24 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) |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| Full Idea: To know if A ∈ B, we look at the set A as a single object, and check if it is among B's members. But if we want to know whether A ⊆ B then we must open up set A and check whether its various members are among the members of B. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:04) | |
| A reaction: This idea is one of the key ideas to grasp if you are going to get the hang of set theory. John ∈ USA ∈ UN, but John is not a member of the UN, because he isn't a country. See Idea 12337 for a special case. |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| Full Idea: The 'ordered pair' <x,y> is defined to be {{x}, {x,y}}; hence it can be proved that <u,v> = <x,y> iff u = x and v = y (given by Kuratowski in 1921). ...The definition is somewhat arbitrary, and others could be used. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:36) | |
| A reaction: This looks to me like one of those regular cases where the formal definitions capture all the logical behaviour of the concept that are required for inference, while failing to fully capture the concept for ordinary conversation. |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| Full Idea: A 'linear ordering' (or 'total ordering') on A is a binary relation R meeting two conditions: R is transitive (of xRy and yRz, the xRz), and R satisfies trichotomy (either xRy or x=y or yRx). | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:62) |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| Full Idea: Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ. A man with an empty container is better off than a man with nothing. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1.03) |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| Full Idea: It might be thought at first that the empty set would be a rather useless or even frivolous set to mention, but from the empty set by various set-theoretic operations a surprising array of sets will be constructed. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:02) | |
| A reaction: This nicely sums up the ontological commitments of mathematics - that we will accept absolutely anything, as long as we can have some fun with it. Sets are an abstraction from reality, and the empty set is the very idea of that abstraction. |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| Full Idea: Given any x we have the singleton {x}, which is defined by the pairing axiom to be {x,x}. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 2:19) | |
| A reaction: An interesting contrivance which is obviously aimed at keeping the axioms to a minimum. If you can do it intuitively with a new axiom, or unintuitively with an existing axiom - prefer the latter! |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| Full Idea: It was observed by several people that for a satisfactory theory of ordinal numbers, Zermelo's axioms required strengthening. The Axiom of Replacement was proposed by Fraenkel and others, giving rise to the Zermelo-Fraenkel (ZF) axioms. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:15) |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| Full Idea: For functions, we know that for any y there exists an appropriate x, but we can't yet form a function H, as we have no way of defining one particular choice of x. Hence we need the axiom of choice. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:48) |
| 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? |
| 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'. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 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) |