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All the ideas for 'Mahaprajnaparamitashastra', 'Understanding the Infinite' and 'Objects and Persons'

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62 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism
Empirical investigation can't discover if holes exist, or if two things share a colour [Merricks]
     Full Idea: Ontology is not empirical, but ontologists do make discoveries; empirical investigation won't discover that holes exist; we see that two things are the same colour, but a philosopher must resolve whether one universal is present in both.
     From: Trenton Merricks (Objects and Persons [2003], Pref)
     A reaction: This is one of the best, simplest and clearest statements I have encountered of the autonomy of philosophy. One may, of course, respond by saying 'who cares?', but then who cares about quarks, or the economy of the Spanish Empire?
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine]
     Full Idea: Second-order set theory is just like first-order set-theory, except that we use the version of Replacement with a universal second-order quantifier over functions from set to sets.
     From: Shaughan Lavine (Understanding the Infinite [1994], VII.4)
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine]
     Full Idea: A member m of M is an 'upper bound' of a subset N of M if m is not less than any member of N. A member m of M is a 'least upper bound' of N if m is an upper bound of N such that if l is any other upper bound of N, then m is less than l.
     From: Shaughan Lavine (Understanding the Infinite [1994], III.4)
     A reaction: [if you don't follow that, you'll have to keep rereading it till you do]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set
Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine]
     Full Idea: Since combinatorial collections are enumerated, some multiplicities may be too large to be gathered into combinatorial collections. But the size of a multiplicity seems quite irrelevant to whether it forms a logical connection.
     From: Shaughan Lavine (Understanding the Infinite [1994], IV.2)
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
Those who reject infinite collections also want to reject the Axiom of Choice [Lavine]
     Full Idea: Many of those who are skeptical about the existence of infinite combinatorial collections would want to doubt or deny the Axiom of Choice.
     From: Shaughan Lavine (Understanding the Infinite [1994], VI.2)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
The Power Set is just the collection of functions from one collection to another [Lavine]
     Full Idea: The Power Set is just he codification of the fact that the collection of functions from a mathematical collection to a mathematical collection is itself a mathematical collection that can serve as a domain of mathematical study.
     From: Shaughan Lavine (Understanding the Infinite [1994], VI.1)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
Replacement was immediately accepted, despite having very few implications [Lavine]
     Full Idea: The Axiom of Replacement (of Skolem and Fraenkel) was remarkable for its universal acceptance, though it seemed to have no consequences except for the properties of the higher reaches of the Cantorian infinite.
     From: Shaughan Lavine (Understanding the Infinite [1994], I)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine]
     Full Idea: The Axiom of Foundation (Zermelo 1930) says 'Every (descending) chain in which each element is a member of the previous one is of finite length'. ..This forbids circles of membership, or ungrounded sets. ..The iterative conception gives this centre stage.
     From: Shaughan Lavine (Understanding the Infinite [1994], V.4)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine]
     Full Idea: The controversy was not about Choice per se, but about the correct notion of function - between advocates of taking mathematics to be about arbitrary functions and advocates of taking it to be about functions given by rules.
     From: Shaughan Lavine (Understanding the Infinite [1994], I)
Pure collections of things obey Choice, but collections defined by a rule may not [Lavine]
     Full Idea: Combinatorial collections (defined just by the members) obviously obey the Axiom of Choice, while it is at best dubious whether logical connections (defined by a rule) do.
     From: Shaughan Lavine (Understanding the Infinite [1994], IV.2)
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine]
     Full Idea: The Peano-Russell notion of class is the 'logical' notion, where each collection is associated with some kind of definition or rule that characterises the members of the collection.
     From: Shaughan Lavine (Understanding the Infinite [1994], IV.1)
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The iterative conception of set wasn't suggested until 1947 [Lavine]
     Full Idea: The iterative conception of set was not so much as suggested, let alone advocated by anyone, until 1947.
     From: Shaughan Lavine (Understanding the Infinite [1994], I)
The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine]
     Full Idea: The iterative conception of sets does not tell us how far to iterate, and so we must start with an Axiom of Infinity. It also presupposes the notion of 'transfinite iteration'.
