display all the ideas for this combination of texts
15 ideas
| 14108 | It would be circular to use 'if' and 'then' to define material implication [Russell] |
| Full Idea: It would be a vicious circle to define material implication as meaning that if one proposition is true, then another is true, for 'if' and 'then' already involve implication. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §037) | |
| A reaction: Hence the preference for defining it by the truth table, or as 'not-p or q'. |
| 14106 | Implication cannot be defined [Russell] |
| Full Idea: A definition of implication is quite impossible. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §016) |
| 14167 | The only classes are things, predicates and relations [Russell] |
| Full Idea: The only classes appear to be things, predicates and relations. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §440) | |
| A reaction: This is the first-order logic view of reality, which has begun to look incredibly impoverished in modern times. Processes certainly demand a hearing, as do modal facts. |
| 4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
| Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality. | |
| From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4 | |
| A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional. |
| 14105 | There seem to be eight or nine logical constants [Russell] |
| Full Idea: The number of logical constants is not great: it appears, in fact, to be eight or nine. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §012) | |
| A reaction: There is, of course, lots of scope for interdefinability. No one is going to disagree greatly with his claim, so it is an interesting fact, which invites some sort of (non-platonic) explanation. |
| 18722 | Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell] |
| Full Idea: Russell explained ¬p by saying that ¬p is true if p is false and false if p is true. But this is not an explanation of negation, for it might apply to propositions other than the negative. | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903]) by Ludwig Wittgenstein - Lectures 1930-32 (student notes) B XI.3 | |
| A reaction: Presumably he is thinking of 'the light is on' and 'the light is off'. A very astute criticism, which seems to be correct. What would Russell say? Perhaps we add that negation is an 'operation' which achieves flipping of the truth-value? |
| 14104 | Constants are absolutely definite and unambiguous [Russell] |
| Full Idea: A constant is something absolutely definite, concerning which there is no ambiguity whatever. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §006) |
| 14114 | Variables don't stand alone, but exist as parts of propositional functions [Russell] |
| Full Idea: A variable is not any term simply, but any term as entering into a propositional function. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §093) | |
| A reaction: So we should think of variables entirely by their role, rather than as having a semantics of their own (pace Kit Fine? - though see Russell §106, p.107). |
| 9038 | We must distinguish what the speaker denotes by a name, from what the name denotes [Evans] |
| Full Idea: There are two related but distinguishable questions concerning proper names: what the speaker denotes (upon an occasion), and what the name denotes. | |
| From: Gareth Evans (The Causal Theory of Names [1973], §I) | |
| A reaction: I don't think any account of language makes sense without this sort of distinction, as in my favourite example: the password is 'swordfish'. So how does language gets its own meanings, independent of what speakers intend? |
| 5824 | How can an expression be a name, if names can change their denotation? [Evans] |
| Full Idea: We need an account of what makes an expression into a name for something that will allow names to change their denotations. | |
| From: Gareth Evans (The Causal Theory of Names [1973], §II) | |
| A reaction: Presumably an example would be 'The Prime Minister is in the building'. Evans proposes to discuss communication, rather than strict meanings and descriptions. |
| 9042 | A private intention won't give a name a denotation; the practice needs it to be made public [Evans] |
| Full Idea: Intentions alone don't bring it about that a name gets a denotation; without the intention being manifest there cannot be the common knowledge required for the practice. | |
| From: Gareth Evans (The Causal Theory of Names [1973], §II) | |
| A reaction: Well, I might have a private name for some hated colleague which I mutter to myself whenever I see her. The way names, and language generally, becomes ossified is by joining the great impersonal sea of the language. ..waves of bones, |
| 9041 | The Causal Theory of Names is wrong, since the name 'Madagascar' actually changed denotation [Evans] |
| Full Idea: Change of denotation is decisive against the Causal Theory of Names. Changes of denotation actually occur: a hearsay report misunderstood by Marco Polo transferred the name 'Madagascar' from a portion of the mainland to the African island. | |
| From: Gareth Evans (The Causal Theory of Names [1973], §I) | |
| A reaction: This doesn't sound decisive, as you could give an intermediate causal account of Marco Polo's mistake. I might take the famous name Winston, and baptise my son with it. And I might have done it because I thought Winston was a German dictator. |
| 14137 | 'Any' is better than 'all' where infinite classes are concerned [Russell] |
| Full Idea: The word 'any' is preferable to the word 'all' where infinite classes are concerned. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §284) | |
| A reaction: The reason must be that it is hard to quantify over 'all' of the infinite members, but it is easier to say what is true of any one of them. |
| 14149 | The Achilles Paradox concerns the one-one correlation of infinite classes [Russell] |
| Full Idea: When the Achilles Paradox is translated into arithmetical language, it is seen to be concerned with the one-one correlation of two infinite classes. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §321) | |
| A reaction: Dedekind's view of infinity (Idea 9826) shows why this results in a horrible tangle. |
| 15895 | Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine] |
| Full Idea: Burali-Forti didn't discover any paradoxes, though his work suggested a paradox to Russell. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Shaughan Lavine - Understanding the Infinite I |