87 ideas
| 15801 | Many philosophers aim to understand metaphysics by studying ourselves [Chisholm] |
| Full Idea: Leibniz, Reid, Brentano and others have held that, by considering certain obvious facts about ourselves, we can arrive at an understanding of the general principles of metaphysics. The present book is intended to confirm that view. | |
| From: Roderick Chisholm (Person and Object [1976], Intro 1) | |
| A reaction: I sympathise, but don't really agree. I see metaphysics as a process of filtering ourselves out of the picture, leaving an account of how things actually are. |
| 15802 | I use variables to show that each item remains the same entity throughout [Chisholm] |
| Full Idea: My use of variables is not merely pedantic; it indicates that the various items on our list pertain to one and the same entity throughout. | |
| From: Roderick Chisholm (Person and Object [1976], Intro 2) | |
| A reaction: I am one of those poor souls who finds modern analytic philosophy challenging simply because I think in terms of old fashioned words, instead of thinking like mathematicians and logicians. This is a nice defence of their approach. |
| 9955 | Contextual definitions replace a complete sentence containing the expression [George/Velleman] |
| Full Idea: A contextual definition shows how to analyse an expression in situ, by replacing a complete sentence (of a particular form) in which the expression occurs by another in which it does not. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: This is a controversial procedure, which (according to Dummett) Frege originally accepted, and later rejected. It might not be the perfect definition that replacing just the expression would give you, but it is a promising step. |
| 10031 | Impredicative definitions quantify over the thing being defined [George/Velleman] |
| Full Idea: When a definition contains a quantifier whose range includes the very entity being defined, the definition is said to be 'impredicative'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: Presumably they are 'impredicative' because they do not predicate a new quality in the definiens, but make use of the qualities already known. |
| 10098 | The 'power set' of A is all the subsets of A [George/Velleman] |
| Full Idea: The 'power set' of A is all the subsets of A. P(A) = {B : B ⊆ A}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10099 | The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}} [George/Velleman] |
| Full Idea: The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}}. The existence of this set is guaranteed by three applications of the Axiom of Pairing. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: See Idea 10100 for the Axiom of Pairing. |
| 10101 |
Cartesian Product A x B: the set of all ordered pairs |
| Full Idea: The 'Cartesian Product' of any two sets A and B is the set of all ordered pairs <a, b> in which a ∈ A and b ∈ B, and it is denoted as A x B. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10103 | Grouping by property is common in mathematics, usually using equivalence [George/Velleman] |
| Full Idea: The idea of grouping together objects that share some property is a common one in mathematics, ...and the technique most often involves the use of equivalence relations. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10104 | 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman] |
| Full Idea: A relation is an equivalence relation if it is reflexive, symmetric and transitive. The 'same first letter' is an equivalence relation on the set of English words. Any relation that puts a partition into clusters will be equivalence - and vice versa. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This is a key concept in the Fregean strategy for defining numbers. |
| 10096 | Even the elements of sets in ZFC are sets, resting on the pure empty set [George/Velleman] |
| Full Idea: ZFC is a theory concerned only with sets. Even the elements of all of the sets studied in ZFC are also sets (whose elements are also sets, and so on). This rests on one clearly pure set, the empty set Φ. ..Mathematics only needs pure sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This makes ZFC a much more metaphysically comfortable way to think about sets, because it can be viewed entirely formally. It is rather hard to disentangle a chair from the singleton set of that chair. |
| 10097 | Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y [George/Velleman] |
| Full Idea: The Axiom of Extensionality says that for all sets x and y, if x and y have the same elements then x = y. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This seems fine in pure set theory, but hits the problem of renates and cordates in the real world. The elements coincide, but the axiom can't tell you why they coincide. |
| 10100 | Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman] |
| Full Idea: The Axiom of Pairing says that for all sets x and y, there is a set z containing x and y, and nothing else. In symbols: ∀x∀y∃z∀w(w ∈ z ↔ (w = x ∨ w = y)). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: See Idea 10099 for an application of this axiom. |
| 17900 | The Axiom of Reducibility made impredicative definitions possible [George/Velleman] |
