Combining Texts

All the ideas for 'Thinking About Mathematics', 'Material Beings' and 'The Myth of the Given'

unexpand these ideas     |    start again     |     specify just one area for these texts


59 ideas

2. Reason / D. Definition / 12. Paraphrase
We could refer to tables as 'xs that are arranged tablewise' [Inwagen]
     Full Idea: We could paraphrase 'some chairs are heavier than some tables' as 'there are xs that are arranged chairwise and there are ys that are arranged tablewise and the xs are heavier than the ys'.
     From: Peter van Inwagen (Material Beings [1990], 11)
     A reaction: Liggins notes that this involves plural quantification. Being 'arranged tablewise' has become a rather notorious locution in modern ontology. We still have to retain identity, to pick out the xs.
4. Formal Logic / G. Formal Mereology / 1. Mereology
Mereology is 'nihilistic' (just atoms) or 'universal' (no restrictions on what is 'whole') [Inwagen, by Varzi]
     Full Idea: Van Ingwagen writes of 'mereological nihilism' (that only mereological atoms exist) and of 'mereological universalism' (adhering to the principle of Unrestricted Composition).
     From: report of Peter van Inwagen (Material Beings [1990], p.72-) by Achille Varzi - Mereology 4.3
     A reaction: They both look mereologically nihilistic to me, in comparison with an account that builds on 'natural' wholes and their parts. You can only be 'unrestricted' if you view the 'wholes' in your vast ontology as pretty meaningless (as Lewis does, Idea 10660).
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
The 'Law' of Excluded Middle needs all propositions to be definitely true or definitely false [Inwagen]
     Full Idea: I think the validity of the 'Law' of Excluded Middle depends on the assumption that every proposition is definitely true or definitely false.
     From: Peter van Inwagen (Material Beings [1990], 18)
     A reaction: I think this is confused. He cites vagueness as the problem, but that is a problem for Bivalence. If excluded middle is read as 'true or not-true', that leaves the meaning of 'not-true' open, and never mentions the bivalent 'false'.
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
     Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2)
     A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle.
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
Variables are just like pronouns; syntactic explanations get muddled over dummy letters [Inwagen]
     Full Idea: Explanations in terms of syntax do not satisfactorily distinguish true variables from dummy or schematic letters. Identifying variables with pronouns, however, provides a genuine explanation of what variables are.
     From: Peter van Inwagen (Material Beings [1990], 02)
     A reaction: I like this because it shows that our ordinary thought and speech use variables all the time ('I've forgotten something - what was it?'). He says syntax is fine for maths, but not for ordinary understanding.
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
There are no heaps [Inwagen]
     Full Idea: Fortunately ....there are no heaps.
     From: Peter van Inwagen (Material Beings [1990], 18)
     A reaction: This is the nihilist view of (inorganic) physical objects. If a wild view solves all sorts of problems, one should take it serious. It is why I take reductive physicalism about the mind seriously. (Well, it's true, actually)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
     Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2)
     A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
     Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4)
     A reaction: The sequence is 'Cauchy' if N exists.
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
     Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7)
     A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
     Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2)
     A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
     Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1)
     A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate.
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
     Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1)
     A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
     Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1)
     A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism.
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
     Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names?
     From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1)
     A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up.
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
     Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2)
     A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare.
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
     Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2)
     A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
     Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1)
     A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
     Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1)
     A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
     Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2)
     A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise.
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
I reject talk of 'stuff', and treat it in terms of particles [Inwagen]
     Full Idea: I have a great deal of difficulty with an ontology that includes 'stuffs' in addition to things. ...I prefer to replace talk of sameness of matter with talk of sameness of particles.
     From: Peter van Inwagen (Material Beings [1990], 14)
     A reaction: Van Inwagen is wedded to the idea that reality is composed of 'simples' - even if physicists seem now to talk of 'fields' as much as they do about objects in the fields. Has philosophy yet caught up with Maxwell?
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
Singular terms can be vague, because they can contain predicates, which can be vague [Inwagen]
     Full Idea: Since singular terms can contain predicates, and since vague predicates are common, vague singular terms are common. For 'the tallest man that Sally knows' there are lots of men for whom it is unclear whether Sally knows them.