     From: Shaughan Lavine (Understanding the Infinite [1994], V.5)
The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine]
     Full Idea: The iterative conception does not provide a conception that unifies the axioms of set theory, ...and it has had very little impact on what theorems can be proved.
     From: Shaughan Lavine (Understanding the Infinite [1994], V.5)
     A reaction: He says he would like to reject the iterative conception, but it may turn out that Foundation enables new proofs in mathematics (though it hasn't so far).
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine]
     Full Idea: Limitation of Size has it that if a collection is the same size as a set, then it is a set. The Axiom of Replacement is characteristic of limitation of size.
     From: Shaughan Lavine (Understanding the Infinite [1994], V.5)
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine]
     Full Idea: A collection M is 'well-ordered' by a relation < if < linearly orders M with a least element, and every subset of M that has an upper bound not in it has an immediate successor.
     From: Shaughan Lavine (Understanding the Infinite [1994], III.4)
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine]
     Full Idea: The distinctive feature of second-order logic is that it presupposes that, given a domain, there is a fact of the matter about what the relations on it are, so that the range of the second-order quantifiers is fixed as soon as the domain is fixed.
     From: Shaughan Lavine (Understanding the Infinite [1994], V.3)
     A reaction: This sounds like a rather large assumption, which is open to challenge. I am not sure whether it was the basis of Quine's challenge to second-order logic. He seems to have disliked its vagueness, because it didn't stick with 'objects'.
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Mathematical proof by contradiction needs the law of excluded middle [Lavine]
     Full Idea: The Law of Excluded Middle is (part of) the foundation of the mathematical practice of employing proofs by contradiction.
     From: Shaughan Lavine (Understanding the Infinite [1994], VI.1)
     A reaction: This applies in a lot of logic, as well as in mathematics. Come to think of it, it applies in Sudoku.
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine]
     Full Idea: Mathematics is today thought of as the study of abstract structure, not the study of quantity. That point of view arose directly out of the development of the set-theoretic notion of abstract structure.
     From: Shaughan Lavine (Understanding the Infinite [1994], III.2)
     A reaction: It sounds as if Structuralism, which is a controversial view in philosophy, is a fait accompli among mathematicians.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
Every rational number, unlike every natural number, is divisible by some other number [Lavine]
     Full Idea: One reason to introduce the rational numbers is that it simplifes the theory of division, since every rational number is divisible by every nonzero rational number, while the analogous statement is false for the natural numbers.
     From: Shaughan Lavine (Understanding the Infinite [1994], VI.3)
     A reaction: That is, with rations every division operation has an answer.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine]
     Full Idea: The chief importance of the Continuum Hypothesis for Cantor (I believe) was that it would show that the real numbers form a set, and hence that they were encompassed by his theory.
     From: Shaughan Lavine (Understanding the Infinite [1994], IV.2)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a necessary condition for the convergence of a sequence [Lavine]
     Full Idea: The Cauchy convergence criterion for a sequence: the sequence S0,S1,... has a limit if |S(n+r) - S(n)| is less than any given quantity for every value of r and sufficiently large values of n. He proved this necessary, but not sufficient.
     From: Shaughan Lavine (Understanding the Infinite [1994], 2.5)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine]
     Full Idea: Roughly speaking, the upper and lower parts of the Dedekind cut correspond to the commensurable ratios greater than and less than a given incommensurable ratio.
     From: Shaughan Lavine (Understanding the Infinite [1994], II.6)
     A reaction: Thus there is the problem of whether the contents of the gap are one unique thing, or many.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Counting results in well-ordering, and well-ordering makes counting possible [Lavine]
     Full Idea: Counting a set produces a well-ordering of it. Conversely, if one has a well-ordering of a set, one can count it by following the well-ordering.
     From: Shaughan Lavine (Understanding the Infinite [1994], III.4)
     A reaction: Cantor didn't mean that you could literally count the set, only in principle.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
The infinite is extrapolation from the experience of indefinitely large size [Lavine]
     Full Idea: My proposal is that the concept of the infinite began with an extrapolation from the experience of indefinitely large size.
     From: Shaughan Lavine (Understanding the Infinite [1994], VIII.2)
     A reaction: I think it might be better to talk of an 'abstraction' than an 'extrapolition', since the latter is just more of the same, which doesn't get you to concept. Lavine spends 100 pages working out his proposal.