| Full Idea: The Axiom of Reducibility ...had the effect of making impredicative definitions possible. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10109 | ZFC can prove that there is no set corresponding to the concept 'set' [George/Velleman] |
| Full Idea: Sets, unlike extensions, fail to correspond to all concepts. We can prove in ZFC that there is no set corresponding to the concept 'set' - that is, there is no set of all sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: This is rather an important point for Frege. However, all concepts have extensions, but they may be proper classes, rather than precisely defined sets. |
| 10108 | As a reduction of arithmetic, set theory is not fully general, and so not logical [George/Velleman] |
| Full Idea: The problem with reducing arithmetic to ZFC is not that this theory is inconsistent (as far as we know it is not), but rather that is not completely general, and for this reason not logical. For example, it asserts the existence of sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: Note that ZFC has not been proved consistent. |
| 10111 | Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman] |
| Full Idea: A hallmark of our realist stance towards the natural world is that we are prepared to assert the Law of Excluded Middle for all statements about it. For all statements S, either S is true, or not-S is true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: Personally I firmly subscribe to realism, so I suppose I must subscribe to Excluded Middle. ...Provided the statement is properly formulated. Or does liking excluded middle lead me to realism? |
| 10129 | A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman] |
| Full Idea: A 'model' of a theory is an assignment of meanings to the symbols of its language which makes all of its axioms come out true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: If the axioms are all true, and the theory is sound, then all of the theorems will also come out true. |
| 10105 | Differences between isomorphic structures seem unimportant [George/Velleman] |
| Full Idea: Mathematicians tend to regard the differences between isomorphic mathematical structures as unimportant. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This seems to be a pointer towards Structuralism as the underlying story in mathematics. The intrinsic character of so-called 'objects' seems unimportant. How theories map onto one another (and onto the world?) is all that matters? |
| 10119 | Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman] |
| Full Idea: Consistency is a purely syntactic property, unlike the semantic property of soundness. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10126 | A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman] |
| Full Idea: If there is a sentence such that both the sentence and its negation are theorems of a theory, then the theory is 'inconsistent'. Otherwise it is 'consistent'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
| 10120 | Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman] |
| Full Idea: Soundness is a semantic property, unlike the purely syntactic property of consistency. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10127 | A 'complete' theory contains either any sentence or its negation [George/Velleman] |
| Full Idea: If there is a sentence such that neither the sentence nor its negation are theorems of a theory, then the theory is 'incomplete'. Otherwise it is 'complete'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: Interesting questions are raised about undecidable sentences, irrelevant sentences, unknown sentences.... |
| 10106 | Rational numbers give answers to division problems with integers [George/Velleman] |
| Full Idea: We can think of rational numbers as providing answers to division problems involving integers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Cf. Idea 10102. |
| 10102 | The integers are answers to subtraction problems involving natural numbers [George/Velleman] |
| Full Idea: In defining the integers in set theory, our definition will be motivated by thinking of the integers as answers to subtraction problems involving natural numbers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Typical of how all of the families of numbers came into existence; they are 'invented' so that we can have answers to problems, even if we can't interpret the answers. It it is money, we may say the minus-number is a 'debt', but is it? Cf Idea 10106. |
| 10107 | Real numbers provide answers to square root problems [George/Velleman] |
| Full Idea: One reason for introducing the real numbers is to provide answers to square root problems. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Presumably the other main reasons is to deal with problems of exact measurement. It is interesting that there seem to be two quite distinct reasons for introducing the reals. Cf. Ideas 10102 and 10106. |
| 9946 | Logicists say mathematics is applicable because it is totally general [George/Velleman] |
