Combining Philosophers

All the ideas for Buddhaghosa, Katherine Hawley and Kurt Gdel

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80 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Philosophers are good at denying the obvious [Hawley]
     Full Idea: Philosophers are skilled at resisting even the most inviting thoughts.
     From: Katherine Hawley (How Things Persist [2001], 5)
     A reaction: Not exactly 'despair', but it does show how far philosophers are able to stray from common sense. Monads, real possible worlds, real sets… Thomas Reid, the philosopher of common sense, might be the antidote.
2. Reason / A. Nature of Reason / 1. On Reason
For clear questions posed by reason, reason can also find clear answers [Gödel]
     Full Idea: I uphold the belief that for clear questions posed by reason, reason can also find clear answers.
     From: Kurt Gödel (works [1930]), quoted by Peter Koellner - On the Question of Absolute Undecidability 1.5
     A reaction: [written in 1961] This contradicts the implication normally taken from his much earlier Incompleteness Theorems.
2. Reason / D. Definition / 8. Impredicative Definition
Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
     Full Idea: Impredicative Definitions are definitions of an object by reference to the totality to which the object itself (and perhaps also things definable only in terms of that object) belong.
     From: Kurt Gödel (Russell's Mathematical Logic [1944], n 13)
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine]
     Full Idea: Gödel's proof wrought an abrupt turn in the philosophy of mathematics. We had supposed that truth, in mathematics, consisted in provability.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Willard Quine - Forward to Gödel's Unpublished
     A reaction: This explains the crisis in the early 1930s, which Tarski's theory appeared to solve.
4. Formal Logic / C. Predicate Calculus PC / 3. Completeness of PC
Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki]
     Full Idea: Gödel proved the completeness of first order predicate logic in his doctoral dissertation of 1930.
     From: report of Kurt Gödel (Completeness of Axioms of Logic [1930]) by Michal Walicki - Introduction to Mathematical Logic History E.2.2
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
We perceive the objects of set theory, just as we perceive with our senses [Gödel]
     Full Idea: We have something like perception of the objects of set theory, shown by the axioms forcing themselves on us as being true. I don't see why we should have less confidence in this kind of perception (i.e. mathematical intuition) than in sense perception.
     From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.483), quoted by Michčle Friend - Introducing the Philosophy of Mathematics 2.4
     A reaction: A famous strong expression of realism about the existence of sets. It is remarkable how the ingredients of mathematics spread themselves before the mind like a landscape, inviting journeys - but I think that just shows how minds cope with abstractions.
Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M]
     Full Idea: Gödel's incompleteness results of 1931 show that all axiom systems precise enough to satisfy Hilbert's conception are necessarily incomplete.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Michael Hallett - Introduction to Zermelo's 1930 paper p.1215
     A reaction: [Hallett italicises 'necessarily'] Hilbert axioms have to be recursive - that is, everything in the system must track back to them.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
     Full Idea: Gödel proved the classical relative consistency of the axiom V = L (which implies the axiom of choice and the generalized continuum hypothesis). This established the full independence of the continuum hypothesis from the other axioms.
     From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Hilary Putnam - Mathematics without Foundations
     A reaction: Gödel initially wanted to make V = L an axiom, but the changed his mind. Maddy has lots to say on the subject.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
     Full Idea: In the superior realist and simple theory of types, the place of the axiom of reducibility is not taken by the axiom of classes, Zermelo's Aussonderungsaxiom.
     From: report of Kurt Gödel (Russell's Mathematical Logic [1944], p.140-1) by Bernard Linsky - Russell's Metaphysical Logic 6.1 n3
     A reaction: This is Zermelo's Axiom of Separation, but that too is not an axiom of standard ZFC.
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett]
     Full Idea: Gödel proved the completeness of standard formalizations of first-order logic, including Frege's original one. However, an implication of his famous theorem on the incompleteness of arithmetic is that second-order logic is incomplete.
     From: report of Kurt Gödel (works [1930]) by Michael Dummett - The Philosophy of Mathematics 3.1
     A reaction: This must mean that it is impossible to characterise arithmetic fully in terms of first-order logic. In which case we can only characterize the features of abstract reality in general if we employ an incomplete system. We're doomed.
