20 ideas
| 13939 | No possible evidence could decide the reality of numbers, so it is a pseudo-question [Carnap] |
| Full Idea: I cannot think of any possible evidence that would be regarded as relevant by both nominalists and realists about numbers, and would decide the controversy, or make one side more probable. Hence I regard the external questions as pseudo-questions. | |
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 4) |
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| Full Idea: One of Hilbert's aims in 'The Foundations of Geometry' was to eliminate number [as measure of lengths and angles] from geometry. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: Presumably this would particularly have to include the elimination of ratios (rather than actual specific lengths). |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| Full Idea: Hilbert's geometrical axioms were existential in character, asserting the existence of certain geometrical objects (points and lines). Euclid's postulates do not assert the existence of anything; they assert the possibility of certain constructions. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Charles Chihara - A Structural Account of Mathematics 01.1 | |
| A reaction: Chihara says geometry was originally understood modally, but came to be understood existentially. It seems extraordinary to me that philosophers of mathematics can have become more platonist over the centuries. |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| Full Idea: In his formal investigation of Euclidean geometry, Hilbert uncovered congruence axioms that implicitly played a role in Euclid's proofs but were not explicitly recognised. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 2 | |
| A reaction: The writers are offering this as a good example of the benefits of a precise and formal approach to foundational questions. It's hard to disagree, but dispiriting if you need a PhD in maths before you can start doing philosophy. |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| Full Idea: Hilbert's formulation of the Euclidean theory is of special interest because (besides being rigorously axiomatised) it does not employ the real numbers in the axioms. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3 | |
| A reaction: Notice that this job was done by Hilbert, and not by the fictionalist Hartry Field. |
| 8748 | Logical positivists incorporated geometry into logicism, saying axioms are just definitions [Carnap, by Shapiro] |
| Full Idea: The logical positivists brought geometry into the fold of logicism. The axioms of, say, Euclidean geometry are simply definitions of primitive terms like 'point' and 'line'. | |
| From: report of Rudolph Carnap (Empiricism, Semantics and Ontology [1950]) by Stewart Shapiro - Thinking About Mathematics 5.3 | |
| A reaction: If the concept of 'line' is actually created by its definition, then we need to know exactly what (say) 'shortest' means. If we are merely describing a line, then our definition can be 'impredicative', using other accepted concepts. |
| 13936 | Questions about numbers are answered by analysis, and are analytic, and hence logically true [Carnap] |
| Full Idea: For the internal question like 'is there a prime number greater than a hundred?' the answers are found by logical analysis based on the rules for the new expressions. The answers here are analytic, i.e., logically true. | |
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 2) |
| 8960 | Internal questions about abstractions are trivial, and external ones deeply problematic [Carnap, by Szabó] |
| Full Idea: Carnap's verdict is that questions regarding the existence of abstracta tend to be trivial when taken as internal and deeply problematic when taken as external. | |
| From: report of Rudolph Carnap (Empiricism, Semantics and Ontology [1950]) by Zoltán Gendler Szabó - Nominalism 6 | |
| A reaction: If the internal aspect of the problem is 'trivial', this would put Carnap in league with fictionalists, who are only committed to entities while playing the current game. What is the status of the theory? Carnap wanted flowers to bloom. |
| 13933 | Existence questions are 'internal' (within a framework) or 'external' (concerning the whole framework) [Carnap] |
| Full Idea: We distinguish two kinds of existence questions: first, entities of a new kind within the framework; we call them 'internal questions'. Second, 'external questions', concerning the existence or reality of the system of entities as a whole. | |
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 2) | |
| A reaction: This nicely disposes of many ontological difficulties, but at the price of labelling most external questions as meaningless, so that the internal answers have very little commitment, and the external (big) questions are now banned. Not for me. |
| 13934 | To be 'real' is to be an element of a system, so we cannot ask reality questions about the system itself [Carnap] |
| Full Idea: To be real in the scientific sense means to be an element of the system; hence this concept cannot be meaningfully applied to the system itself. | |
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 2) |
| 13938 | A linguistic framework involves commitment to entities, so only commitment to the framework is in question [Carnap] |