| Full Idea: The logicist idea is that if mathematics is logic, and logic is the most general of disciplines, one that applies to all rational thought regardless of its content, then it is not surprising that mathematics is widely applicable. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: Frege was keen to emphasise this. You are left wondering why pure logic is applicable to the physical world. The only account I can give is big-time Platonism, or Pythagoreanism. Logic reveals the engine-room of nature, where the design is done. |
| 10125 | The classical mathematician believes the real numbers form an actual set [George/Velleman] |
| Full Idea: Unlike the intuitionist, the classical mathematician believes in an actual set that contains all the real numbers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 17899 | Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman] |
| Full Idea: The first-order version of the induction axiom is weaker than the second-order, because the latter applies to all concepts, but the first-order applies only to concepts definable by a formula in the first-order language of number theory. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7 n7) |
| 10128 | The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman] |
| Full Idea: The idea behind the proofs of the Incompleteness Theorems is to use the language of Peano Arithmetic to talk about the formal system of Peano Arithmetic itself. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: The mechanism used is to assign a Gödel Number to every possible formula, so that all reasonings become instances of arithmetic. |
| 17902 | A successor is the union of a set with its singleton [George/Velleman] |
| Full Idea: For any set x, we define the 'successor' of x to be the set S(x) = x U {x}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This is the Fregean approach to successor, where the Dedekind approach takes 'successor' to be a primitive. Frege 1884:§76. |
| 10133 | Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman] |
| Full Idea: The derivability of Peano's Postulates from Hume's Principle in second-order logic has been dubbed 'Frege's Theorem', (though Frege would not have been interested, because he didn't think Hume's Principle gave an adequate definition of numebrs). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8 n1) | |
| A reaction: Frege said the numbers were the sets which were the extensions of the sets created by Hume's Principle. |
| 10130 | Set theory can prove the Peano Postulates [George/Velleman] |
| Full Idea: The Peano Postulates can be proven in ZFC. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
| 10089 | Talk of 'abstract entities' is more a label for the problem than a solution to it [George/Velleman] |
| Full Idea: One might well wonder whether talk of abstract entities is less a solution to the empiricist's problem of how a priori knowledge is possible than it is a label for the problem. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Intro) | |
| A reaction: This pinpoints my view nicely. What the platonist postulates is remote, bewildering, implausible and useless! |
| 10131 | If mathematics is not about particulars, observing particulars must be irrelevant [George/Velleman] |
| Full Idea: As, in the logicist view, mathematics is about nothing particular, it is little wonder that nothing in particular needs to be observed in order to acquire mathematical knowledge. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002]) | |
| A reaction: At the very least we can say that no one would have even dreamt of the general system of arithmetic is they hadn't had experience of the particulars. Frege thought generality ensured applicability, but extreme generality might entail irrelevance. |
| 10092 | In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc. [George/Velleman] |
| Full Idea: In the unramified theory of types, all objects are classified into a hierarchy of types. The lowest level has individual objects that are not sets. Next come sets whose elements are individuals, then sets of sets, etc. Variables are confined to types. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: The objects are Type 0, the basic sets Type 1, etc. |
| 10094 | The theory of types seems to rule out harmless sets as well as paradoxical ones. [George/Velleman] |
| Full Idea: The theory of types seems to rule out harmless sets as well as paradoxical ones. If a is an individual and b is a set of individuals, then in type theory we cannot talk about the set {a,b}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Since we cheerfully talk about 'Cicero and other Romans', this sounds like a rather disasterous weakness. |
| 10095 | Type theory has only finitely many items at each level, which is a problem for mathematics [George/Velleman] |
| Full Idea: A problem with type theory is that there are only finitely many individuals, and finitely many sets of individuals, and so on. The hierarchy may be infinite, but each level is finite. Mathematics required an axiom asserting infinitely many individuals. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Most accounts of mathematics founder when it comes to infinities. Perhaps we should just reject them? |
| 17901 | Type theory prohibits (oddly) a set containing an individual and a set of individuals [George/Velleman] |