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
     Full Idea: 'Mathematical Logic' is a precise and complete formulation of formal logic, and is both a section of mathematics covering classes, relations, symbols etc, and also a science prior to all others, with ideas and principles underlying all sciences.
     From: Kurt Gödel (Russell's Mathematical Logic [1944], p.447)
     A reaction: He cites Leibniz as the ancestor. In this database it is referred to as 'theory of logic', as 'mathematical' seems to be simply misleading. The principles of the subject are standardly applied to mathematical themes.
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
Part of the sense of a proper name is a criterion of the thing's identity [Hawley]
     Full Idea: A Fregean dictum is that part of the sense of proper name is a criterion of identity for the thing in question.
     From: Katherine Hawley (How Things Persist [2001], 3.8)
     A reaction: [She quotes Dummett 1981:545] We are asked to choose between this and the Kripke rigid/dubbing/causal account, with effectively no content.
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Reference to a totality need not refer to a conjunction of all its elements [Gödel]
     Full Idea: One may, on good grounds, deny that reference to a totality necessarily implies reference to all single elements of it or, in other words, that 'all' means the same as an infinite logical conjunction.
     From: Kurt Gödel (Russell's Mathematical Logic [1944], p.455)
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel]
     Full Idea: At that time (c.1930) a concept of objective mathematical truth as opposed to demonstrability was viewed with greatest suspicion and widely rejected as meaningless.
     From: Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 28.2
     A reaction: [quoted from a letter] This is the time of Ramsey's redundancy account, and before Tarski's famous paper of 1933. It is also the high point of Formalism, associated with Hilbert.
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner]
     Full Idea: The inherent limitations of the axiomatic method were first brought to light by the incompleteness theorems.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Koellner - On the Question of Absolute Undecidability 1.1
5. Theory of Logic / K. Features of Logics / 2. Consistency
Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P]
     Full Idea: Second Incompleteness Theorem: roughly, nice theories that include enough basic arithmetic can't prove their own consistency.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 1.5
     A reaction: On the face of it, this sounds less surprising than the First Theorem. Philosophers have often noticed that it seems unlikely that you could use reason to prove reason, as when Descartes just relies on 'clear and distinct ideas'.
5. Theory of Logic / K. Features of Logics / 3. Soundness
If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh]
     Full Idea: Gödel showed PA cannot be proved consistent from with PA. But 'reflection principles' can be added, which are axioms partially expressing the soundness of PA, by asserting what is provable. A Global Reflection Principle asserts full soundness.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Halbach,V/Leigh,G.E. - Axiomatic Theories of Truth (2013 ver) 1.2
     A reaction: The authors point out that this needs a truth predicate within the language, so disquotational truth won't do, and there is a motivation for an axiomatic theory of truth.
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner]
     Full Idea: Gödel was quick to point out that his original incompleteness theorems did not produce instances of absolute undecidability and hence did not undermine Hilbert's conviction that for every precise mathematical question there is a discoverable answer.
     From: report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro
     A reaction: The normal simplistic view among philosophes is that Gödel did indeed decisively refute the optimistic claims of Hilbert. Roughly, whether Hilbert is right depends on which axioms of set theory you adopt.
Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel]
     Full Idea: Where Gödel's First Theorem sabotages logicist ambitions, the Second Theorem sabotages Hilbert's Programme.
     From: comment on Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 36
     A reaction: Neo-logicism (Crispin Wright etc.) has a strategy for evading the First Theorem.
The undecidable sentence can be decided at a 'higher' level in the system [Gödel]
     Full Idea: My undecidable arithmetical sentence ...is not at all absolutely undecidable; rather, one can always pass to 'higher' systems in which the sentence in question is decidable.
     From: Kurt Gödel (On Formally Undecidable Propositions [1931]), quoted by Peter Koellner - On the Question of Absolute Undecidability 1.1
     A reaction: [a 1931 MS] He says the reals are 'higher' than the naturals, and the axioms of set theory are higher still. The addition of a truth predicate is part of what makes the sentence become decidable.
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A logical system needs a syntactical survey of all possible expressions [Gödel]
     Full Idea: In order to be sure that new expression can be translated into expressions not containing them, it is necessary to have a survey of all possible expressions, and this can be furnished only by syntactical considerations.