The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine]
     Full Idea: The indiscernibility of indefinitely large sizes will be a critical part of the theory of indefinitely large sizes.
     From: Shaughan Lavine (Understanding the Infinite [1994], VIII.2)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
The intuitionist endorses only the potential infinite [Lavine]
     Full Idea: The intuitionist endorse the actual finite, but only the potential infinite.
     From: Shaughan Lavine (Understanding the Infinite [1994], VI.2)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine]
     Full Idea: The symbol 'aleph-nought' denotes the cardinal number of the set of natural numbers. The symbol 'aleph-one' denotes the next larger cardinal number. 'Aleph-omega' denotes the omega-th cardinal number.
     From: Shaughan Lavine (Understanding the Infinite [1994], III.3)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
Ordinals are basic to Cantor's transfinite, to count the sets [Lavine]
     Full Idea: The ordinals are basic because the transfinite sets are those that can be counted, or (equivalently for Cantor), those that can be numbered by an ordinal or are well-ordered.
     From: Shaughan Lavine (Understanding the Infinite [1994], III.4)
     A reaction: Lavine observes (p.55) that for Cantor 'countable' meant 'countable by God'!
Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine]
     Full Idea: The paradox of the largest ordinal (the 'Burali-Forti') is that the class of all ordinal numbers is apparently well-ordered, and so it has an ordinal number as order type, which must be the largest ordinal - but all ordinals can be increased by one.
     From: Shaughan Lavine (Understanding the Infinite [1994], III.5)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine]
     Full Idea: The paradox of the largest cardinal ('Cantor's Paradox') says the diagonal argument shows there is no largest cardinal, but the class of all individuals (including the classes) must be the largest cardinal number.
     From: Shaughan Lavine (Understanding the Infinite [1994], III.5)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set theory will found all of mathematics - except for the notion of proof [Lavine]
     Full Idea: Every theorem of mathematics has a counterpart with set theory - ...but that theory cannot serve as a basis for the notion of proof.
     From: Shaughan Lavine (Understanding the Infinite [1994], V.3)
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine]
     Full Idea: In modern mathematics virtually all work is only up to isomorphism and no one cares what the numbers or points and lines 'really are'.
     From: Shaughan Lavine (Understanding the Infinite [1994], VI.1)
     A reaction: At least that leaves the field open for philosophers, because we do care what things really are. So should everybody else, but there is no persuading some people.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Intuitionism rejects set-theory to found mathematics [Lavine]
     Full Idea: Intuitionism in philosophy of mathematics rejects set-theoretic foundations.
     From: Shaughan Lavine (Understanding the Infinite [1994], V.3 n33)
7. Existence / B. Change in Existence / 4. Events / a. Nature of events
Prolonged events don't seem to endure or exist at any particular time [Merricks]
     Full Idea: That events endure is difficult to reconcile with the claim that, say, the American Civil War existed; for such an event seems never to have been 'wholly present' at any single time.
     From: Trenton Merricks (Objects and Persons [2003], §3 n14)
     A reaction: A nice problem example for those who, like Kim, want their ontology to include events. Personally I am happy to allow some vagueness here. The Civil War only became an 'event' on the day it finished. An event's time need not be an instant.
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
A crumbling statue can't become vague, because vagueness is incoherent [Merricks]
     Full Idea: Some would say that annihilating grains of stone from the statue of David (playing the 'Sorites Game') could never make its identity vague, because metaphysical vagueness is simply unintelligible.
     From: Trenton Merricks (Objects and Persons [2003], §2.II)
     A reaction: He cites Russell, Dummett and Lewis in support. But Russell is a logical atomist, and Lewis says identity is composition. It strikes me as obvious that identity can be vague; the alternative is the absurdities of the Sorites paradox.
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
Intrinsic properties are those an object still has even if only that object exists [Merricks]
     Full Idea: Intrinsic properties are, by and large, those properties that an object can exemplify even if that object and its parts (if any) are the only objects that exist.
     From: Trenton Merricks (Objects and Persons [2003], §4.I)
     A reaction: This leads to all sorts of properties that seemed intrinsic turning out to be relational. In what sense would a single object have mass, or impenetrability?