| Full Idea: If a is an individual and b is a set of individuals, then in the theory of types we cannot talk about the set {a,b}, since it is not an individual or a set of individuals, ...but it is hard to see what harm can come from it. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10114 | Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman] |
| Full Idea: In the first instance all bounded quantifications are finitary, for they can be viewed as abbreviations for conjunctions and disjunctions. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) | |
| A reaction: This strikes me as quite good support for finitism. The origin of a concept gives a good guide to what it really means (not a popular view, I admit). When Aristotle started quantifying, I suspect of he thought of lists, not totalities. |
| 10134 | Much infinite mathematics can still be justified finitely [George/Velleman] |
| Full Idea: It is possible to use finitary reasoning to justify a significant part of infinitary mathematics. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8) | |
| A reaction: This might save Hilbert's project, by gradually accepting into the fold all the parts which have been giving a finitist justification. |
| 10123 | The intuitionists are the idealists of mathematics [George/Velleman] |
| Full Idea: The intuitionists are the idealists of mathematics. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10124 | Gödel's First Theorem suggests there are truths which are independent of proof [George/Velleman] |
| Full Idea: For intuitionists, truth is not independent of proof, but this independence is precisely what seems to be suggested by Gödel's First Incompleteness Theorem. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8) | |
| A reaction: Thus Gödel was worse news for the Intuitionists than he was for Hilbert's Programme. Gödel himself responded by becoming a platonist about his unprovable truths. |
| 15832 | Events are states of affairs that occur at certain places and times [Chisholm] |
| Full Idea: We will restrict events to those states of affairs which occur at certain places and times. | |
| From: Roderick Chisholm (Person and Object [1976], 4.6) | |
| A reaction: If I say 'the bomb may explode sometime', that doesn't seem to refer to an event. Philosophers like Chisholm bowl along, defining left, right and centre, and never seem to step back from their system and ask obvious critical questions. |
| 15829 | The mark of a state of affairs is that it is capable of being accepted [Chisholm] |
| Full Idea: We will say that the mark of a state of affairs is the fact that it is capable of being accepted. | |
| From: Roderick Chisholm (Person and Object [1976], 4.2) | |
| A reaction: I find this a quite bewildering proposal. It means that it is impossible for there to be a state of affairs which is beyond human conception, but why commit to that? |
| 15809 | A state of affairs pertains to a thing if it implies that it has some property [Chisholm] |
| Full Idea: A state of affairs pertains to a thing if it implies the thing to have a certain property. | |
| From: Roderick Chisholm (Person and Object [1976], 1.4) | |
| A reaction: For this to work, we must include extrinsic and relational properties, and properties which are derived from mere predication. I think this is bad metaphysics, and leads to endless confusions. |
| 15828 | I propose that events and propositions are two types of states of affairs [Chisholm] |
| Full Idea: I will propose that events are said to constitute one type of states of affairs, and propositions another | |
| From: Roderick Chisholm (Person and Object [1976], 4.1) | |
| A reaction: I would much prefer to distinguish between the static and the dynamic, so we have a static or timeless state of affairs, and a dynamic event or process. Propositions I take to be neither. He really means 'facts', which subsume the whole lot. |
| 13120 | Chisholm divides things into contingent and necessary, and then individuals, states and non-states [Chisholm, by Westerhoff] |
| Full Idea: Chisholm's Ontological Categories: ENTIA - {Contingent - [Individual - (Boundaries)(Substances)] [States - (Events)]} {Necessary - [States] [Non-States - (Attributes)(Substance)]} | |
| From: report of Roderick Chisholm (A Realistic Theory of Categories [1996], p.3) by Jan Westerhoff - Ontological Categories §01 | |
| A reaction: [I am attempting a textual representation of a tree diagram! The bracket-styles indicate the levels.] |
| 15827 | Some properties, such as 'being a widow', can be seen as 'rooted outside the time they are had' [Chisholm] |
| Full Idea: Some properties may be said to be 'rooted outside the times at which they are had'. Examples are the property of being a widow and the property of being a future President. | |
| From: Roderick Chisholm (Person and Object [1976], 3.4) | |
| A reaction: This is the sort of mess you when you treat the category in which an object belongs as if it was one of its properties. We categorise because of properties. |
| 15830 | Some properties can never be had, like being a round square [Chisholm] |