     From: Peter van Inwagen (Material Beings [1990], 17)
9. Objects / A. Existence of Objects / 1. Physical Objects
Material objects are in space and time, move, have a surface and mass, and are made of some stuff [Inwagen]
     Full Idea: A thing is a material object if it occupies space and endures through time and can move about in space (literally move, unlike a shadow or wave or reflection) and has a surface and has a mass and is made of a certain stuff or stuffs.
     From: Peter van Inwagen (Material Beings [1990], 01)
     A reaction: It is not at all clear what electrons (which must count for him as 'simples') are made of.
Maybe table-shaped particles exist, but not tables [Inwagen, by Lowe]
     Full Idea: Van Ingwagen holds that although table-shaped collections of particles exist, tables do not.
     From: report of Peter van Inwagen (Material Beings [1990], Ch.13) by E.J. Lowe - The Possibility of Metaphysics 2.3
     A reaction: I find this idea appealing. See the ideas of Trenton Merricks. When you get down to micro-level, it is hard to individuate a table among the force fields, and hard to distinguish a table from a smashed or burnt table. An ontology without objects?
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
Nihilism says composition between single things is impossible [Inwagen]
     Full Idea: Nihilism about objects says there is a Y such that the Xs compose it if and only if there is only one of the Xs.
     From: Peter van Inwagen (Material Beings [1990], 08)
     A reaction: He says that Unger, the best known 'nihilist' about objects, believes a different version - claiming there are composites, but they never make up the ordinary objects we talk about.
If there are no tables, but tables are things arranged tablewise, the denial of tables is a contradiction [Liggins on Inwagen]
     Full Idea: Van Inwagen says 'there are no tables', and 'there are tables' means 'there are some things arranged tablewise'. Presumably 'there are no tables' negates the latter claim, saying no things are arranged tablewise. But he should think that is false.
     From: comment on Peter van Inwagen (Material Beings [1990], 10) by David Liggins - Nihilism without Self-Contradiction 3
     A reaction: Liggins's nice paper shows that Van Inwagen is in a potential state of contradiction when he starts saying that there are no tables, but that there are things arranged tablewise, and that they amount to tables. Liggins offers him an escape.
Actions by artefacts and natural bodies are disguised cooperations, so we don't need them [Inwagen]
     Full Idea: All the activities apparently carried out by shelves and stars and other artefacts and natural bodies can be understood as disguised cooperative activities. And, therefore, we are not forced to grant existence to any artefacts or natural bodies.
     From: Peter van Inwagen (Material Beings [1990], 12)
     A reaction: In 'the crowd tore her to pieces' are we forced to accept the existence of a crowd? We can't say 'Jack tore her to pieces' and 'Jill tore her to pieces'. If a plural quantification is unavoidable, we have to accept the plurality. Perhaps.
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
Every physical thing is either a living organism or a simple [Inwagen]
     Full Idea: The thesis about composition and parthood that I am advocating has far-reaching ontological consequences: that every physical thing is either a living organism or a simple.
     From: Peter van Inwagen (Material Beings [1990], 10)
     A reaction: A 'simple' is a placeholder for anything considered to be a fundamental unit of existence (such as an electron or a quark). This amazingly sharp distinction strikes me as utterly implausible. There is too much in the middle ground.
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
The statue and lump seem to share parts, but the statue is not part of the lump [Inwagen]
     Full Idea: Those who believe that the statue is distinct from the lump should concede that whatever shares a part with the statue shares a part with the lump but deny that the statue is a part of the lump.
     From: Peter van Inwagen (Material Beings [1990], 05)
     A reaction: Standard mereology says if they share all their parts then they are the same thing, so it is hard to explain how they are 'distinct'. The distinction is only modal - that they could be separated (by squashing, or by part substitution).
If you knead clay you make an infinite series of objects, but they are rearrangements, not creations [Inwagen]
     Full Idea: If you can make a (random) gollyswoggle by accident by kneading clay, then you must be causing the generation and corruption of a series of objects of infinitesimal duration. ...We have not augmented the furniture of the world but only rearranged it.
     From: Peter van Inwagen (Material Beings [1990], 13)
     A reaction: Van Inwagen's final conclusion is a bit crazy, but I am in sympathy with his general scepticism about what sorts of things definitively constitute 'objects'. He overrates simples, and he overrates lives.