     From: Kurt Gödel (Russell's Mathematical Logic [1944], p.448)
     A reaction: [compressed]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
Set-theory paradoxes are no worse than sense deception in physics [Gödel]
     Full Idea: The set-theoretical paradoxes are hardly any more troublesome for mathematics than deceptions of the senses are for physics.
     From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.271), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 03.4
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman]
     Full Idea: Gödel's far-reaching work on the nature of logic and formal systems reveals that there can be no single consistent theory from which all mathematical truths can be derived.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.8
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
     Full Idea: The generalized Continuum Hypothesis says that there exists no cardinal number between the power of any arbitrary set and the power of the set of its subsets.
     From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464)
The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
     Full Idea: Gödel proved that the Continuum Hypothesis was not inconsistent with the axioms of set theory.
     From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15
If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
     Full Idea: Gödel proved that (if set theory is consistent) we cannot refute the continuum hypothesis, and Cohen proved that (if set theory is consistent) we cannot prove it either.
     From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by William D. Hart - The Evolution of Logic 10
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner]
     Full Idea: Eventually Gödel ...expressed the hope that there might be a generalised completeness theorem according to which there are no absolutely undecidable sentences.
     From: report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro
     A reaction: This comes as a bit of a shock to those who associate him with the inherent undecidability of reality.
The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel]
     Full Idea: The concept of truth of sentences in a language cannot be defined in the language. This is the true reason for the existence of undecidable propositions in the formal systems containing arithmetic.
     From: Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 21.6
     A reaction: [from a letter by Gödel] So they key to Incompleteness is Tarski's observations about truth. Highly significant, as I take it.
Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey]
     Full Idea: Gödel's theorem states that either arithmetic is incomplete, or it is inconsistent.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Georges Rey - Contemporary Philosophy of Mind 8.7
First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P]
     Full Idea: First Incompleteness Theorem: any properly axiomatised and consistent theory of basic arithmetic must remain incomplete, whatever our efforts to complete it by throwing further axioms into the mix.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 1.2
     A reaction: This is because it is always possible to formulate a well-formed sentence which is not provable within the theory.
Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman]
     Full Idea: The vast continent of arithmetical truth cannot be brought into systematic order by laying down a fixed set of axioms and rules of inference from which every true mathematical statement can be formally derived. For some this was a shocking revelation.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by E Nagel / JR Newman - Gödel's Proof VII.C
     A reaction: Good news for philosophy, I'd say. The truth cannot be worked out by mechanical procedures, so it needs the subtle and intuitive intelligence of your proper philosopher (Parmenides is the role model) to actually understand reality.
Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna]
     Full Idea: Gödel's Second Incompleteness Theorem says that true unprovable sentences are clearly semantic consequences of the axioms in the sense that they are necessarily true if the axioms are true. So semantic consequence outruns provability.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Robert Hanna - Rationality and Logic 5.3
First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman]
     Full Idea: First Incompleteness Theorem: If S is a sufficiently powerful formal system, then if S is consistent then S is syntactically incomplete.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6
     A reaction: Gödel found a single sentence, effectively saying 'I am unprovable in S', which is neither provable nor refutable in S.
Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman]
     Full Idea: Second Incompleteness Theorem: If S is a sufficiently powerful formal system, then if S is consistent then S cannot prove its own consistency
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6
     A reaction: This seems much less surprising than the First Theorem (though it derives from it). It was always kind of obvious that you couldn't use reason to prove that reason works (see, for example, the Cartesian Circle).
There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P]
     Full Idea: The original Gödel construction gives us a sentence that a theory shows is true if and only if it satisfies the condition of being unprovable-in-that-theory.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 20.5
'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg]
     Full Idea: An approximation of Gödel's Theorem imagines a statement 'This system of mathematics can't prove this statement true'. If the system proves the statement, then it can't prove it. If the statement can't prove the statement, clearly it still can't prove it.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15
     A reaction: Gödel's contribution to this simple idea seems to be a demonstration that formal arithmetic is capable of expressing such a statement.
Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
     Full Idea: It has turned out that the solution of certain arithmetical problems requires the use of assumptions essentially transcending arithmetic.
     From: Kurt Gödel (Russell's Mathematical Logic [1944], p.449)
     A reaction: A nice statement of the famous result, from the great man himself, in the plainest possible English.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Mathematical objects are as essential as physical objects are for perception [Gödel]
     Full Idea: Classes and concepts may be conceived of as real objects, ..and are as necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions, with neither case being about 'data'.
