46 ideas
| 2557 | Analytical philosophy seems to have little interest in how to tell a good analysis from a bad one [Rorty] |
| Full Idea: There is nowadays little attempt to bring "analytic philosophy" to self-consciousness by explaining how to tell a successful from an unsuccessful analysis. | |
| From: Richard Rorty (Philosophy and the Mirror of Nature [1980], 4.1) |
| 2556 | Rational certainty may be victory in argument rather than knowledge of facts [Rorty] |
| Full Idea: We can think of "rational certainty" as a matter of victory in argument rather than relation to an object known. | |
| From: Richard Rorty (Philosophy and the Mirror of Nature [1980], 3.4) |
| 4726 | Rorty seems to view truth as simply being able to hold one's view against all comers [Rorty, by O'Grady] |
| Full Idea: Rorty seems to view truth as simply being able to hold one's view against all comers. | |
| From: report of Richard Rorty (Philosophy and the Mirror of Nature [1980]) by Paul O'Grady - Relativism Ch.4 | |
| A reaction: This may be a caricature of Rorty, but he certainly seems to be in the business of denying truth as much as possible. This strikes me as the essence of pragmatism, and as a kind of philosophical nihilism. |
| 2549 | For James truth is "what it is better for us to believe" rather than a correct picture of reality [Rorty] |
| Full Idea: Truth is, in James' phrase, "what it is better for us to believe", rather than "the accurate representation of reality". | |
| From: Richard Rorty (Philosophy and the Mirror of Nature [1980], Intro) |
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| Full Idea: Until the 1960s standard truth-table semantics were the only ones that there were. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.10.1) | |
| A reaction: The 1960s presumably marked the advent of possible worlds. |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| Full Idea: 'dom R' indicates the 'domain' of a relation, that is, the set of all objects that are members of ordered pairs and that have that relation. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| Full Idea: 'fld R' indicates the 'field' of a relation, that is, the set of all objects that are members of ordered pairs on either side of the relation. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| Full Idea: 'ran R' indicates the 'range' of a relation, that is, the set of all objects that are members of ordered pairs and that are related to by the first objects. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| Full Idea: We write F : A → B to indicate that A maps into B, that is, the domain of relating things is set A, and the things related to are all in B. If we add that F = B, then A maps 'onto' B. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
|
Full Idea:
F(x) is a 'function', which indicates the unique value which y takes in |
|
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| Full Idea: A relation is 'symmetric' on a set if every ordered pair in the set has the relation in both directions. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| Full Idea: A relation is 'transitive' on a set if the relation can be carried over from two ordered pairs to a third. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| Full Idea: The 'powerset' of a set is all the subsets of a given set. Thus: PA = {x : x ⊆ A}. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| Full Idea: Two sets are 'disjoint' iff their intersection is empty (i.e. they have no members in common). | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| Full Idea: The 'domain' of a relation is the set of all objects that are members of ordered pairs that are members of the relation. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| Full Idea: A 'relation' is a set of ordered pairs. The ordering relation on the numbers 0-3 is captured by - in fact it is - the set of ordered pairs {<0,1>,<0,2>,<0,3>,<1,2>,<1,3>,<2,3>}. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) | |
| A reaction: This can't quite be a definition of order among numbers, since it relies on the notion of a 'ordered' pair. |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| Full Idea: A 'function' is a relation which is single-valued. That is, for each object, there is only one object in the function set to which that object is related. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| Full Idea: A function 'maps A into B' if the domain of relating things is set A, and the things related to are all in B. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| Full Idea: A function 'maps A onto B' if the domain of relating things is set A, and the things related to are set B. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| Full Idea: A relation is 'reflexive' on a set if every member of the set bears the relation to itself. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| Full Idea: A relation satisfies 'trichotomy' on a set if every ordered pair is related (in either direction), or the objects are identical. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| Full Idea: A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| Full Idea: An 'equivalence relation' is a binary relation which is reflexive, and symmetric, and transitive. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| Full Idea: Equivalence classes will 'partition' a set. That is, it will divide it into distinct subsets, according to each relation on the set. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| Full Idea: The process is dubbed 'conversational implicature' when the inference is not from the content of what has been said, but from the fact that it has been said. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.7.3) |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| Full Idea: The point of logic is to give an account of the notion of validity,..in two standard ways: the semantic way says that a valid inference preserves truth (symbol |=), and the proof-theoretic way is defined in terms of purely formal procedures (symbol |-). | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.3..) | |
| A reaction: This division can be mirrored in mathematics, where it is either to do with counting or theorising about things in the physical world, or following sets of rules from axioms. Language can discuss reality, or play word-games. |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| Full Idea: A is a logical truth (tautology) (|= A) iff it is a semantic consequence of the empty set of premises (φ |= A), that is, every interpretation makes A true. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.3.4) | |
| A reaction: So the final column of every line of the truth table will be T. |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| Full Idea: A truth assignment 'satisfies' a formula, or set of formulae, if it evaluates as True when all of its components have been assigned truth values. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.2) | |
| A reaction: [very roughly what Enderton says!] The concept becomes most significant when a large set of wff's is pronounced 'satisfied' after a truth assignment leads to them all being true. |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| Full Idea: If every proof-theoretically valid inference is semantically valid (so that |- entails |=), the proof theory is said to be 'sound'. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.7) |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| Full Idea: If every semantically valid inference is proof-theoretically valid (so that |= entails |-), the proof-theory is said to be 'complete'. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.7) |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| Full Idea: If a wff is tautologically implied by a set of wff's, it is implied by a finite subset of them; and if every finite subset is satisfiable, then so is the whole set of wff's. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 2.5) | |
| A reaction: [Enderton's account is more symbolic] He adds that this also applies to models. It is a 'theorem' because it can be proved. It is a major theorem in logic, because it brings the infinite under control, and who doesn't want that? |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| Full Idea: A set of expressions is 'decidable' iff there exists an effective procedure (qv) that, given some expression, will decide whether or not the expression is included in the set (i.e. doesn't contradict it). | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.7) | |
| A reaction: This is obviously a highly desirable feature for a really reliable system of expressions to possess. All finite sets are decidable, but some infinite sets are not. |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| Full Idea: The Enumerability Theorem says that for a reasonable language, the set of valid wff's can be effectively enumerated. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 2.5) | |
| A reaction: There are criteria for what makes a 'reasonable' language (probably specified to ensure enumerability!). Predicates and functions must be decidable, and the language must be finite. |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| Full Idea: Not all sentences using 'if' are conditionals. Consider 'if you want a banana, there is one in the kitchen'. The rough test is that a conditional can be rewritten as 'that A implies that B'. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.6.4) |
| 2548 | If knowledge is merely justified belief, justification is social [Rorty] |
| Full Idea: If we have a Deweyan conception of knowledge, as what we are justified in believing, we will see "justification" as a social phenomenon. | |
| From: Richard Rorty (Philosophy and the Mirror of Nature [1980], Intro) | |
| A reaction: I find this observation highly illuminating (though I probably need to study Dewey to understand it). There just is no absolute about whether someone is justified. How justified do you want to be? |
| 9382 | Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge] |
| Full Idea: I call 'entitlement' (as opposed to justification) the epistemic rights or warrants that need not be understood by or even be accessible to the subject. | |
| From: Tyler Burge (Content Preservation [1993]), quoted by Paul Boghossian - Analyticity Reconsidered §III | |