9. Objects / C. Structure of Objects / 3. Matter of an Object
I assume matter is particulate, made up of 'simples' [Inwagen]
     Full Idea: I assume in this book that matter is ultimately particulate. Every material being is composed of things that have no proper parts: 'elementary particles' or 'mereological atoms' or 'metaphysical simples'.
     From: Peter van Inwagen (Material Beings [1990], Pref)
     A reaction: It may be that modern physics doesn't support this, if 'fields' is the best term for what is fundamental. Best to treat his book as hypothetical - IF there are just simples, proceed as follows.
9. Objects / C. Structure of Objects / 5. Composition of an Object
If contact causes composition, do two colliding balls briefly make one object? [Inwagen]
     Full Idea: If composition just requires contact, if I cause the cue ball to rebound from the eight ball, do I thereby create a short-lived object shaped like two slightly flattened spheres in contact?
     From: Peter van Inwagen (Material Beings [1990], 03)
     A reaction: [compressed]
If bricks compose a house, that is at least one thing, but it might be many things [Inwagen]
     Full Idea: If composition just requires contact, that tells us that the bricks of a house compose at least one thing; it does not tell us that they also compose at most one thing.
     From: Peter van Inwagen (Material Beings [1990], 04)
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
I think parthood involves causation, and not just a reasonably stable spatial relationship [Inwagen]
     Full Idea: I propose that parthood essentially involves causation. Too many philosophers have supposed that objects compose something when and only when they stand in some (more or less stable) spatial relationship to one another.
     From: Peter van Inwagen (Material Beings [1990], 09)
     A reaction: I have to say that I like this, even though it comes from a thinker who is close to nihilism about ordinary non-living objects. He goes on to say that only a 'life' provides the right sort of causal relationship.
We can deny whole objects but accept parts, by referring to them as plurals within things [Inwagen, by Liggins]
     Full Idea: Van Inwagen's claim that nothing has parts causes incredulity. ..But the problem is not with endorsing the sentence 'Some things have parts'; it is with interpreting this sentence by means of singular resources rather than plural ones.
     From: report of Peter van Inwagen (Material Beings [1990], 7) by David Liggins - Nihilism without Self-Contradiction
     A reaction: Van Inwagen notoriously denies the existence of normal physical objects. Liggins shows that modern formal plural quantification gives a better way of presenting his theory, by accepting tables and parts of tables as plurals of basic entities.
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
Special Composition Question: when is a thing part of something? [Inwagen]
     Full Idea: The Special Composition Question asks, In what circumstances is a thing a (proper) part of something?
     From: Peter van Inwagen (Material Beings [1990], 02)
     A reaction: [He qualifies this formulation as 'misleading'] It's a really nice basic question for the metaphysics of objects.
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
The essence of a star includes the released binding energy which keeps it from collapse [Inwagen]
     Full Idea: I think it is part of the essence of a star that the radiation pressures that oppose the star's tendency to gravitational collapse has its source in the release of no-longer-needed nuclear binding energy when colliding nuclei fuse in the star's hot core.
     From: Peter van Inwagen (Material Beings [1990], 07)
     A reaction: A perfect example of giving the essence of something as the bottom level of its explanation. This even comes from someone who doesn't really believe in stars!
9. Objects / D. Essence of Objects / 11. Essence of Artefacts
The persistence of artifacts always covertly involves intelligent beings [Inwagen]
     Full Idea: Statements that are apparently about the persistence of artifacts make covert reference to the dispositions of intelligent beings to maintain certain arrangements of matter.
     From: Peter van Inwagen (Material Beings [1990], 13)
     A reaction: If you build a self-sustaining windmill that pumps water, that seems to have an identity of its own, apart from the intentions of whoever makes it and repairs it. The function of an artefact is not just the function we want it to have.
9. Objects / E. Objects over Time / 7. Intermittent Objects
When an electron 'leaps' to another orbit, is the new one the same electron? [Inwagen]
     Full Idea: Is the 'new' electron in the lower orbit the one that was in the higher orbit? Physics, as far as I can tell, has nothing to say about this.
     From: Peter van Inwagen (Material Beings [1990], 14)
     A reaction: I suspect that physicists would say that philosophers are worrying about such questions because they haven't grasped the new conceptual scheme that emerged in 1926. The poor mutts insist on hanging on to 'objects'.