9. Objects / A. Existence of Objects / 1. Physical Objects
I say that most of the objects of folk ontology do not exist [Merricks]
     Full Idea: I argue against the existence of most of the objects alleged to exist by what we might call 'folk ontology'.
     From: Trenton Merricks (Objects and Persons [2003], §1)
     A reaction: This is the programme for Merricks's heroic book, denying (quite plausibly) the need for large objects in our ontology. It seems that ontology must multiply its entities prodigiously, or else be austere in the extreme. Is there no middle way?
Is swimming pool water an object, composed of its mass or parts? [Merricks]
     Full Idea: Some - such as those who endorse unrestricted composition or those who believe in a kind of entity called 'a mass' - say that 'the water in the swimming pool' refers to a big material object.
     From: Trenton Merricks (Objects and Persons [2003], §2.I)
     A reaction: A well-chosen example to support his thesis that large objects don't (strictly) exist. We certainly must not say (in Quine fashion) that we must accept the ontology of our phrases. I cut nature at the joints, and I say a pool is an obvious joint.
9. Objects / A. Existence of Objects / 5. Simples
We can eliminate objects without a commitment to simples [Merricks]
     Full Idea: Eliminativism about physical objects does not require a commitment to (or against) simples.
     From: Trenton Merricks (Objects and Persons [2003], §1.I)
     A reaction: His strategy is to eliminate objects in favour of whatever it is (an unknown) to which objects actually reduce. His point seems to be clearly correct, just as I might eliminate 'life' from my ontology, without quite knowing what it is.
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
Merricks agrees that there are no composite objects, but offers a different semantics [Merricks, by Liggins]
     Full Idea: Merricks agrees with van Inwagen that there are no composite objects, but disagrees with him about the semantics of talk about material objects.
     From: report of Trenton Merricks (Objects and Persons [2003]) by David Liggins - Nihilism without Self-Contradiction 4
     A reaction: Van Inwagen has one semantics for folk talk, and another semantics 'for the philosophy room'. Merricks seems to have an error theory of folk semantics (i.e. the folk don't understand what they are saying).
The 'folk' way of carving up the world is not intrinsically better than quite arbitrary ways [Merricks]
     Full Idea: It is hard to see why the folk way of carving up the material world should - barring further argument - be elevated to a loftier status than the unrestricted compositionist way.
     From: Trenton Merricks (Objects and Persons [2003], §3.III)
     A reaction: There are some right ways to carve up the world, though there is also the capacity to be quite arbitrary, if it is useful, or even amusing. Thus Cyprus is an island (fact), Britons are a nation (useful), and Arsenal fans are sad (amusing).
If atoms 'arranged baseballwise' break a window, that analytically entails that a baseball did it [Merricks, by Thomasson]
     Full Idea: Given the proper understanding of 'arranged baseballwise', the fact that atoms arranged baseballwise are causally relevant to a shattering analytically entails that a baseball is.
     From: report of Trenton Merricks (Objects and Persons [2003], 3) by Amie L. Thomasson - Ordinary Objects 01.3
     A reaction: This is the key argument of Thomasson's book. Presumably, following Idea 14471, 'I bought some atoms arranged baseballwise' is held to entail 'I bought a baseball'. That seems to beg the question against Van Inwagen and Merricks.
Overdetermination: the atoms do all the causing, so the baseball causes no breakage [Merricks]
     Full Idea: The Overdetermination Argument: a baseball is irrelevant to whether its atoms shatter a window, the shattering is caused by the atoms in concert, the shattering is not overdetermined, so if the baseball exists it doesn't cause the shattering.
     From: Trenton Merricks (Objects and Persons [2003], 3)
     A reaction: An obvious thought is that no individual atom does any sort of breaking at all - it is only when they act as a team, and an appropriate name for the team is a 'baseball', and the team is real.
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Clay does not 'constitute' a statue, as they have different persistence conditions (flaking, squashing) [Merricks]
     Full Idea: A statue is not identical with its constituent lump of clay because they have different persistence conditions; the statue, but not the lump, could survive the loss of a few smallish bits, and the lump, but not the statue, could survive being squashed.
     From: Trenton Merricks (Objects and Persons [2003], §2.III)
     A reaction: I don't see why a lump can't survive losing a few bits (if the lump never had a precise identity), but it is hard to argue that squashing is a problem. However, presumably the identity (or constitution) between lump and statue is not a necessity.
