22 ideas
| 21704 | 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B] |
| Full Idea: The ban on 'impredicative' definitions says you can't define a class in terms of a totality to which that class must be seen as belonging. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: So that would be defining 'citizen' in terms of the community to which the citizen belongs? If you are asked to define 'community' and 'citizen' together, where do you start? But how else can it be done? Russell's Reducibility aimed to block this. |
| 5745 | Quine says quantified modal logic creates nonsense, bad ontology, and false essentialism [Melia on Quine] |
| Full Idea: Quine charges quantified modal systems of logic with giving rise to unintended sense or nonsense, committing us to an incomprehensible ontology, and entailing an implausible or unsustainable Aristotelian essentialism. | |
| From: comment on Willard Quine (Existence and Quantification [1966]) by Joseph Melia - Modality Ch.3 | |
| A reaction: A nice summary. Personally I like essentialism in accounts of science (see Nature|Laws of Nature|Essentialism), so would like to save it in metaphysics. Possible worlds ontology may be very surprising, rather than 'incomprehensible'. |
| 21705 | Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B] |
| Full Idea: The Axiom of Reducibility avoids impredicativity, by asserting that for any predicate of given arguments defined by quantifying over higher-order functions or classes, there is another co-extensive but predicative function of the same type of arguments. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: Eventually the axiom seemed too arbitrary, and was dropped. Linsky's book explores it. |
| 8789 | Various strategies try to deal with the ontological commitments of second-order logic [Hale/Wright on Quine] |
| Full Idea: Quine said higher-order logic is 'set theory in sheep's clothing', and there is concern about the ontology that is involved. One approach is to deny quantificational ontological commitments, or say that the entities involved are first-order objects. | |
| From: comment on Willard Quine (Existence and Quantification [1966]) by B Hale / C Wright - Logicism in the 21st Century 8 | |
| A reaction: [compressed] The second strategy is from Boolos. This question seems to be right at the heart of the strategy of exploring our ontology through the study of our logic. |
| 21727 | Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B] |
| Full Idea: The theory of definite descriptions may eliminate apparent commitment to such entities as the present King of France, but certainly not to the present Queen of England. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7.3) |
| 21719 | Extensionalism means what is true of a function is true of coextensive functions [Linsky,B] |
| Full Idea: With the principle of extensionality anything true of one propositional functions will be true of every coextensive one. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.3) |
| 21723 | The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B] |
| Full Idea: The problem for logicism was to find definitions of the primitive notions of Peano's theory, number, successor and 0, in terms of logical notions, so that the postulates could then be derived by logic alone. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7) | |
| A reaction: Both Frege and Russell defined numbers as equivalence classes. Successor is easily defined (in various ways) in set theory. An impossible set can exemplify zero. The trouble for logicism is this all relies on sets. |
| 21721 | Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B] |
| Full Idea: The higher types are needed for intensional phenomena, cases where the same class is picked out by distinct propositional functions. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.4) | |
| A reaction: I take it that in this way 'x is renate' can be distinguished from 'x is cordate', a task nowadays performed by possible worlds. |
| 21703 | Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B] |
| Full Idea: The types is 'ramified' because there are further differences between the type of a function defined in terms of a quantifier ranging over other functions and the type of those other functions, despite the functions applying to the same simple type. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: Not sure I understand this, but it evidently created difficulties for dealing with actual mathematics, and Ramsey showed how you could manage without the ramifications. |
| 21714 | The ramified theory subdivides each type, according to the range of the variables [Linsky,B] |
| Full Idea: The original ramified theory of types ...furthern subdivides each of the types of the 'simple' theory according to the range of the bound variables used in the definition of each propositional function. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6) | |
| A reaction: For a non-intiate like me it certainly sounds disappointing that such a bold and neat theory because a tangle of complications. Ramsey and Russell in the 1920s seem to have dropped the ramifications. |
| 21713 | Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B] |
| Full Idea: It is often thought that Logicism was a failure, because after Frege's contradiction, Russell required obviously nonlogical principles, in order to develop mathematics. The axioms of Reducibility, Infinity and Choice are cited. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6) | |
| A reaction: Infinity and Choice remain as axioms of the standard ZFC system of set theory, which is why set theory is always assumed to be 'up to its neck' in ontological commitments. Linsky argues that Russell saw ontology in logic. |
| 21715 | For those who abandon logicism, standard set theory is a rival option [Linsky,B] |