9. Objects / E. Objects over Time / 9. Ship of Theseus
If you reject transitivity of vague identity, there is no Ship of Theseus problem [Inwagen]
     Full Idea: If you have rejected the Principle of the Transitivity of (vague) Identity, it is hard to see how the problem of the Ship of Theseus could arise.
     From: Peter van Inwagen (Material Beings [1990], 18)
     A reaction: I think this may well be the best solution to the whole problem
9. Objects / F. Identity among Objects / 1. Concept of Identity
We should talk of the transitivity of 'identity', and of 'definite identity' [Inwagen]
     Full Idea: In some contexts, the principle of 'the transitivity of identity' should be called 'the transitivity of definite identity'.
     From: Peter van Inwagen (Material Beings [1990], 18)
     A reaction: He is making room for a person to retain identity despite having changed. Applause from me.
10. Modality / C. Sources of Modality / 5. Modality from Actuality
Actuality proves possibility, but that doesn't explain how it is possible [Inwagen]
     Full Idea: A proof of actuality is a proof of possibility, but that does not invariably explain the possibility whose existence it demonstrates, for we may know that a certain thing is actual (and hence possible) but have no explanation of how it could be possible.
     From: Peter van Inwagen (Material Beings [1990], 12)
     A reaction: I like this, because my project is to see all of philosophy in terms of explanation rather than of description.
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Counterparts reduce counterfactual identity to problems about similarity relations [Inwagen]
     Full Idea: Counterpart Theory essentially reduces all problems about counterfactual identity to problems about choosing appropriate similarity relations. That is, Counterpart Theory essentially eliminates problems of counterfactual identity as such.
     From: Peter van Inwagen (Material Beings [1990], 14)
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
A merely possible object clearly isn't there, so that is a defective notion [Inwagen]
     Full Idea: The notion of a merely possible object is an even more defective notion than the notion of a borderline object; after all, a merely possible object is an object that definitely isn't there.
     From: Peter van Inwagen (Material Beings [1990], 19)
Merely possible objects must be consistent properties, or haecceities [Inwagen]
     Full Idea: Talk of merely possible objects may be redeemed in either maximally consistent sets of properties or in haecceities.
     From: Peter van Inwagen (Material Beings [1990], 19)
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
     Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1)
     A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach.
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
The 'doctrine of the given' is correct; some beliefs or statements are self-justifying [Chisholm]
     Full Idea: In my opinion, the 'doctrine of the given' is correct in saying that there are some beliefs or statements which are 'self-justifying' and that among such beliefs are statements some of which concern appearances or 'ways of being appeared to'.
     From: Roderick Chisholm (The Myth of the Given [1964], §12)
     A reaction: To boldly assert that they are 'self-justifying' invites a landslide of criticisms, pointing at a regress. It might be better to say they are self-evident, or intuitively known, or primitive, or true by the natural light of reason.
27. Natural Reality / B. Modern Physics / 3. Chromodynamics / a. Chromodynamics
The strong force pulls, but also pushes apart if nucleons get too close together [Inwagen]
     Full Idea: The strong force doesn't always pull nucleons together, but pushes them apart if they get too close.
     From: Peter van Inwagen (Material Beings [1990], 07)
     A reaction: Philosophers tend to learn their physics from other philosophers. But that's because philosophers are brilliant at picking out the interesting parts of physics, and skipping the boring stuff.
27. Natural Reality / F. Chemistry / 2. Modern Elements
Is one atom a piece of gold, or is a sizable group of atoms required? [Inwagen]
     Full Idea: A physicist once told me that of course a gold atom was a piece of gold, and a physical chemist has assured me that the smallest possible piece of gold would have to be composed of sixteen or seventeen atoms.
     From: Peter van Inwagen (Material Beings [1990], 01)
     A reaction: The issue is at what point all the properties that we normally begin to associate with gold begin to appear. One water molecule can hardly have a degree of viscosity or liquidity.
27. Natural Reality / G. Biology / 2. Life
At the lower level, life trails off into mere molecular interaction [Inwagen]
     Full Idea: The lives of the lower links of the Great Chain of Being trail off into vague, temporary episodes of molecular interaction.