| Full Idea: If someone accepts a framework for a kind of entities, then he must admit the entities as possible designata. Thus the question of the admissibility of entities is reduced to the question of the acceptability of the linguistic framework for the entities. | |
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 4) | |
| A reaction: Despite the many differences of opinion between Quine and Carnap, this appears to be a straight endorsement by Carnap of the Quinean conception of ontological commitment. |
| 13935 | We only accept 'things' within a language with formation, testing and acceptance rules [Carnap] |
| Full Idea: To accept the thing world means nothing more than to accept a certain form of language, in other words, to accept rules for forming statements and for testing, accepting, or rejecting them. | |
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 2) | |
| A reaction: If you derive your metaphysics from your language, then objects are linguistic conventions. But why do we accept conventions about objects? |
| 13932 | Empiricists tend to reject abstract entities, and to feel sympathy with nominalism [Carnap] |
| Full Idea: Empiricists are in general rather suspicious with respect to any kind of abstract entities like properties, classes, relations, numbers, propositions etc. They usually feel more sympathy with nominalists than with realists (in the medieval sense). | |
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 1) | |
| A reaction: The obvious reason is that you can't have sense experiences of abstract entities. I like the question 'what are they made of?' rather than the question 'how can I experience them?'. |
| 13937 | New linguistic claims about entities are not true or false, but just expedient, fruitful or successful [Carnap] |
| Full Idea: The acceptance of new linguistic forms about entities cannot be judged as being either true or false because it is not an assertion. It can only be judged as being more or less expedient, fruitful, conducive to the aim for which the language is intended. | |
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 3) | |
| A reaction: The obvious problem seems to be that a complete pack of lies might be successful for a very long time, if it plugged a critical hole in a major theory. Is success judged financially? How do we judge success without mentioning truth? |
| 13940 | All linguistic forms in science are merely judged by their efficiency as instruments [Carnap] |
| Full Idea: The acceptance or rejection of abstract (or any other) linguistic forms in any branch of science will finally be decided by their efficiency as instruments. | |
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 5) |
| 7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
| Full Idea: If you define qualia as intrinsic properties of experiences considered in isolation from all their causes and effects, logically independent of all dispositional properties, then they are logically guaranteed to elude all broad functional analysis. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.8) | |
| A reaction: This is a good point - it seems daft to reify qualia and imagine them dangling in mid-air with all their vibrant qualities - but that is a long way from saying there is nothing more to qualia than functional roles. Functions must be exlained too. |
| 7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
| Full Idea: All the work done by the imagined homunculus in the Cartesian Theater must be distributed among various lesser agencies in the brain, none of which is conscious. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: Dennett's account crucially depends on consciousness being much more fragmentary than most philosophers claim it to be. It is actually full of joints, which can come apart. He may be right. |
| 7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
| Full Idea: As long as your homunculi are more stupid and ignorant than the intelligent agent they compose, the nesting of homunculi within homunculi can be finite, bottoming out, eventually, with agents so unimpressive they can be replaced by machines. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.6) | |
| A reaction: [Dennett first proposed this in 'Brainstorms' 1978]. This view was developed well by Lycan. I rate it as one of the most illuminating ideas in the modern philosophy of mind. All complex systems (like aeroplanes) have this structure. |
| 7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
| Full Idea: I don't maintain, of course, that human consciousness does not exist; I maintain that it is not what people often think it is. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: I consider Dennett to be as near as you can get to an eliminativist, but he is not stupid. As far as I can see, the modern philosopher's bogey-man, the true total eliminativist, simply doesn't exist. Eliminativists usually deny propositional attitudes. |
| 7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
| Full Idea: Neuro-science matters because - and only because - we have discovered that the many different neuromodulators and other chemical messengers that diffuse throughout the brain have functional roles that make important differences. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.1) | |
| A reaction: I agree with Dennett that this is the true ground for pessimism about spectacular breakthroughs in artificial intelligence, rather than abstract concerns about irreducible features of the mind like 'qualia' and 'rationality'. |