| A reaction: I espouse a coherentism that has both internal and external components, and is mediated socially. In Burge's sense, animals will sometimes have 'entitlement'. I prefer, though, not to call this 'knowledge'. 'Entitled true belief' is good. |
| 6599 | Knowing has no definable essence, but is a social right, found in the context of conversations [Rorty] |
| Full Idea: If we see knowing not as having an essence, described by scientists or philosophers, but rather as a right, by current standards, to believe, then we see conversation as the ultimate context within which knowledge is to be understood. | |
| From: Richard Rorty (Philosophy and the Mirror of Nature [1980], Ch.5), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.5 | |
| A reaction: This teeters towards ridiculous relativism (e.g. what if the conversation is among a group of fools? - Ah, there are no fools! Politically incorrect!). However, knowledge can be social, provided we are healthily elitist. Scientists know more than us. |
| 2566 | You can't debate about whether to have higher standards for the application of words [Rorty] |
| Full Idea: The decision about whether to have higher than usual standards for the application of words like "true" or "good" or "red" is, as far as I can see, not a debatable issue. | |
| From: Richard Rorty (Philosophy and the Mirror of Nature [1980], 6.6) |
| 2553 | The mind is a property, or it is baffling [Rorty] |
| Full Idea: All that is needed for the mind-body problem to be unintelligible is for us to be nominalist, to refuse firmly to hypostasize individual properties. | |
| From: Richard Rorty (Philosophy and the Mirror of Nature [1980], 1.3) | |
| A reaction: Edelman says the mind is a process rather than a property. It might vanish if the clockspeed was turned right down? Nominalism here sounds like behaviourism or instrumentalism. Would Dennett plead guilty? |
| 2550 | Pain lacks intentionality; beliefs lack qualia [Rorty] |
| Full Idea: We can't define the mental as intentional because pains aren't about anything, and we can't define it as phenomenal because beliefs don't feel like anything. | |
| From: Richard Rorty (Philosophy and the Mirror of Nature [1980], 1.2) | |
| A reaction: Nice, but simplistic? There is usually an intentional object for a pain, and the concepts which we use to build beliefs contain the residue of remembered qualia. It seems unlikely that any mind could have one without the other (even a computer). |
| 2554 | Is intentionality a special sort of function? [Rorty] |
| Full Idea: Following Wittgenstein, we shall treat the intentional as merely a subspecies of the functional. | |
| From: Richard Rorty (Philosophy and the Mirror of Nature [1980], 1.3) | |
| A reaction: Intriguing but obscure. Sounds wrong to me. The intentional refers to the content of thoughts, but function concerns their role. They have roles because they have content, so they can't be the same. |
| 2565 | Nature has no preferred way of being represented [Rorty] |
| Full Idea: Nature has no preferred way of being represented. | |
| From: Richard Rorty (Philosophy and the Mirror of Nature [1980], 6.5) | |
| A reaction: Tree rings accidentally represent the passing of the years. If God went back and started again would she or he opt for a 'preferred way'? |
| 2560 | Can meanings remain the same when beliefs change? [Rorty] |
| Full Idea: For cooler heads there must be some middle view between "meanings remain and beliefs change" and "meanings change whenever beliefs do". | |
| From: Richard Rorty (Philosophy and the Mirror of Nature [1980], 6.2) | |
| A reaction: The second one seems blatanty false. How could we otherwise explain a change in belief? But obviously some changes in belief (e.g. about electrons) produce a change in meaning. |
| 2562 | A theory of reference seems needed to pick out objects without ghostly inner states [Rorty] |
| Full Idea: The need to pick out objects without the help of definitions, essences, and meanings of terms produced, philosophers thought, a need for a "theory of reference". | |
| From: Richard Rorty (Philosophy and the Mirror of Nature [1980], 6.3) | |
| A reaction: Frege's was very perceptive in noting that meaning and reference are not the same. Whether we need a 'theory' of reference is unclear. It is worth describing how it occurs. |
| 2559 | Davidson's theory of meaning focuses not on terms, but on relations between sentences [Rorty] |
| Full Idea: A theory of meaning, for Davidson, is not an assemblage of "analyses" of the meanings of individual terms, but rather an understanding of the inferential relations between sentences. | |
| From: Richard Rorty (Philosophy and the Mirror of Nature [1980], 6.1) | |
| A reaction: Put that way, the influence of Frege on Davidson is obvious. Purely algebraic expressions can have inferential relations, using variables and formal 'sentences'. |
| 2558 | Since Hegel we have tended to see a human as merely animal if it is outside a society [Rorty] |
| Full Idea: Only since Hegel have philosophers begun toying with the idea that the individual apart from his society is just one more animal. | |
| From: Richard Rorty (Philosophy and the Mirror of Nature [1980], 4.3) |