| Full Idea: There are properties which nothing can possibly have; an example is the property of being both round and square. | |
| From: Roderick Chisholm (Person and Object [1976], 4.2) | |
| A reaction: This is a rather bizarre Meinongian claim. For a start it sounds like two properties not one. Is there a property of being both 'over here' and 'over there'? We might say the round-square property must exist, for God to fail to implement it (?) |
| 15804 | If some dogs are brown, that entails the properties of 'being brown' and 'being canine' [Chisholm] |
| Full Idea: The state of affairs which is some dogs being brown may be said to entail (make it necessarily so) the property of 'being brown', as well as the properties of 'being canine' and 'being both brown and canine'. | |
| From: Roderick Chisholm (Person and Object [1976], 1.4) | |
| A reaction: And the property of 'being such that it is both brown and canine and brown or canine'. Etc. This is dangerous nonsense. Making all truths entail the existence of some property means we can no longer get to grips with real properties. |
| 15810 | Maybe we can only individuate things by relating them to ourselves [Chisholm] |
| Full Idea: It may well be that the only way we have, ultimately, of individuating anything is to relate it uniquely to ourselves. | |
| From: Roderick Chisholm (Person and Object [1976], 1.5) | |
| A reaction: I'm guessing that Chisholm is thinking of 'ourselves' as meaning just himself, but I'm thinking this is plausible if he means the human community. I doubt whether there is much a philosopher can say on individuation that is revealing or precise. |
| 15805 | Being the tallest man is an 'individual concept', but not a haecceity [Chisholm] |
| Full Idea: Being the tallest man and being President of the United States are 'individual concepts', but not haecceities. | |
| From: Roderick Chisholm (Person and Object [1976], 1.4) | |
| A reaction: Chisholm introduces this term, to help him explain his haecceity more clearly. (His proposal on that adds a lot of fog to this area of metaphysics). |
| 15807 | A haecceity is a property had necessarily, and strictly confined to one entity [Chisholm] |
| Full Idea: An individual essence or haecceity is a narrower type of individual concept. This is a property which is had necessarily, and which it is impossible for any other thing to have. | |
| From: Roderick Chisholm (Person and Object [1976], 1.4) | |
| A reaction: [Apologies to Chisholm for leaving out the variables from his definition of haecceity. See Idea 15802] See also Idea 15805. The tallest man is unique, but someone else could become the tallest man. No one else could acquire 'being Socrates'. |
| 15814 | A peach is sweet and fuzzy, but it doesn't 'have' those qualities [Chisholm] |
| Full Idea: Our idea of a peach is not an idea of something that 'has' those particular qualities, but the concrete thing that 'is' sweet and round and fuzzy. | |
| From: Roderick Chisholm (Person and Object [1976], 1.6) | |
| A reaction: This is the beginnings of his 'adverbial' account of properties, with which you have to sympathise. It tries to eliminate the possibility of some propertyless thing, to which properties can then be added, like sprinkling sugar on it. |
| 12852 | If x is ever part of y, then y is necessarily such that x is part of y at any time that y exists [Chisholm, by Simons] |
| Full Idea: Chisholm has an axiom: if x is a proper part of y, then necessarily if y exists then x is part of it. If x is ever part of y, they y is necessarily such that x is part of y at any time that y exists. | |
| From: report of Roderick Chisholm (Person and Object [1976], p.149) by Peter Simons - Parts 5.3 | |
| A reaction: This is Chisholm's notorious mereological essentialism, that all parts are necessary, and change of part means change of thing. However, it looks to me more like a proposal about what properties are necessary, not what are essential. |
| 15808 | A traditional individual essence includes all of a thing's necessary characteristics [Chisholm] |
| Full Idea: According to the traditional account of individual essence, each thing has only one individual essence and it includes all the characteristics that the thing has necessarily. | |
| From: Roderick Chisholm (Person and Object [1976], 1.4) | |
| A reaction: Chisholm is steeped in medieval theology, but I don't think this is quite what Aristotle meant. Everyone nowadays has to exclude the 'trivial' necessary properties, for a start. But why? I'm contemplating things which survive the loss of their essence. |
| 11966 | If there are essential properties, how do you find out what they are? [Chisholm] |
| Full Idea: It seems to me that if Adam does have essential properties, there is no procedure at all for finding out what they are. | |
| From: Roderick Chisholm (Identity through Possible Worlds [1967], p.85) | |
| A reaction: My tentative suggestion is that the essential properties are those which explain the nature, power, function and role of Adam in the 'actual' world. Whatever possibilities he acquires, he had better retain the capacity to be the First Man. |
| 12851 | Intermittence is seen in a toy fort, which is dismantled then rebuilt with the same bricks [Chisholm, by Simons] |
