world, and our concept of identity.
Concrete and abstract objects are distinct because the former have causal powers and relations [Lowe]
     Full Idea: Concrete objects possess causal powers and relations, but abstract objects are incapable of having causal powers or relations.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.368)
     A reaction: Is this an observation or a definition? One might claim that an abstraction (such as a political ideal) can acquire causal power through a conscious mnd.
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall]
     Full Idea: Situation semantics is a variation of the truth-conditional approach, taking the salient unit of analysis not to be the possible world, or some complete consistent index, but rather the more modest 'situation'.
     From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.4)
     A reaction: When I read Davidson (and implicitly Frege) this is what I always assumed was meant. The idea that worlds are meant has crept in to give truth conditions for modal statements. Hence situation semantics must cover modality.
19. Language / D. Propositions / 1. Propositions
Propositions commit to content, and not to any way of spelling it out [Beall/Restall]
     Full Idea: Our talk of propositions expresses commitment to the general notion of content, without a commitment to any particular way of spelling this out.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.1)
     A reaction: As a fan of propositions I like this. It leaves open the question of whether the content belongs to the mind or the language. Animals entertain propositions, say I.
26. Natural Theory / C. Causation / 5. Direction of causation
If the concept of a cause says it precedes its effect, that rules out backward causation by definition [Lowe]
     Full Idea: You can't include in your concept of causation a clause stipulating that the cause occurred earlier than the effect, because that would rule out backward causation by definition.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.176)
     A reaction: It may, though, be the case that backward causes can't occur, and time is essential to causes. The problem is our inability to know this for sure.
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
The theories of fact causation and event causation are both worth serious consideration [Lowe]
     Full Idea: The theories of fact causation and event causation are both worth serious consideration.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.173)
     A reaction: This is slippery ground because both 'facts' and 'events' have uncertain ontological status, and seem partly conventional rather than natural. Events might be natural surges or transformations of energy?
It seems proper to say that only substances (rather than events) have causal powers [Lowe]
     Full Idea: It seems proper to say that events of themselves possess no causal powers; only persisting objects (individual substances) possess causal powers.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.211)
     A reaction: This requires events to be reduced to substances, which invites Aristotle's question of where the movement comes from. In physcis, 'energy' is the key concept.
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
Causal overdetermination is either actual overdetermination, or pre-emption, or the fail-safe case [Lowe]
     Full Idea: In causation there is 'overdetermination' (c and d occurred, and were both sufficient for e), 'pre-emption' (c and d occurred, and d would have stepped in if c hadn't), or 'fail-safe' (if c hadn't occurred, d would have occurred and done it).
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.179)
     A reaction: Two safety nets together, two safety nets spaced apart, or a second net which pops in if the first breaks. Nice distinctions.
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
Causation may be instances of laws (seen either as constant conjunctions, or as necessities) [Lowe]
     Full Idea: Causation relations between events may an instance of a causal law, with laws either interpreted as constant conjunctions (Hume), or as necessitation among universals (Armstrong).
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.190)
     A reaction: Hume's version is a thin idea of a law, but we can dream about the metaphysical status of laws, even if we don't know much about them. Lowe says a cause without a law is perfectly intelligible.
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
Hume showed that causation could at most be natural necessity, never metaphysical necessity [Lowe]
     Full Idea: One thing Hume has taught us is that the necessity which causation involves is at most 'natural' or 'physical' necessity, not metaphysical necessity.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.182)
     A reaction: Given Hume's epistemological scepticism, I don't think he would claim to have shown such a thing. See G.Strawson's book. Metaphysical necessity of causation is possible, but unknowable.
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
The normative view says laws show the natural behaviour of natural kind members [Lowe, by Mumford/Anjum]
     Full Idea: For Lowe law statements are in a sense about what 'ought' to be the case. The 'ought' is not an explicitly moral or anthropomorphic one but instead tells us what is the natural behaviour of kind members.
     From: report of E.J. Lowe (A Survey of Metaphysics [2002]) by S.Mumford/R.Lill Anjum - Getting Causes from Powers 8.6
     A reaction: This is the 'normative' view of laws (as opposed to the intentional, dispositional, or regularity accounts). They cite Lowe 1989 Ch.8. The obvious immediate problem is things which evolved for one purpose and end up being used for another.
26. Natural Theory / D. Laws of Nature / 9. Counterfactual Claims
'If he wasn't born he wouldn't have died' doesn't mean birth causes death, so causation isn't counterfactual [Lowe]
     Full Idea: Counterfactual analyses of event causation don't seem to work, because 'if Napoleon hadn't been born he wouldn't have died' is true, but doesn't mean his birth caused his death.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.161)
     A reaction: Nice counterexample, which looks pretty conclusive. Birth makes death possible; it creates the necessary conditions within which it can be caused.
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
If motion is change of distance between objects, it involves no intrinsic change in the objects [Lowe]
     Full Idea: If motion just is change of distance between two objects, it does not involve any kind of intrinsic change in the objects in question.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.242)
     A reaction: It sound respectably relativistic, but I doubt the definition. x is moving relative to y, then y attains x's velocity, so x ceases to move? Maybe.
27. Natural Reality / C. Space / 3. Points in Space
Surfaces, lines and points are not, strictly speaking, parts of space, but 'limits', which are abstract [Lowe]
     Full Idea: Surfaces, lines and points are not, strictly speaking, parts of space at all, but just 'limits' of certain kinds, and as such 'abstract' entities.
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.254)
     A reaction: This is fairly crucial when dealing with Zeno's paradoxes. How many points in a line? How long to get through a point?
27. Natural Reality / C. Space / 5. Relational Space
If space is entirely relational, what makes a boundary, or a place unoccupied by physical objects? [Lowe]
     Full Idea: If space does not exist at all, but is only relations between objects, what could one possibly mean by saying that there is a place which is unoccupied by any material object? And what determines whether space is bounded?
     From: E.J. Lowe (A Survey of Metaphysics [2002], p.264)
     A reaction: Correct. People who assert that space is only relational have been misled by what we can know about space, not what it is.