22 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) |
| 15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
| Full Idea: The common feature of every designating term is that designation may change from state to state - thus it can be formalized by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3) | |
| A reaction: Specifying the objects sounds OK, but specifying states sounds rather tough. |
| 15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
| Full Idea: To first order modal logic (with quantification over objects) we can add a second kind of quantification, over intensions. An intensional object, or individual concept, will be modelled by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.3) |
| 15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
| Full Idea: Awareness logic enriched Hintikka's epistemic models with an awareness function, mapping each state to the set of formulas we are aware of at that state. This reflects some bound on the resources we can bring to bear. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) | |
| A reaction: [He cites Fagin and Halpern 1988 for this] |
| 15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
| Full Idea: In justification logics, the logics of knowledge are extended by making reasons explicit. A logic of proof terms was created, with a semantics. In this, mathematical truths are known for explicit reasons, and these provide a measure of complexity. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics. | |
| From: Melvin Fitting (Intensional Logic [2007], §1) |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □. | |
| From: Melvin Fitting (Intensional Logic [2007], §3.3) | |
| A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic. |
| 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) |
| 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. |
| 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. |
| 14592 | Some abstract things have a beginning and end, so may exist in time (though not space) [Swoyer] |
| Full Idea: Many things that seem to be abstract also seem to have a beginning (and ending) in time, such as a language like Urdu. It may be tempting to say that such things exist in time but not in space, but where exactly? | |
| From: Chris Swoyer (Abstract Entities [2008], 1.1) | |
| A reaction: A few distinctions might be needed. Urdu-speaking is an ability of certain people. We abstract from that their 'language'. There is nothing there apart from that ability. It has no more abstract existence than the 'weather'. |
| 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. |
| 14594 | Ontologists seek existence and identity conditions, and modal and epistemic status for a thing [Swoyer] |
| Full Idea: Four things philosophers often want to know about a given sort of entity are: its existence conditions, its identity conditions, its modal status, and its epistemic status. | |
| From: Chris Swoyer (Abstract Entities [2008], 3) | |
| A reaction: I prefer 'modal profile' to 'modal status'. The 'existence conditions' sound rather epistemic. Why does the existence of anything require 'conditions' other than just existing? I suspect identity is irrelevant if humans aren't around. |
| 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. |
| 14595 | Can properties exemplify other properties? [Swoyer] |
| Full Idea: Can properties themselves exemplify properties? | |
| From: Chris Swoyer (Abstract Entities [2008], 3) | |
| A reaction: Since I espouse a rather strict causal view of true properties, and lump the rest into the category of 'predicates', I am inclined to answer 'no' to this. Most people would disagree. 'Bright red' seems to be an example. But it isn't. |
| 14593 | Quantum field theory suggests that there are, fundamentally, no individual things [Swoyer] |
| Full Idea: Quantum field theory strongly suggests that there are (at the fundamental level) no individual, particular things. | |
| From: Chris Swoyer (Abstract Entities [2008], 2.1) | |
| A reaction: When people introduce quantum theory into ontological discussions I reach for my shotgun, but it does rather look as if things turn to mush at the bottom level. |
| 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? |
| 15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
| Full Idea: Definite descriptions pick out different objects in different possible worlds quite naturally. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.4) | |
| A reaction: A definite description can pick out the same object in another possible world, or a very similar one, or an object which has almost nothing in common with the others. |
| 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) |