| Full Idea: Chisholm poses the problem of intermittence with the case of a toy fort which is built from toy bricks, taken apart, and then reassembled with the same bricks in the same position. | |
| From: report of Roderick Chisholm (Person and Object [1976], p.90) by Peter Simons - Parts 5.3 | |
| A reaction: You could strengthen the case, or the problem, by using those very bricks to build a ship during the interval. Or building a fort with a different design. Most people would be happy to say that same object (token) has been rebuilt. |
| 15806 | The property of being identical with me is an individual concept [Chisholm] |
| Full Idea: I wish to urge that the property of being identical with me is an individual concept. | |
| From: Roderick Chisholm (Person and Object [1976], 1.4) | |
| A reaction: I can just about live with the claim (for formal purposes) that I am identical with myself, but I strongly resist my then having a 'property' consisting of 'being identical with myself' (or 'not being identical with somone else' etc.). |
| 15826 | There is 'loose' identity between things if their properties, or truths about them, might differ [Chisholm] |
| Full Idea: I suggest that there is a 'loose' sense of identity that is consistent with saying 'A has a property that B does not have', or 'some things are true of A but not of B'. | |
| From: Roderick Chisholm (Person and Object [1976], 3.2) | |
| A reaction: He is trying to explicate Bishop Butler's famous distinction between 'strict and philosophical' and 'loose and popular' senses. We might want to claim that the genuine identity relation is the 'loose' one (pace the logicians and mathematicians). |
| 11965 | Could possible Adam gradually transform into Noah, and vice versa? [Chisholm] |
| Full Idea: If Adam lived for 931 years in a possible world, instead of his actual 930 years, ..then Adam and Noah could gradually exchange their ages and other properties...and we could trace Adam in a world back to the actual Noah, and vice versa. | |
| From: Roderick Chisholm (Identity through Possible Worlds [1967], p.81-2) | |
| A reaction: [very compressed] Chisholm was one of the first to raise this problem for possible worlds, though it had been Quine's objection to modal logic all along. Only Adam having essential properties seems to stop this slippery slope, says Chisholm. |
| 19569 | We have a basic epistemic duty to believe truth and avoid error [Chisholm, by Kvanvig] |
| Full Idea: Chisholm says our fundamental epistemic duties arise from the fundamental duty to (do one's best to) believe the truth and avoid error. | |
| From: report of Roderick Chisholm (Theory of Knowledge (2nd ed 1977) [1966]) by Jonathan Kvanvig - Truth is not the Primary Epistemic Goal 'Epistemic' | |
| A reaction: Since it strikes me as impossible to perceive something as being true, and yet still not believe it (except in moments of shock), I don't see why we need to introduce dubious claims about 'duty' here. Stupidity isn't a failure of duty. |
| 15819 | Do sense-data have structure, location, weight, and constituting matter? [Chisholm] |
| Full Idea: Does a red sense-datum or appearance have a back side as well as a front? Where is it located? Does it have any weight? What is it made of? | |
| From: Roderick Chisholm (Person and Object [1976], 1.8) | |
| A reaction: A reductive physicalist like myself is not so troubled by questions like this, which smack of Descartes's non-spatial argument for dualism. |
| 15816 | 'I feel depressed' is more like 'he runs slowly' than like 'he has a red book' [Chisholm] |
| Full Idea: The sentences 'I feel depressed' and 'I feel exuberant' are related in the way in which 'He runs slowly' and 'He runs swiftly' are related, and not in the way in which 'He has a red book' and 'He has a brown book' are related. | |
| From: Roderick Chisholm (Person and Object [1976], 1.8) | |
| A reaction: Ducasse 1942 and Chisholm 1957 seem to be the sources of the adverbial theory. I gather Chisholm gave it up late in his career. The adverbial theory seems sort of right, but it doesn't illuminate what is happening. |
| 15817 | If we can say a man senses 'redly', why not also 'rectangularly'? [Chisholm] |
| Full Idea: If we say a man 'senses redly', may we also say that he 'senses rhomboidally' or 'senses rectangularly'? There is no reason why not. | |
| From: Roderick Chisholm (Person and Object [1976], 1.8) | |
| A reaction: This is Chisholm replying to one of the best known objections to the adverbial theory. Can we sense 'wobblyrhomboidallywithpinkdots-ly'? Can we perceive 'landscapely'? The problem is bigger than he thinks. |
| 15818 | So called 'sense-data' are best seen as 'modifications' of the person experiencing them [Chisholm] |
| Full Idea: We may summarise my way of looking at appearing by saying that so-called appearances or sense-data are 'affections' or 'modifications' of the person who is said to experience them. | |
| From: Roderick Chisholm (Person and Object [1976], 1.8) | |
| A reaction: Hm. That seems to transfer the ontological problem of the redness of the tomato from the tomato to the perceiver, but leave the basic difficulty untouched. I think we need to pull apart the intrinsic and subjective ingredients here. |