     From: Kurt Gödel (Russell's Mathematical Logic [1944], p.456)
     A reaction: Note that while he thinks real objects are essential for mathematics, be may not be claiming the same thing for our knowledge of logic. If logic contains no objects, then how could mathematics be reduced to it, as in logicism?
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
     Full Idea: Evidently the 'given' underlying mathematics is closely related to the abstract elements contained in our empirical ideas.
     From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], Suppl)
     A reaction: Yes! The great modern mathematical platonist says something with which I can agree. He goes on to hint at a platonic view of the structure of the empirical world, but we'll let that pass.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Impredicative definitions are admitted into ordinary mathematics [Gödel]
     Full Idea: Impredicative definitions are admitted into ordinary mathematics.
     From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464)
     A reaction: The issue is at what point in building an account of the foundations of mathematics (if there be such, see Putnam) these impure definitions should be ruled out.
Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro]
     Full Idea: Gödel defended impredicative definitions on grounds of ontological realism. From that perspective, an impredicative definition is a description of an existing entity with reference to other existing entities.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Stewart Shapiro - Thinking About Mathematics 5.3
     A reaction: This is why constructivists must be absolutely precise about definition, where realists only have to do their best. Compare building a car with painting a landscape.
7. Existence / C. Structure of Existence / 5. Supervenience / d. Humean supervenience
A homogeneous rotating disc should be undetectable according to Humean supervenience [Hawley]
     Full Idea: Imagine a perfectly homogeneous non-atomistic disc. A record of all the non-relational information about the world at that moment will not reveal whether the disc is rotating about a vertical axis through. This tells against Humean supervenience.
     From: Katherine Hawley (How Things Persist [2001], 3.2)
     A reaction: [Armstrong 1980 originated this, and it is famously discussed by Kripke in lectures] There will, of course, be dispositions present because of the rotation, but Lewis excludes any such modal truths.
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
Non-linguistic things cannot be indeterminate, because they don't have truth-values at all [Hawley]
     Full Idea: Non-linguistic objects, properties, and states of affairs cannot be indeterminate because they cannot have determinate truth-values either. No cloud is indeterminate, just as no cloud is either determinately true or determinately false.
     From: Katherine Hawley (How Things Persist [2001], 4.1)
     A reaction: If vagueness must be linguistic, this means animals can never experience it, which I doubt. Presumably 'this is a cloud' is only made vague by the vagueness of the object, rather than by the vagueness of the sentence?
Maybe for the world to be vague, it must be vague in its foundations? [Hawley]
     Full Idea: There is a question of whether there must be 'vagueness all the way down' for the world to be vague. One view is that if there is a base level of precisely describably facts, upon which all the others supervene, then the world is not really vague.
     From: Katherine Hawley (How Things Persist [2001], 4.5)
     A reaction: My understanding of the physics is that it is non-vague all the way down, and then you get to the base level which is hopelessly vague!
7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
Epistemic vagueness seems right in the case of persons [Hawley]
     Full Idea: The epistemic account of vagueness is particularly attractive where persons are concerned.
     From: Katherine Hawley (How Things Persist [2001], 4.14)
     A reaction: You'll have to see her text for details. Interesting that there might be different views of what vagueness is for different cases. Or putting it another way, absolutely everything (said, thought, existing or done) might be vague in some way!
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
Supervaluation refers to one vaguely specified thing, through satisfaction by everything in some range [Hawley]
     Full Idea: Supervaluationists take a present-tense predication as concerning a single, but vaguely specified, moment. …It is indeterminate which of a range of moments enters into the truth conditions, but it is true if satisfied by every member of the range.
     From: Katherine Hawley (How Things Persist [2001], 2.7)
     A reaction: She is discussing stage theory, but this is a helpful clarification of the idea of supervaluation. Something can be satisfied by a whole bunch of values, even though you are not sure which one.
Supervaluationism takes what the truth-value would have been if indecision was resolved [Hawley]
     Full Idea: A supervaluationist approach involves consideration of what the truth value of the utterance would have been if semantic indecision had been resolved in this way or that.