| Full Idea: ZF set theory is seen as a rival to logicism as a foundational scheme. Set theory is for those who have given up the project of reducing mathematics to logic. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.1) | |
| A reaction: Presumably there are other rivals. Set theory has lots of ontological commitments. One could start at the other end, and investigate the basic ontological commitments of arithmetic. I have no idea what those might be. |
| 16966 | Philosophers tend to distinguish broad 'being' from narrower 'existence' - but I reject that [Quine] |
| Full Idea: It has been fairly common in philosophy early and late to distinguish between being, as the broadest concept, and existence, as narrower. This is no distinction of mine; I mean 'exist' to cover all there is. | |
| From: Willard Quine (Existence and Quantification [1966], p.100) | |
| A reaction: I sort of agree with Quine, but 'being' has a role in philosophy that is not required in science and daily life, as the name of the central problem of ontology, which probably has to be broken down before any progress can happen. |
| 16965 | All we have of general existence is what existential quantifiers express [Quine] |
| Full Idea: Existence is what existential quantification expresses. …It is unreasonable to ask for an explication of (general) existence in simpler terms. …We may still ask what counts as evidence for existential quantifications. | |
| From: Willard Quine (Existence and Quantification [1966], p.97) | |
| A reaction: This has been orthodoxy for the last 60 years, with philosophers talking of 'quantifying over' instead of 'exists'. But are we allowed second-order logic, and plural quantification, and vague domains? |
| 16963 | Existence is implied by the quantifiers, not by the constants [Quine] |
| Full Idea: In the quantification '(∃)(x=a)', it is the existential quantifier, not the 'a' itself, which carries the existential import. | |
| From: Willard Quine (Existence and Quantification [1966], p.94) | |
| A reaction: The Fregean idea seems to be that the criterion of existence is participation in an equality, but here the equality seems not more than assigning a name. Why can't I quantify over 'sakes', in 'for the sake of the children'? |
| 16964 | Theories are committed to objects of which some of its predicates must be true [Quine] |
| Full Idea: Another way of saying what objects a theory requires is to say that they are the objects that some of the predicates of the theory have to be true of, in order for the theory to be true. | |
| From: Willard Quine (Existence and Quantification [1966], p.95) | |
| A reaction: The other was for the objects to be needed by the bound variables of the theory. This is the first-order approach, that predication is a commitment to an object. So what of predicates which have no application? |
| 4216 | Express a theory in first-order predicate logic; its ontology is the types of bound variable needed for truth [Quine, by Lowe] |
| Full Idea: According to Quine, we find the ontological commitments of a theory by expressing it in first-order predicate logic, then determining what kind of entities must be admitted as bound variables if the theory is true. | |
| From: report of Willard Quine (Existence and Quantification [1966]) by E.J. Lowe - A Survey of Metaphysics p.216 | |
| A reaction: To me this is horribly wrong. The ontological commitments of our language is not the same as ontology. What are the ontological commitments of a pocket calculator? |
| 18966 | Ontological commitment of theories only arise if they are classically quantified [Quine] |
| Full Idea: I hold that the question of the ontological commitment of a theory does not properly arise except as that theory is expressed in classical quantificational form. | |
| From: Willard Quine (Existence and Quantification [1966], p.106) | |
| A reaction: He is attacking substitutional quantification for its failure to commit. I smell circularity. If it must be quantified in the first-order classical manner, that restricts your ontology to objects before you've even started. Chicken/egg. |
| 14490 | You can be implicitly committed to something without quantifying over it [Thomasson on Quine] |
| Full Idea: Quine's test for ontological commitment ignores the fact that there are often implicit commitments to certain kinds of entities even where we are not yet quantifying over them. | |
| From: comment on Willard Quine (Existence and Quantification [1966]) by Amie L. Thomasson - Ordinary Objects 09.4 | |
| A reaction: Put this with the obvious problem (of which Quine is aware) that we don't quantify over 'sakes' in 'for the sake of the children', and quantification and commitment have been rather clearly pulled apart. |
| 16961 | In formal terms, a category is the range of some style of variables [Quine] |
| Full Idea: In terms of formalized quantification theory, each category comprises the range of some distinctive style of variable. | |
| From: Willard Quine (Existence and Quantification [1966], p.92) | |
| A reaction: I add this for those who dream of formalising everything, but be warned that even Quine thought it of little help in deciding on the categories. Presumably there would be some variable that ranged across tigers. |
| 21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |
| Full Idea: Rather than directly constructing properties as sets of objects and proving neat facts about properties by proxy, we can assert biconditionals, such as that an object has a property if and only if it is in a certain set. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7.6) | |
| A reaction: Linsky is describing Russell's method of logical construction. I'm not clear what is gained by this move, but at least it is a variant of the usual irritating expression of properties as sets of objects. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |