32 ideas
| 18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
| Full Idea: Frege rejected the traditional categories as importing psychological and linguistic impurities into logic. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by Ian Rumfitt - The Boundary Stones of Thought 1.2 | |
| A reaction: Resisting such impurities is the main motivation for making logic entirely symbolic, but it doesn't follow that the traditional categories have to be dropped. |
| 14273 | Conditional Proof is only valid if we accept the truth-functional reading of 'if' [Edgington] |
| Full Idea: Conditional Proof seems sound: 'From X and Y, it follows that Z. So from X it follows that if Y,Z'. Yet for no reading of 'if' which is stronger that the truth-functional reading is CP valid, at least if we accept ¬(A&¬B);A; therefore B. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.2) | |
| A reaction: See the section of ideas on Conditionals (filed under 'Modality') for a fuller picture of this issue. Edgington offers it as one of the main arguments in favour of the truth-functional reading of 'if' (though she rejects that reading). |
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| Full Idea: Just as functions are fundamentally different from objects, so also functions whose arguments are and must be functions are fundamentally different from functions whose arguments are objects. The latter are first-level, the former second-level, functions. | |
| From: Gottlob Frege (Function and Concept [1891], p.38) | |
| A reaction: In 1884 he called it 'second-order'. This is the standard distinction between first- and second-order logic. The first quantifies over objects, the second over intensional entities such as properties and propositions. |
| 8492 | Relations are functions with two arguments [Frege] |
| Full Idea: Functions of one argument are concepts; functions of two arguments are relations. | |
| From: Gottlob Frege (Function and Concept [1891], p.39) | |
| A reaction: Nowadays we would say 'two or more'. Another interesting move in the aim of analytic philosophy to reduce the puzzling features of the world to mathematical logic. There is, of course, rather more to some relations than being two-argument functions. |
| 8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
| Full Idea: I am of the opinion that arithmetic is a further development of logic, which leads to the requirement that the symbolic language of arithmetic must be expanded into a logical symbolism. | |
| From: Gottlob Frege (Function and Concept [1891], p.30) | |
| A reaction: This may the the one key idea at the heart of modern analytic philosophy (even though logicism may be a total mistake!). Logic and arithmetical foundations become the master of ontology, instead of the servant. The jury is out on the whole enterprise. |
| 18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
| Full Idea: Frege regarded the existence of horses as a property of the concept 'horse'. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by Fred Sommers - Intellectual Autobiography 'Realism' |
| 4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
| Full Idea: Frege's theory of properties (which he calls 'concepts') yields too few properties, by identifying coextensive properties, and also too many, by letting every predicate express a property. | |
| From: comment on Gottlob Frege (Function and Concept [1891]) by DH Mellor / A Oliver - Introduction to 'Properties' §2 | |
| A reaction: Seems right; one extension may have two properties (have heart/kidneys), two predicates might express the same property. 'Cutting nature at the joints' covers properties as well as objects. |
| 8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
| Full Idea: I regard a regular definition of 'object' as impossible, since it is too simple to admit of logical analysis. Briefly: an object is anything that is not a function, so that an expression for it does not contain any empty place. | |
| From: Gottlob Frege (Function and Concept [1891], p.32) | |
| A reaction: Here is the core of the programme for deriving our ontology from our logic and language, followed through by Russell and Quine. Once we extend objects beyond the physical, it becomes incredibly hard to individuate them. |
| 14281 | A thing works like formal probability if all the options sum to 100% [Edgington] |
| Full Idea: One's degrees of belief in the members of an idealised partition should sum to 100%. That is all there is to the claim that degrees of belief should have the structure of probabilities. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 3.1) |
| 14284 | Conclusion improbability can't exceed summed premise improbability in valid arguments [Edgington] |
| Full Idea: If (and only if) an argument is valid, then in no probability distribution does the improbability of its conclusion exceed the sum of the improbabilities of its premises. We can call this the Probability Preservation Principle. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 3.2) | |
| A reaction: [Ernest Adams is credited with this] This means that classical logic is in some way probability-preserving as well as truth-preserving. |
| 14270 | Simple indicatives about past, present or future do seem to form a single semantic kind [Edgington] |
| Full Idea: Straightforward statements about the past, present or future, to which a conditional clause is attached - the traditional class of indicative conditionals - do (in my view) constitute a single semantic kind. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 1) | |
| A reaction: This contrasts with Idea 14269, where the future indicatives are group instead with the counterfactuals. |
| 14269 | Maybe forward-looking indicatives are best classed with the subjunctives [Edgington] |
| Full Idea: According to some theorists, the forward-looking 'indicatives' (those with a 'will' in the main clause) belong with the 'subjunctives' (those with a 'would' in the main clause), and not with the other 'indicatives'. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 1) | |
| A reaction: [She cites Gibbard, Dudman and 1988 Bennett; Jackson defends the indicative/subjunctive division, and recent Bennett defends it too] It is plausible to say that 'If you will do x' is counterfactual, since it hasn't actually happened. |
| 14275 | Truth-function problems don't show up in mathematics [Edgington] |
| Full Idea: The main defects of the truth-functional account of conditionals don't show up in mathematics. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.3) | |
| A reaction: These problems are the paradoxes associated with the material conditional ⊃. Too often mathematical logic has been the tail that wagged the dog in modern philosophy. |
| 14274 | Inferring conditionals from disjunctions or negated conjunctions gives support to truth-functionalism [Edgington] |
| Full Idea: If either A or B is true, then you are intuitively justified in believe that If ¬A, B. If you know that ¬(A&B), then you may justifiably infer that if A, ¬B. The truth-functionalist gets both of these cases (disjunction and negated conjunction) correct. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.1) | |
| A reaction: [compressed version] This summarises two of Edgington's three main arguments in favour of the truth-functional account of conditions (along with the existence of Conditional Proof). It is elementary classical logic which supports truth-functionalism. |
| 14276 | The truth-functional view makes conditionals with unlikely antecedents likely to be true [Edgington] |
| Full Idea: The truth-functional view of conditionals has the unhappy consequence that all conditionals with unlikely antecedents are likely to be true. To think it likely that ¬A is to think it likely that a sufficient condition for the truth of A⊃B obtains. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.3) | |
| A reaction: This is Edgington's main reason for rejecting the truth-functional account of conditionals. She says it removes our power to discriminate between believable and unbelievable conditionals, which is basic to practical reasoning. |
| 14290 | Doctor:'If patient still alive, change dressing'; Nurse:'Either dead patient, or change dressing'; kills patient! [Edgington] |
| Full Idea: The doctor says "If the patient is still alive in the morning, change the dressing". As a truth-functional command this says "Make it that either the patient is dead in the morning, or change the dressing", so the nurse kills the patient. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 5) | |
| A reaction: Isn't philosophy wonderful? |
| 14271 | Non-truth-functionalist say 'If A,B' is false if A is T and B is F, but deny that is always true for TT,FT and FF [Edgington] |
| Full Idea: Non-truth-functional accounts agree that 'If A,B' is false when A is true and B is false; and that it is sometimes true for the other three combinations of truth-values; but they deny that the conditional is always true in each of these three cases. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.1) | |
| A reaction: Truth-functional connectives like 'and' and 'or' don't add any truth-conditions to the values of the propositions, but 'If...then' seems to assert a relationship that goes beyond its component propositions, so non-truth-functionalists are right. |
| 14272 | I say "If you touch that wire you'll get a shock"; you don't touch it. How can that make the conditional true? [Edgington] |
| Full Idea: Non-truth-functionalists agree that when A is false, 'If A,B' may be either true or false. I say "If you touch that wire, you will get an electric shock". You don't touch it. Was my remark true or false? They say it depends on the wire etc. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.1) | |
| A reaction: This example seems to me to be a pretty conclusive refutation of the truth-functional view. How can the conditional be implied simply by my failure to touch the wire (which is what benighted truth-functionalists seem to believe)? |
| 14282 | On the supposition view, believe if A,B to the extent that A&B is nearly as likely as A [Edgington] |
| Full Idea: Accepting Ramsey's suggestion that 'if' and 'on the supposition that' come to the same thing, we get an equation which says ...you believe if A,B to the extent that you think that A&B is nearly as likely as A. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 3.1) |
| 14278 | Truth-functionalists support some conditionals which we assert, but should not actually believe [Edgington] |
| Full Idea: There are compounds of conditionals which we confidently assert and accept which, by the lights of the truth-functionalist, we do not have reason to believe true, such as 'If it broke if it was dropped, it was fragile', when it is NOT dropped. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.5) | |
| A reaction: [The example is from Gibbard 1981] The fact that it wasn't dropped only negates the nested antecedent, not the whole antecedent. I suppose it also wasn't broken, and both negations seem to be required. |
| 14287 | Does 'If A,B' say something different in each context, because of the possibiites there? [Edgington] |
| Full Idea: A pragmatic constraint might say that as different possibilities are live in different conversational settings, a different proposition may be expressed by 'If A,B' in different conversational settings. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 4.1) | |
| A reaction: Edgington says that it is only the truth of the proposition, not its content, which changes with context. I'm not so sure. 'If Hitler finds out, we are in trouble' says different things in 1914 and 1944. |
| 6871 | We can't only believe things if we are currently conscious of their justification - there are too many [Goldman] |
| Full Idea: Strong internalism says only current conscious states can justify beliefs, but this has the problem of Stored Beliefs, that most of our beliefs are stored in memory, and one's conscious state includes nothing that justifies them. | |
| From: Alvin I. Goldman (Internalism Exposed [1999], §2) | |
| A reaction: This point seems obviously correct, but one could still have a 'fairly strong' version, which required that you could always call into consciousness the justificiation for any belief that you happened to remember. |
| 6872 | Internalism must cover Forgotten Evidence, which is no longer retrievable from memory [Goldman] |
| Full Idea: Even weak internalism has the problem of Forgotten Evidence; the agent once had adequate evidence that she subsequently forgot; at the time of epistemic appraisal, she no longer has adequate evidence that is retrievable from memory. | |
| From: Alvin I. Goldman (Internalism Exposed [1999], §3) | |
| A reaction: This is certainly a basic problem for any account of justification. It will rule out any strict requirement that there be actual mental states available to support a belief. Internalism may be pushed to include non-conscious parts of the mind. |
| 6874 | Internal justification needs both mental stability and time to compute coherence [Goldman] |
| Full Idea: The problem for internalists of Doxastic Decision Interval says internal justification must avoid mental change to preserve the justification status, but must also allow enough time to compute the formal relations between beliefs. | |
| From: Alvin I. Goldman (Internalism Exposed [1999], §4) | |
| A reaction: The word 'compute' implies a rather odd model of assessing coherence, which seems instantaneous for most of us where everyday beliefs are concerned. In real mental life this does not strike me as a problem. |
| 6873 | Coherent justification seems to require retrieving all our beliefs simultaneously [Goldman] |
| Full Idea: The problem of Concurrent Retrieval is a problem for internalism, notably coherentism, because an agent could ascertain coherence of her entire corpus only by concurrently retrieving all of her stored beliefs. | |
| From: Alvin I. Goldman (Internalism Exposed [1999], §3) | |
| A reaction: Sounds neat, but not very convincing. Goldman is relying on scepticism about short-term memory, but all belief and knowledge will collapse if we go down that road. We couldn't do simple arithmetic if Goldman's point were right. |
| 6875 | Reliability involves truth, and truth is external [Goldman] |
| Full Idea: Reliability involves truth, and truth (on the usual assumption) is external. | |
| From: Alvin I. Goldman (Internalism Exposed [1999], §6) | |
| A reaction: As an argument for externalism this seems bogus. I am not sure that truth is either 'internal' or 'external'. How could the truth of 3+2=5 be external? Facts are mostly external, but I take truth to be a relation between internal and external. |
| 9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
| Full Idea: Concepts, for Frege, are the ontological counterparts of predicative expressions. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: That sounds awfully like what many philosophers call 'universals'. Frege, as a platonist (at least about numbers), I would take to be in sympathy with that. At least we can say that concepts seem to be properties. |
| 10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
| Full Idea: Frege had a notorious difficulty over the concept 'horse', when he suggests that if we wish to assert something about a concept, we are obliged to proceed indirectly by speaking of an object that represents it. | |
| From: report of Gottlob Frege (Function and Concept [1891], Ch.2.II) by Bob Hale - Abstract Objects | |
| A reaction: This sounds like the thin end of a wedge. The great champion of objects is forced to accept them here as a façon de parler, when elsewhere they have ontological status. |
| 8488 | A concept is a function whose value is always a truth-value [Frege] |
| Full Idea: A concept in logic is closely connected with what we call a function. Indeed, we may say at once: a concept is a function whose value is always a truth-value. ..I give the name 'function' to what is meant by the 'unsaturated' part. | |
| From: Gottlob Frege (Function and Concept [1891], p.30) | |
| A reaction: So a function becomes a concept when the variable takes a value. Problems arise when the value is vague, or the truth-value is indeterminable. |
| 9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
| Full Idea: For Frege, concepts differ from objects in being inherently incomplete in nature. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This is because they are 'unsaturated', needing a quantified variable to complete the sentence. This could be a pointer towards Quine's view of properties, as simply an intrinsic feature of predication about objects, with no separate identity. |
| 4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
| Full Idea: From sameness of meaning there does not follow sameness of thought expressed. A fact about the Morning Star may express something different from a fact about the Evening Star, as someone may regard one as true and the other false. | |
| From: Gottlob Frege (Function and Concept [1891], p.14) | |
| A reaction: This all gets clearer if we distinguish internalist and externalist theories of content. Why take sides on this? Why not just ask 'what is in the speaker's head?', 'what does the sentence mean in the community?', and 'what is the corresponding situation?' |
| 8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |
| Full Idea: The ontological proof of God's existence suffers from the fallacy of treating existence as a first-level concept. | |
| From: Gottlob Frege (Function and Concept [1891], p.38 n) | |
| A reaction: [See Idea 8490 for first- and second-order functions] This is usually summarised as the idea that existence is a quantifier rather than a predicate. |