9. Objects / C. Structure of Objects / 5. Composition of an Object
'Unrestricted composition' says any two things can make up a third thing [Merricks]
     Full Idea: If my dog and the top half of my tree compose an object, this is defended under the title of 'unrestricted (universal) composition', the thesis that any two things compose something.
     From: Trenton Merricks (Objects and Persons [2003], §1.II)
     A reaction: David Lewis is cited amongst those defending this thesis. My intuition is against this thesis, because I think identity is partly dictated by nature, and is not entirely conventional. You can force an identity, but you feel the 'restriction'.
Composition as identity is false, as identity is never between a single thing and many things [Merricks]
     Full Idea: One of the most obvious facts about identity is that it holds one-one (John and Mr Smith) and perhaps many-many (John+Mary and Mr Smith+Miss Jones), but never one-many. It follows that composition as identity (things are their parts) is false.
     From: Trenton Merricks (Objects and Persons [2003], §1.IV)
     A reaction: This assumes that 'having identity' and 'being identical to' are the same concept. I agree with his conclusion, but am not convinced by the argument. I'm not even quite clear why John and May can't be identical to the Smiths.
Composition as identity is false, as it implies that things never change their parts [Merricks]
     Full Idea: Composition as identity implies that no persisting object ever changes its parts, which is clearly false, so composition as identity is false.
     From: Trenton Merricks (Objects and Persons [2003], §1.IV)
     A reaction: Presumably Lewis can say that when a thing subtly changes its parts, it really does lose its strict identity, but becomes another 'time-slice' or close 'counterpart' of the original object. This is a coherent view, but I disagree. I'm a believer.
There is no visible difference between statues, and atoms arranged statuewise [Merricks]
     Full Idea: If we imagine a world like ours except that, while there are atoms arranged statuewise in that world, there are no statues, ...no amount of looking around could distinguish that imagined world from ours.
     From: Trenton Merricks (Objects and Persons [2003], §2.V)
     A reaction: This is one of his arguments for ontological eliminativism about physical objects. If we accept the argument, it will wreak havoc with our entire ontology, and we will end up anti-realists. I say you have to see statues - you just can't miss them.
9. Objects / C. Structure of Objects / 6. Constitution of an Object
'Composition' says things are their parts; 'constitution' says a whole substance is an object [Merricks]
     Full Idea: Composition as identity claims that a single object is identical with the many parts it comprises; constitution as identity says that a single object (a statue) is identical with a single object (clay) that 'constitutes' it.
     From: Trenton Merricks (Objects and Persons [2003], §1 n11)
     A reaction: The constitution view has been utilised (by Lynn Rudder Baker) to give an account of personal identity as constituted by a human body. Neither sounds quite right to me; the former view misses something about reality; the latter doesn't explain much.
It seems wrong that constitution entails that two objects are wholly co-located [Merricks]
     Full Idea: Many philosophers deny that two numerically distinct physical objects could be 'wholly co-located'.
     From: Trenton Merricks (Objects and Persons [2003], §2.III)
     A reaction: A fish can be located in a river; the Appenines can be located in Italy. If you accept the objection you will probably have to accept identity-as-composition, or object-eliminativism. One object can have two causal roles, supporting two identities.
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
Objects decompose (it seems) into non-overlapping parts that fill its whole region [Merricks]
     Full Idea: Intuitively, an object's parts at one level of decomposition are parts of that object that do not overlap and that, collectively, fill the whole region the object fills.
     From: Trenton Merricks (Objects and Persons [2003], §1.II)
     A reaction: A nice case where 'intuition' must be cited as the basis for the claim, and yet it is hard to see how anyone could possibly disagree. Exhibit 73 in favour of rationalism. This ideas shows the structure of nature and the workings of our minds.
9. Objects / E. Objects over Time / 13. No Identity over Time
Eliminativism about objects gives the best understanding of the Sorites paradox [Merricks]
     Full Idea: I say we should endorse eliminativism about physical objects, because it offers the most plausible understanding of what occurs during the Sorites Game (eliminating grains of a thing one at a time).
     From: Trenton Merricks (Objects and Persons [2003], §2.II)
     A reaction: That is one route to go in explaining the paradox (i.e. by saying there never was a 'heap' in the first place). I suspect a better route is to say that heaps really exist as natural phenomena, but they suffer from vague identity and borderline cases.