     From: Katherine Hawley (How Things Persist [2001], 4.1)
     A reaction: At last, a lovely account of supervaluation in plain English that anyone can understand! Why don't they all do that? Well, done Katherine Hawley! ['semantic indecision' is uncertainty about what your words mean!]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Maybe the only properties are basic ones like charge, mass and spin [Hawley]
     Full Idea: Some philosophers suspect that properties are few and far between, that there are only properties like charge, mass, spin, and so on.
     From: Katherine Hawley (How Things Persist [2001], 5.1)
     A reaction: I think properties are very sparse, and mainly consist of physical powers, but I am not sure what I think of this. It may be 'mere semantics'. Complex properties still seem to be properties. Powers combine to make properties, I suggest.
9. Objects / A. Existence of Objects / 1. Physical Objects
An object is 'natural' if its stages are linked by certain non-supervenient relations [Hawley]
     Full Idea: I suggest that our distinction between natural and unnatural (gerrymandered) objects corresponds to a distinction between series of stages which are and are not linked by certain non-supervenient relations.
     From: Katherine Hawley (How Things Persist [2001], 5.5)
     A reaction: See Idea 16213 for the nature of these 'relations'. I don't understand how an abstraction (as I take it) like a relation can unify a physical object. A trout-turkey is unified by a relation of some sort. Hawley defends Stage Theory.
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
Are sortals spatially maximal - so no cat part is allowed to be a cat? [Hawley]
     Full Idea: Many philosophers believe that sortal predicates are spatially maximal - for example, that no cat can be a proper spatial part of a cat.
     From: Katherine Hawley (How Things Persist [2001], 2.1)
     A reaction: This sounds reasonable until you cut the tail off a cat. Presumably what remains is a cat? So presumably that smaller part was always a cat? Only essentialism can make sense of this! You can't just invent rules for sortals.
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
The modal features of statue and lump are disputed; when does it stop being that statue? [Hawley]
     Full Idea: It is difficult to establish a consensus about the modal features of the statue and the lump. Could that statue be made of a different lump? Could that statue of Goliath have been spherical? Not a realistic statue of Goliath, but still the same statue?
     From: Katherine Hawley (How Things Persist [2001], 6)
     A reaction: The problem is with a wild wacky sculptor, who might say it is a statue of Goliath no matter what shape the lump takes. 'Goliath had a spherical character'. Sometimes we will say (pace Evans) it is 'roughly identical' to the original statue.
Perdurantists can adopt counterpart theory, to explain modal differences of identical part-sums [Hawley]
     Full Idea: Perdurance theory claims that lumps and statues differ modally whilst always being made of the same parts. A natural way to make this less mysterious is for perdurantists to adopt counterpart theory, where objects in different worlds are never identical.
     From: Katherine Hawley (How Things Persist [2001], 6.2)
     A reaction: This, of course, is exactly the system created by David Lewis. Personally I rather like counterparts, but perdurance seems a tad crazy.
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Vagueness is either in our knowledge, in our talk, or in reality [Hawley]
     Full Idea: There are three main views of vagueness: the Epistemic view says we talk precisely, but don't know what we talk precisely about; the Semantic view is that it is loose talk, or semantic indecision; the Ontic view says it is part of how the world is.
     From: Katherine Hawley (How Things Persist [2001], 4.1)
     A reaction: [My summary of two paragraphs] She associates Williamson with the first view, Lewis with the second, and Van Inwagen with the third.
Indeterminacy in objects and in properties are not distinct cases [Hawley]
     Full Idea: There is no important distinction to be drawn between cases where indeterminacy is due to the object involved and cases where indeterminacy is due to the property involved.
     From: Katherine Hawley (How Things Persist [2001], 4.2)
     A reaction: You could always paraphrase the object's situation propertywise, or the property's situation objectwise. 'His baldness is indeterminate'; 'where does the mountainous terrain end?'
9. Objects / C. Structure of Objects / 6. Constitution of an Object
The constitution theory is endurantism plus more than one object in a place [Hawley]
     Full Idea: Constitution theorists are endurance theorists who believe that there can be more than one object exactly occupying a spatial region at a certain moment.
     From: Katherine Hawley (How Things Persist [2001], 5.1)
     A reaction: I increasingly think that this is a ridiculous view. The constitution of an object isn't a further object. A constitution is a necessary requirement for a physical object. Hylomorphism! Constitutions can't be separate - they must constitute something!