     From: Peter van Inwagen (Material Beings [1990], 18)
     A reaction: His case involves conceding all sorts of vagueness to life, but asserting the utter distinctness of the full blown cases of more elaborate life. I don't really concede the distinction.
A tumour may spread a sort of life, but it is not a life, or an organism [Inwagen]
     Full Idea: A tumour is not an organism (or a parasite) and there is no self-regulating event that is its life. It does not fill one space, but is a locus within which a certain sort of thing is happening: the spreading of a certain sort of (mass-term) life.
     From: Peter van Inwagen (Material Beings [1990], 09)
Being part of an organism's life is a matter of degree, and vague [Inwagen]
     Full Idea: Being caught up in the life of an organism is, like being rich or being tall, a matter of degree, and is in that sense a vague condition.
     From: Peter van Inwagen (Material Beings [1990], 17)
     A reaction: Van Inwagen is trying to cover himself, given that he makes a sharp distinction between living organisms, which are unified objects, and everything else, which isn't. There may be a vague centre to a 'life', as well as vague boundaries.
Some events are only borderline cases of lives [Inwagen]
     Full Idea: There are events of which it is neither definitely true nor definitely false that those events are lives. I do not see how we can deny this.
     From: Peter van Inwagen (Material Beings [1990], 18)
     A reaction: Very frustrating, since this is my main objection to Van Inwagen's distinction between unified lives and mere collections of simples. Some boundaries are real enough, despite their vagueness, and others indicate that there is no real distinction.
Unlike waves, lives are 'jealous'; it is almost impossible for them to overlap [Inwagen]
     Full Idea: A wave is not a 'jealous' event. Lives, however, are jealous. It cannot be that the activities of the Xs constitute at one and the same time two lives. Only in certain special cases can two lives overlap.
     From: Peter van Inwagen (Material Beings [1990], 09)
One's mental and other life is centred on the brain, unlike any other part of the body [Inwagen]
     Full Idea: One's life - not simply one's mental life - is centered in the activity of the simples that virtually compose one's brain in a way in which it is not centered in the activity of any of the other simples that compose one.
     From: Peter van Inwagen (Material Beings [1990], 15)
     A reaction: This justifies the common view that 'one follows one's brain'. I take that to mean that my brain embodies my essence. I would read 'centered on' as 'explains'.
The chemical reactions in a human life involve about sixteen elements [Inwagen]
     Full Idea: There are sixteen or so chemical elements involved in those chemical reactions that collectively constitute the life of a human being.
     From: Peter van Inwagen (Material Beings [1990], 09)
Life is vague at both ends, but could it be totally vague? [Inwagen]
     Full Idea: Individual human lives are infected with vagueness at both ends. ...But could there be a 'borderline life'?
     From: Peter van Inwagen (Material Beings [1990], 18)
     A reaction: Van Inwagen says (p.239) that there may be wholly vague lives, though it would suit his case better if there were not.
A flame is like a life, but not nearly so well individuated [Inwagen]
     Full Idea: A flame, though it is a self-maintaining event, does not seem to be nearly so well individuated as a life.
     From: Peter van Inwagen (Material Beings [1990], 09)
     A reaction: This is to counter the standard problem that if you attempt to define 'life', fire turns out to tick nearly all the same boxes. The concept of 'individuated' often strikes me as unsatisfactory. How does a bonfire fail to be individuated?
If God were to 'reassemble' my atoms of ten years ago, the result would certainly not be me [Inwagen]
     Full Idea: If God were to 'reassemble' the atoms that composed me ten years ago, the resulting organism would certainly not be me.
     From: Peter van Inwagen (Material Beings [1990], 13)
     A reaction: What is obvious to Van Inwagen is not obvious to me. He thinks lives are special. Such examples just leave us bewildered about what counts as 'the same', because our concept of sameness wasn't designed to deal with such cases.
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
There is no reason to think that mere existence is a valuable thing [Inwagen]
     Full Idea: There is no reason to suppose - whatever Saint Anselm and Descartes may have thought - that mere existence is a valuable thing.
     From: Peter van Inwagen (Material Beings [1990], 12)
     A reaction: This is one of the simplest and most powerful objections to the Ontological Argument. God's existence may be of great value, but the existence of Hitler wasn't.