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
If my counterpart is happy, that is irrelevant to whether I 'could' have been happy [Merricks]
     Full Idea: The existence of someone in another world who is a lot like me, but happier, is irrelevant to whether I - this very person - could have been happier, even if we call that other-worldly someone 'my counterpart'.
     From: Trenton Merricks (Objects and Persons [2003], §1.IV)
     A reaction: He says this is a familiar objection. I retain a lingering deterministic doubt about whether it ever makes to sense to say that I 'could' have been happy, given that I am not. It does seem to make sense to say that I was close to happiness, but missed it.
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
The 'warrant' for a belief is what turns a true belief into knowledge [Merricks]
     Full Idea: The 'warrant' for a belief is that, whatever it is, that makes the difference between mere true belief and knowledge.
     From: Trenton Merricks (Objects and Persons [2003], §7.II)
     A reaction: Hence a false belief could be well justified, but it could never be warranted. This makes warrant something like the externalist view of justification, a good supporting situation for a belief, rather than an inner awareness of support for it.
16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body
You hold a child in your arms, so it is not mental substance, or mental state, or software [Merricks]
     Full Idea: When you hold your child, you do exactly that - hold the child himself or herself - and not some stand-in. This implies that we are not two substances, and we are not mental states nor akin to software.
     From: Trenton Merricks (Objects and Persons [2003], §4)
     A reaction: And it is not just a brain, either. This is a nice simple example to support the sensible view that a person is a type of animal. Like all other physical objects that is a bit vague, so we should not be distracted by borderline cases like brain bisection.
16. Persons / D. Continuity of the Self / 3. Reference of 'I'
Maybe the word 'I' can only refer to persons [Merricks]
     Full Idea: One might say that the word 'I' can only have a person as its reference.
     From: Trenton Merricks (Objects and Persons [2003], §2.IV)
     A reaction: To infer the existence of persons from this would be to commit what I think of as the Linguistic Fallacy, of deducing ontology directly from language. We might allow (Dennett fashion) that folk categories require the fiction of persons.
16. Persons / F. Free Will / 7. Compatibilism
Free will and determinism are incompatible, since determinism destroys human choice [Merricks]
     Full Idea: The main recent support for incompatibilism is the 'no choice' argument: we have no choice that the past and the laws of nature entail human actions, we have no choice about what the past or the laws are like, so we have no choice about our actions.
     From: Trenton Merricks (Objects and Persons [2003], §6.III)
     A reaction: Since I consider free will to be an absurd chimera, I think this argument involves a total misunderstanding of what a 'choice' is. Since the human brain is a wonderfully sophisticated choosing machine, our whole life consists of choices.
17. Mind and Body / D. Property Dualism / 4. Emergentism
Human organisms can exercise downward causation [Merricks]
     Full Idea: Human organisms have non-redundant causal powers, and so can exercise downward causation.
     From: Trenton Merricks (Objects and Persons [2003], §4.VII)
     A reaction: The hallmark of property dualism. This notion needs a lot more expansion and exploration than Merricks gives it, and I don't think it will be enough to provide 'free will', or even, as Merricks hopes, to place humans in a distinct ontological category.
18. Thought / C. Content / 7. Narrow Content
Before Creation it is assumed that God still had many many mental properties [Merricks]
     Full Idea: The belief of theists that God might never have created implies that there is a possible world that contains just a single entity with many conscious mental properties.
     From: Trenton Merricks (Objects and Persons [2003], §4.II)
     A reaction: So if we believe content is wide, we must believe that God was incapable of thought before creation, and thus couldn't plan creation, and so didn't create, and so the Creator is a logical impossibility. Cool.
The hypothesis of solipsism doesn't seem to be made incoherent by the nature of mental properties [Merricks]
     Full Idea: The hypothesis of solipsism, that I - an entity with many conscious mental properties - am all that exists, while surely false, is not rendered incoherent simply by the nature of the mental properties.
     From: Trenton Merricks (Objects and Persons [2003], §4.II)
     A reaction: This, along with the thought of a pre-Creation God, is a nice intuitive case for showing that we strongly believe in some degree of narrow content.
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
     Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
     From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
     A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').