Constitution theory needs sortal properties like 'being a sweater' to distinguish it from its thread [Hawley]
     Full Idea: Constitution theorists need to posit sortal properties of 'being a thread' or 'being a sweater', as grounds for the differences betwween the sweater and the thread that constitutes it.
     From: Katherine Hawley (How Things Persist [2001], 5.1)
     A reaction: This is further grounds for thinking the constitution view ridiculous, because there are no such properties. 'Being a sweater' is a category, which something belongs in if it has all the properties of a sweater. The final property triggers sweaterhood.
If the constitution view says thread and sweater are two things, why do we talk of one thing? [Hawley]
     Full Idea: The constitution theorists, who claim that the sweater and the thread are different things, should offer some explanation of why we tend to say that there is just one thing there. They must simply claim that we 'do not count by identity'.
     From: Katherine Hawley (How Things Persist [2001], 5.8)
     A reaction: Her example is a sweater knitted from a single piece of thread. Presumably we could count by sortal identity, so there is one thread here, and there is one sweater here. We just can't add the two together. No ontological arithmetic.
9. Objects / E. Objects over Time / 2. Objects that Change
'Adverbialism' explains change by saying an object has-at-some-time a given property [Hawley]
     Full Idea: Another strategy for the problem of change says that instantiation - the having of properties - is time-indexed, or relative to times, although properties themselves are not. This 'adverbialism' says that object has-at-t some property.
     From: Katherine Hawley (How Things Persist [2001], 1.5)
     A reaction: [She cites Johnson, Lowe and Haslanger for this] Promising. The question is whether the time index is attached to the object, to the property, or to the instantiation. The middle one is wrong. There aren't two properties - green-at-t1 and green-at-t2.
Presentism solves the change problem: the green banana ceases, so can't 'relate' to the yellow one [Hawley]
     Full Idea: Adopting presentism solves the problem of change, since it means that, once the banana is yellow, there just is no green banana, and the question of the relationship between yesterday's green banana and today's yellow one therefore does not arise.
     From: Katherine Hawley (How Things Persist [2001], 1.7)
     A reaction: Change remains kind of odd, but it is no longer the puzzlement of two things being the same when they are admitted to be different. There is only ever one thing. This is my preferred account, I think. I certainly hope past bananas don't exist.
The problem of change arises if there must be 'identity' of a thing over time [Hawley]
     Full Idea: It is the insistence on identity between objects wholly present at different times which gives rise to the problem of change.
     From: Katherine Hawley (How Things Persist [2001], 2.2)
     A reaction: My solution is to say things are the 'same', in a slightly loose non-transitive way, rather than formally identical, which is a concept from maths, not from reality.
9. Objects / E. Objects over Time / 3. Three-Dimensionalism
Endurance theory can relate properties to times, or timed instantiations to properties [Hawley]
     Full Idea: Endurance theory might claim a banana stands (atemporally) in different relations to different times (being-green-at to Monday), ..or has different instantiation relations to different properties (instantiates-on-Monday to being green).
     From: Katherine Hawley (How Things Persist [2001], 1.3)
     A reaction: She suggests that the first approach is more plausible for endurantists. I think she is right (assuming these are the only two options). Monday awaits a banana, but yellow doesn't.
Endurance is a sophisticated theory, covering properties, instantiation and time [Hawley]
     Full Idea: Endurance theory is not just a default 'no-theory' theory, for it must incorporate a sophisticated account of properties and instantiation, and requires a certain view of time if it is even to be formulable.
     From: Katherine Hawley (How Things Persist [2001], 1.8)
     A reaction: A bit odd to claim it is a sophisticated theory when it is held (at least in our culture) by absolutely everyone apart from a few philosophers and physicists. The sophistication may come with trying to describe it using current metaphysical vocabulary.
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
How does perdurance theory explain our concern for our own future selves? [Hawley]
     Full Idea: A question for perdurance theory is whether it can account for the special concern we feel for our own future selves.
     From: Katherine Hawley (How Things Persist [2001], 1.8)
     A reaction: That is one of those questions that begins to look very mysterious whatever your theory. I favour endurantism, but me next year looks a very remote person for me to be concerned about, in comparison with the people around me now.