| 8790 | 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. |
| 15831 | Explanations have states of affairs as their objects [Chisholm] |
| Full Idea: I suggest that states of affairs constitute the objects of the theory of explanation. | |
| From: Roderick Chisholm (Person and Object [1976], 4.4) | |
| A reaction: It is good to ask what the constituents of a theory of explanation might be. He has an all-embracing notion of state of affairs, whereas I would say that events and processes are separate. See Idea 15828. |
| 15811 | I am picked out uniquely by my individual essence, which is 'being identical with myself' [Chisholm] |
| Full Idea: What picks me out uniquely, without relating me to some other being? It can only be the property of 'being me' or 'being identical with myself', which can only be an individual essence or haecceity, a property I cannot fail to have. | |
| From: Roderick Chisholm (Person and Object [1976], 1.5) | |
| A reaction: Only a philosopher (and a modern analytic one at that) would imagine that this was some crucial insight into how we know our own identities. |
| 15815 | Sartre says the ego is 'opaque'; I prefer to say that it is 'transparent' [Chisholm] |
| Full Idea: Sartre says the ego is 'opaque'; I would think it better to say that the ego is 'transparent'. | |
| From: Roderick Chisholm (Person and Object [1976], 1.8) | |
| A reaction: Insofar as we evidently have a self, I would say it is neither. It is directly experienced, through willing, motivation, and mental focus. |
| 15813 | People use 'I' to refer to themselves, with the meaning of their own individual essence [Chisholm] |
| Full Idea: Each person uses the first person pronoun to refer to himself, and in such a way that its reference (Bedeutung) is to himself and its intention (Sinn) is his own individual essence. | |
| From: Roderick Chisholm (Person and Object [1976], 1.5) | |
| A reaction: I think this is exactly right, and may be the basis of the way we essentialise in our understanding of the rest of reality. I have a strong notion of what is essential in me and what is not. |
| 15803 | Bad theories of the self see it as abstract, or as a bundle, or as a process [Chisholm] |
| Full Idea: Some very strange theories of the self suggest it is an abstract object, such as a class, or a property, or a function. Some theories imply that I am a collection, or a bundle, or a structure, or an event, or a process (or even a verb!). | |
| From: Roderick Chisholm (Person and Object [1976], Intro 4) | |
| A reaction: I certainly reject the abstract lot, but the second lot doesn't sound so silly to me, especially 'structure' and 'process'. I don't buy the idea that the Self is an indivisible monad. It is a central aspect of brain process - the prioritiser of thought. |
| 3444 | If actions are not caused by other events, and are not causeless, they must be caused by the person [Chisholm] |
| Full Idea: If the action is not caused by some other event, and it is not causeless, this leaves the possibility that it is caused by something else instead, and this something can only be the agent, the man. | |
| From: Roderick Chisholm (Human Freedom and the Self [1964], p.28) |
| 3446 | For Hobbes (but not for Kant) a person's actions can be deduced from their desires and beliefs [Chisholm] |
| Full Idea: According to Hobbes, if we fully know what a man desires and believes, and we know the state of his physical stimuli, we may logically deduce what he will try to do. But Kant says no such statements can ever imply what a man will do. | |
| From: Roderick Chisholm (Human Freedom and the Self [1964], p.32) |
| 9268 | If free will miraculously interrupts causation, animals might do that; why would we want to do it? [Frankfurt on Chisholm] |
| Full Idea: Chisholm holds the quaint doctrine that human freedom entails an absence of causal determination; a free action is a miracle. This gives no basis for doubting that animals have such freedom; and why would we care whether we can interrupt the causal order? | |
| From: comment on Roderick Chisholm (Human Freedom and the Self [1964]) by Harry G. Frankfurt - Freedom of the Will and concept of a person §IV | |
| A reaction: [compressed] Chisholm is the spokesman for 'agent causation', Frankfurt for freedom as second-level volitions. I'm with Frankfurt. The belief in 'agents' and 'free will' may sound plausible, until the proposal is spelled out in causal terms. |
| 15821 | Determinism claims that every event has a sufficient causal pre-condition [Chisholm] |
| Full Idea: Determinism is the proposition that, for every event that occurs, there occurs a sufficient causal condition of that event. | |
| From: Roderick Chisholm (Person and Object [1976], 2.2) | |
| A reaction: You need an ontology of events to put it precisely this way. Doesn't it also work the other way: that there is an event for every sufficient causal condition? The beginning and the end of reality pose problems. |
| 10110 | Corresponding to every concept there is a class (some of them sets) [George/Velleman] |
