22 ideas
| 18776 | Contextual definitions eliminate descriptions from contexts [Linsky,B] |
| Full Idea: A 'contextual' definition shows how to eliminate a description from a context. | |
| From: Bernard Linsky (Quantification and Descriptions [2014], 2) | |
| A reaction: I'm trying to think of an example, but what I come up with are better described as 'paraphrases' than as 'definitions'. |
| 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. |
| 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. |
| 18774 | Definite descriptions, unlike proper names, have a logical structure [Linsky,B] |
| Full Idea: Definite descriptions seem to have a logical structure in a way that proper names do not. | |
| From: Bernard Linsky (Quantification and Descriptions [2014], 1.1.1) | |
| A reaction: Thus descriptions have implications which plain names do not. |
| 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. |
| 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. |
| 19743 | A notebook counts as memory, if is available to consciousness and guides our actions [Clark/Chalmers] |
| Full Idea: Beliefs are partly constituted by features of the environment. ....a notebook plays for one person the same role that memory plays for another. ...The information is reliably there, available to consciousness, and to guide action, just as belief is. | |
| From: A Clark / D Chalmers (The Extended Mind [1998], §4) | |
| A reaction: This is the modern externalist approach to beliefs (along with broad content and external cognition systems). Not quite what we used to mean by beliefs, but we'll get used to it. I believe Plato wrote what it said in his books. Is memory just a role? |
| 3914 | Language arranges sensory experience to form a world-order [Whorf] |
| Full Idea: Language first of all is a classification and arrangement of the stream of sensory experience which results in a certain world-order. | |
| From: Benjamin Lee Whorf (Punctual and segmentive Hopi verbs [1936], p.55) | |
| A reaction: This is only true to a limited degree. See Davidson's 'On the very idea of a conceptual scheme'. All humans share a world-order, to some extent. |
| 3916 | Hopi consistently prefers verbs and events to nouns and things [Whorf] |
| Full Idea: Hopi, with its preference for verbs, as contrasted to our own liking for nouns, perpetually turns our propositions about things into propositions about events. | |
| From: Benjamin Lee Whorf (An American Indian model of the Universe [1936], p.63) | |
| A reaction: This should provoke careful thought about ontology - without concluding that it is entirely relative to language. |
| 3917 | Scientific thought is essentially a specialised part of Indo-European languages [Whorf] |
| Full Idea: What we call "scientific thought" is a specialisation of the western Indo-European type of language. | |
| From: Benjamin Lee Whorf (An American Indian model of the Universe [1936], p.246) | |
| A reaction: This is the beginnings of an absurd extreme relativist view of science, based on a confusion about meaning and thought. |
| 6176 | A mechanism can count as 'cognitive' whether it is in the brain or outside it [Clark/Chalmers, by Rowlands] |
| Full Idea: If the operation of a brain implant inside the brain is a cognitive operation, why should it not count as a cognitive operation when it is outside the brain? There are many mechanisms which would count as cognitive if they were inside the subject. | |
| From: report of A Clark / D Chalmers (The Extended Mind [1998]) by Mark Rowlands - Externalism Ch.9 | |
| A reaction: This argues for externalism of the vehicle of thought, rather than its content. The idea is that there is no significant difference between remembering a phone number and writing it on a bit of paper. I find it hard to disagree. |
| 19741 | If something in the world could equally have been a mental process, it is part of our cognition [Clark/Chalmers] |
| Full Idea: If, as we confront some task, a part of the world functions as a process which, were it done in the head, we would have no hesitation in recognising as part of the cognitive process, then that part of the world is part of the cognitive process. | |
| From: A Clark / D Chalmers (The Extended Mind [1998], §2) | |
| A reaction: In some sense they are obviously right that our cognitive activities spill out into books, calculators, record-keeping. It seems more like an invitation to shift the meaning of the word 'mind', than a proof that we have got it wrong. |
| 19742 | Consciousness may not extend beyond the head, but cognition need not be conscious [Clark/Chalmers] |
| Full Idea: Many identify the cognitive with the conscious, and it seems far from plausible that consciousness extends outside the head in these cases. But not every cognitive process, at least on standard usage, is a conscious process. | |
| From: A Clark / D Chalmers (The Extended Mind [1998], §3) | |
| A reaction: This gives you two sorts of externalism about mind to consider. No, three, if you say there is extended conceptual content, then extended cognition processes, then extended consciousness. Depends what you mean by 'consciousness'. |
| 19744 | If a person relies on their notes, those notes are parted of the extended system which is the person [Clark/Chalmers] |
| Full Idea: If Otto relies on his notebook, what this comes to is that Otto himself is best regarded as an extended system, a coupling of biological organism and external resources. | |
| From: A Clark / D Chalmers (The Extended Mind [1998], §5) | |
| A reaction: You start to get giddy as you read this stuff. If two people constantly share a notebook, they begin to blend into one another. It inclines me towards a more 'animalist' view of the nature of a person or a self. |
| 3915 | The Hopi have no concept of time as something flowing from past to future [Whorf] |
| Full Idea: A Hopi has no general notion or intuition of time as a smooth flowing continuum in which everything in the universe proceeds at an equal rate, out of a future, through a present, into a past. | |
| From: Benjamin Lee Whorf (An American Indian model of the Universe [1936], p.57) | |
| A reaction: If true, this would not so much support relativism of language as the view that that conception of time is actually false. |