Perdurance needs an atemporal perspective, to say that the object 'has' different temporal parts [Hawley]
     Full Idea: Perdurance relies on our having an 'atemporal' perspective from which we can truly say a banana has both yellow and green parts, where this 'has' is not in the present tense. ..Perdurance theory cannot be expressed straightforwardly in the present tense.
     From: Katherine Hawley (How Things Persist [2001], 1.2)
     A reaction: This seems to require the tenseless B-series view of time. It seems to need a tenseless view of the past, but what does it have to say about the future?
If an object is the sum of all of its temporal parts, its mass is staggeringly large! [Hawley]
     Full Idea: The mass of an object is the sum of its nonoverlapping parts. Analogy would suggest that a persisting banana has, atemporally speaking, a mass that is the sum of all the masses of the 100g temporal parts, a worryingly large figure.
     From: Katherine Hawley (How Things Persist [2001], 2.1)
     A reaction: This is an objection to the Perdurance view that an object is the sum of all of its temporal parts. Their duration tends towards instantaneous, so the aggregate mass tends towards infinity. She says they should deny atemporal mass.
Perdurance says things are sums of stages; Stage Theory says each stage is the thing [Hawley]
     Full Idea: According to Perdurance Theory, it is long-lived sums of stages which are tennis balls, whereas according to Stage Theory, it is the stages themselves which are tennis balls.
     From: Katherine Hawley (How Things Persist [2001], 2.2)
     A reaction: These seem to be the two options if you are a four-dimensionalist, though Fine says you could be a weird three-dimensionalist and choose stage theory.
If a life is essentially the sum of its temporal parts, it couldn't be shorter or longer than it was? [Hawley]
     Full Idea: It seems that perdurance theory should identify Descartes with the sum of his temporal parts, but that means Descartes essentially lived for 54 years, which seems absurd, as he could have lived longer or less long than he in fact did.
     From: Katherine Hawley (How Things Persist [2001], 6.10)
     A reaction: [She credits Van Inwagen with this] I'm not clear why a counterpart of Descartes could not have a shorter or longer sum of parts, and still be Descartes. If the sum is rigidly designated, that is a problem for endurance too.
9. Objects / E. Objects over Time / 5. Temporal Parts
Stage Theory seems to miss out the link between stages of the same object [Hawley]
     Full Idea: The first worry for Stage Theory is that many present stages are bananas, and many stages tomorrow are bananas, but this seems to omit the important fact that some of those stages are intimately linked, that certain stages are the same banana.
     From: Katherine Hawley (How Things Persist [2001], 2.3)
     A reaction: Hawley has a theory to do with external relations, which I didn't find very persuasive. Just to say stages have a 'relation' seems too abstract. Stages of disparate things can also have 'relations', but presumably the wrong sort.
Stage Theory says every stage is a distinct object, which gives too many objects [Hawley]
     Full Idea: The second worry for Stage Theory is that there are far too many bananas in the world on this account.
     From: Katherine Hawley (How Things Persist [2001], 2.3)
     A reaction: The point is that each (instantaneous) stage is considered to be a whole banana (as opposed to one sum of all the stages of the banana, in the Perdurance view). A pretty serious problem, which she tries to deal with.
An isolated stage can't be a banana (which involves suitable relations to other stages) [Hawley]
     Full Idea: A single isolated stage could not be a banana, because in order to be a banana a stage must be suitably related to other stages with appropriate properties.
     From: Katherine Hawley (How Things Persist [2001], 3.4.1)
     A reaction: This seems at odds with the claim that each stage is the whole thing (rather than the long temporal 'worm' of perdurance theory). Isolated stages are instantaneous, so can't be anything, really. Her 'relations' seem hand-wavy to me. Connections?
Stages of one thing are related by extrinsic counterfactual and causal relations [Hawley]
     Full Idea: I claim that there are relations between the distinct stages of a persisting object which are not determined by the intrinsic properties of those stages. …The later stages depend, counterfactually and causally, upon the earlier stages.
     From: Katherine Hawley (How Things Persist [2001], 3.5)
     A reaction: This is the heart of her theory. How can there be a causal link between two stages which is not the result of intrinsic properties of the stages? This begins to sound like Malebranche's Occasionalism.
The stages of Stage Theory seem too thin to populate the world, or to be referred to [Hawley]
     Full Idea: A third worry for Stage Theory is that the momentary stages themselves are just too thin to populate the world, and too thin to be the objects of reference.
     From: Katherine Hawley (How Things Persist [2001], 2.3)
     A reaction: Her three objections to her own theory add up to sufficient to refute it, in my view, though a large chunk of her book is spent trying to refute the objections.
Stages must be as fine-grained in length as change itself, so any change is a new stage [Hawley]
     Full Idea: To account for change, stages and temporal parts must be as fine-grained as change: a material thing must have as many stages or parts as it is in incompatible states during its lifetime.
     From: Katherine Hawley (How Things Persist [2001], 2.4)
     A reaction: There seems to be a dilemma for stages here, of being so fat that they are divisible and change, or so thin that they barely exist. Lose-lose, I'd say.
9. Objects / F. Identity among Objects / 8. Leibniz's Law
If two things might be identical, there can't be something true of one and false of the other [Hawley]
     Full Idea: We can call the 'transference principle' the claim that if it is indeterminate whether two objects are identical, then nothing determinately true of one can be determinately false of the other.
     From: Katherine Hawley (How Things Persist [2001], 4.9)
     A reaction: The point is that Leibniz's Law could immediately be invoked to show there is no possibility of their identity.
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
To decide whether something is a counterpart, we need to specify a relevant sortal concept [Hawley]
     Full Idea: When asked whether a possible object is a counterpart of something, we need to specify which sortal we are interested in.
     From: Katherine Hawley (How Things Persist [2001], 6.2)
     A reaction: The compares this to the 'respect' in which two things are similar. For example, what would count as a counterpart of the current British Prime Minister? De re or de dicto reference?
16. Persons / D. Continuity of the Self / 5. Concerns of the Self
On any theory of self, it is hard to explain why we should care about our future selves [Hawley]
     Full Idea: It is rather difficult to say why one should care about one's future self, even on an endurance theory account of the self.
     From: Katherine Hawley (How Things Persist [2001], 3.9)
     A reaction: A nice passing remark, that strikes me forcibly as one of those basic mysteries of experience that philosophers can only gawp at, and have no theory to offer.
17. Mind and Body / C. Functionalism / 2. Machine Functionalism
Basic logic can be done by syntax, with no semantics [Gödel, by Rey]
     Full Idea: Gödel in his completeness theorem for first-order logic showed that a certain set of syntactically specifiable rules was adequate to capture all first-order valid arguments. No semantics (e.g. reference, truth, validity) was necessary.
     From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Georges Rey - Contemporary Philosophy of Mind 8.2
     A reaction: This implies that a logic machine is possible, but we shouldn't raise our hopes for proper rationality. Validity can be shown for purely algebraic arguments, but rationality requires truth as well as validity, and that needs propositions and semantics.
25. Social Practice / F. Life Issues / 1. Causing Death
Human killing is worse if the victim is virtuous [Buddhaghosa]
     Full Idea: In the case of humans killing is the more blameworthy the more virtuous the victim is.
     From: Buddhaghosa (Papancasudani [c.400], 9.7-10)
     A reaction: This sentiment has almost become a taboo in western society, and yet it is present all the time. The greatest outcry is about murders of really good citizens. Occasionally the murder of a villain causes little regret.
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
Causation is nothing more than the counterfactuals it grounds? [Hawley]
     Full Idea: Counterfactual accounts of causation say that a causal connection is exhausted by the counterfactuals it appears to ground.
     From: Katherine Hawley (How Things Persist [2001], 3.5)
     A reaction: I am bewildered as to how this became a respectable view in philosophy. I quite understand that this might exhaust the 'logic' of causal relations. Presumably you can have counterfactuals in mathematics which are not causal?
27. Natural Reality / D. Time / 3. Parts of Time / b. Instants
Time could be discrete (like integers) or dense (rationals) or continuous (reals) [Hawley]
     Full Idea: There seem to be three possible ways for time to be fine-grained. The ordering of instants could be discrete (like the integers), dense (like the rational numbers) or continuous (like the real numbers).
     From: Katherine Hawley (How Things Persist [2001], 2.5)
     A reaction: She seems to assume that time must be 'grained', but I would take the continuous view to imply that there is no grain at all (which is bad news for her version of stage theory).