display all the ideas for this combination of texts
9 ideas
| 13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
| Full Idea: On the question of the nature of genuine logical consequence, ...the most popular answer is the semantic, or model-theoretic one. | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.5) | |
| A reaction: Reading the literature, one might be tempted to think that this is the only account that anyone takes seriously. Substitutional semantics seems an interesting alternative. |
| 13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
| Full Idea: Another answer to the question about the nature of logical consequence is a proof-theoretic one, according to which it is more a matter of provability than of truth-preservation. | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.5) | |
| A reaction: I don't like this, and prefer the model-theoretic or substitutional accounts. Whether you can prove that something is a logical consequence seems to me entirely separate from whether you can see that it is so. Gödel seems to agree. |
| 13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
| Full Idea: The 'modal' account of logical consequence is that it is not possible for the premises to be true and the consequent false (under some suitable notion of possibility). | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.5) | |
| A reaction: Sider gives a nice summary of five views of logical consequence, to which Shapiro adds substitutional semantics. |
| 13680 | Maybe logical consequence is a primitive notion [Sider] |
| Full Idea: There is a 'primitivist' account, according to which logical consequence is a primitive notion. | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.5) | |
| A reaction: While sympathetic to substitutional views (Idea 13674), the suggestion here pushes me towards thinking that truth must be at the root of it. The trouble, though, is that a falsehood can be a good logical consequence of other falsehoods. |
| 13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
| Full Idea: A 'theorem' is defined as the last line of a proof in which each line is either an axiom or follows from earlier lines by a rule. | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.7) | |
| A reaction: In other words, theorems are the axioms and their implications. |
| 6877 | Entailment is logical requirement; it may be not(p and not-q), but that has problems [Mautner] |
| Full Idea: Entailment is the modern word saying that p logically follows from q. Its simplest definition is that you cannot have both p and not-q, but this has the problem that if p is impossible it will entail every possible proposition, which seems unacceptable. | |
| From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.169) | |
| A reaction: The word 'entail' was introduced by G.E. Moore in 1920, in preference to 'imply'. It seems clear that we need terms for (say) active implication (q must be true if p is true) and passive implication (p must be false if q is false). |
| 6880 | Strict implication says false propositions imply everything, and everything implies true propositions [Mautner] |
| Full Idea: Strict implication [not(p and not-q)] carries the paradoxes that a false proposition (p) implies any proposition (q), and a true proposition (q) is materially implied by any proposition (p). | |
| From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.270) | |
| A reaction: This seems to show that we have two drastically different notions of implication; one (the logician's) is boring and is defined by a truth table; the other (the ordinary interesting one) says if you have one truth you can deduce a second. |
| 6879 | 'Material implication' is defined as 'not(p and not-q)', but seems to imply a connection between p and q [Mautner] |
| Full Idea: 'Material implication' is a term introduced by Russell which is defined as 'the conjunction of p and not-q is false', but carries a strong implication that p implies q, and so there must be some kind of connection between them, which is misleading. | |
| From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.270) | |
| A reaction: Mautner says statements of the form 'if p then q' are better called 'conditionals' than 'material implications'. Clearly there is a need for more precise terminology here, as the underlying concepts seem simple enough. |
| 6878 | A person who 'infers' draws the conclusion, but a person who 'implies' leaves it to the audience [Mautner] |
| Full Idea: 'Implying' is different from 'inferring', because a person who infers draws the conclusion, but a person who implies leaves it to the audience to draw the conclusion. | |
| From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.279) | |
| A reaction: I had always taken it just that the speaker does the implying and the audience does the inferring. Of course a speaker may not know what he or she is implying, but an audience must be aware of what it is inferring. |