| Full Idea: Corresponding to every concept there is a class (some classes will be sets, the others proper classes). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) |
| 20062 | If a desire leads to a satisfactory result by an odd route, the causal theory looks wrong [Chisholm] |
| Full Idea: If someone wants to kill his uncle to inherit a fortune, and having this desire makes him so agitated that he loses control of his car and kills a pedestrian, who turns out to be his uncle, the conditions of the causal theory seem to be satisfied. | |
| From: Roderick Chisholm (Freedom and Action [1966]), quoted by Rowland Stout - Action 6 'Deviant' | |
| A reaction: This line of argument has undermined all sorts of causal theories that were fashionable in the 1960s and 70s. Explanation should lead to understanding, but a deviant causal chain doesn't explain the outcome. The causal theory can be tightened. |
| 20054 | There has to be a brain event which is not caused by another event, but by the agent [Chisholm] |
| Full Idea: There must be some event A, presumably some cerebral event, which is not caused by any other event, but by the agent. | |
| From: Roderick Chisholm (Freedom and Action [1966], p.20), quoted by Rowland Stout - Action 4 'Agent' | |
| A reaction: I'm afraid this thought strikes me as quaintly ridiculous. What kind of metaphysics can allow causation outside the natural nexus, yet occuring within the physical brain? This is a relic of religious dualism. Let it go. |
| 3442 | Responsibility seems to conflict with events being either caused or not caused [Chisholm] |
| Full Idea: The free will problem is that humans seem to be responsible, but this seems to conflict with the idea that every event is caused by some other event, and it also conflicts with the view that the action is not caused at all. | |
| From: Roderick Chisholm (Human Freedom and the Self [1964], p.24) |
| 3443 | Desires may rule us, but are we responsible for our desires? [Chisholm] |
| Full Idea: If a flood of desires causes a weak-willed man to give in to temptation, …the question now becomes, is he responsible for the beliefs and desires he happens to have? | |
| From: Roderick Chisholm (Human Freedom and the Self [1964], p.25) |
| 15824 | There are mere omissions (through ignorance, perhaps), and people can 'commit an omission' [Chisholm] |
| Full Idea: If a man does not respond to a greeting, if he was unaware that he was addressed then his failure to respond may be a mere omission. But if he intended to snub the man, then he could be said to have 'committed the omission'. | |
| From: Roderick Chisholm (Person and Object [1976], 2.6) | |
| A reaction: Chisholm has an extensive knowledge of Catholic theology. These neat divisions are subject to vagueness and a continuum of cases in real life. |
| 7844 | The Golden Rule is accepted everywhere, and gives a fixed target for morality [Voltaire] |
| Full Idea: Pascal asks where we can find a fixed point in morality. The answer is in that single maxim accepted by all nations: "Do not do to others what you would not like to have done to you". | |
| From: Francois-Marie Voltaire (Philosophical Letters from England [1733], 25) | |
| A reaction: Should I only offer to my guests foods which I myself like? If I don't mind a bit of pain, is it all right to inflict it? It is a sensible rule, but not precise enough for philosophy. |
| 15822 | The concept of physical necessity is basic to both causation, and to the concept of nature [Chisholm] |
| Full Idea: It is generally agreed, I think, that the concept of physical necessity, or a law of nature, is fundamental to the theory of causation and, more generally, to the concept of nature. | |
| From: Roderick Chisholm (Person and Object [1976], 2.3) | |
| A reaction: This seems intuitively right, but we might be able to formulate a concept of nature that had a bit less necessity in it, especially if we read a few books on quantum theory first. |
| 15823 | Some propose a distinct 'agent causation', as well as 'event causation' [Chisholm] |
| Full Idea: Sometimes a distinction is made between 'event causation' and 'agent causation' and it has been suggested that there is an unbridgeable gap between the two. | |
| From: Roderick Chisholm (Person and Object [1976], 2.5) | |
| A reaction: Nope, don't buy that. I connect it with Davidson's 'anomalous monism', that tries to combine one substance with separate laws of action. The metaphysical price for such a theory is too high to pay. |
| 3445 | Causation among objects relates either events or states [Chisholm] |
| Full Idea: Between natural objects we may say that causation is a relation between events or states of affairs. | |
| From: Roderick Chisholm (Human Freedom and the Self [1964], p.28) |
| 15820 | A 'law of nature' is just something which is physically necessary [Chisholm] |
| Full Idea: When we say something is 'physically necessary' we can replace it with 'law of nature'. | |
| From: Roderick Chisholm (Person and Object [1976], 2.2) | |
| A reaction: [plucked out of context even more than usual!] This is illuminating about what contemporary philosophers (such as Armstrong) seem to mean by a law of nature. It is not some grand equation, but a small local necessary connection. |