73 ideas
| 20186 | Unlike knowledge, wisdom cannot be misused [Zagzebski] |
| Full Idea: A distinctive mark of wisdom is that it cannot be misused, whereas knowledge surely can be misused. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], I 1.2) | |
| A reaction: She will argue, with Aristotle, that this is because wisdom (and maybe 'true' knowledge) must include 'phronesis' (practical wisdom), which is the key to all the virtues, intellectual and moral. This idea is striking, and obviously correct. |
| 19694 | Wisdom is the property of a person, not of their cognitive state [Zagzebski, by Whitcomb] |
| Full Idea: Zagzebski takes wisdom as literally properties of persons, not persons' cognitive states. | |
| From: report of Linda Trinkaus Zagzebski (Virtues of the Mind [1996], p.59-60) by Dennis Whitcomb - Wisdom 'Twofold' | |
| A reaction: Not sure about this. Zagzebski uses this idea to endorse epistemic virtue. But knowledge and ignorance are properties of persons too. There can be, though, a precise mental state involved in knowledge, but not in wisdom. |
| 20221 | Precision is only one of the virtues of a good definition [Zagzebski] |
| Full Idea: Precision is but one virtue of a definition, one that must be balanced against simplicity, elegance, conciseness, theoretical illumination, and practical usefulness. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 2.1) | |
| A reaction: Illumination looks like the dream virtue for a good definition. Otherwise it is just ticked as accurate and stowed away. 'True justified belief' is a very illuminating definition of knowledge - if it is right. But it's not very precise. |
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| Full Idea: The standard requirement of definitions involves 'eliminability' (any defined terms must be replaceable by primitives) and 'non-creativity' (proofs of theorems should not depend on the definition). | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 7) | |
| A reaction: [He cites Russell and Whitehead as a source for this view] This is the austere view of the mathematician or logician. But almost every abstract concept that we use was actually defined in a creative way. |
| 20220 | Objection by counterexample is weak, because it only reveals inaccuracies in one theory [Zagzebski] |
| Full Idea: Objection by counterexample is the weakest sort of attack a theory can undergo. Even when the objection succeeds, it shows only that a theory fails to achieve complete accuracy. It does not distinguish among the various rival theories. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 2.1) | |
| A reaction: Typically counterexamples are used to refute universal generalisations (i.e. by 'falsification'), but canny theorists avoid those, or slip in a qualifying clause. Counterexamples are good for exploring a theory's coverage. |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
| Full Idea: The set-theory account of infinity doesn't just say that we can keep on counting, but that the natural numbers are an actual infinite set. This is necessary to make sense of the powerset of ω, as the set of all its subsets, and thus even bigger. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5) | |
| A reaction: I don't personally find this to be sufficient reason to commit myself to the existence of actual infinities. In fact I have growing doubts about the whole role of set theory in philosophy of mathematics. Shows how much I know. |
| 9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
| Full Idea: In the early versions of set theory ('naïve' set theory), the axiom of comprehension assumed that for any condition there is a set of objects satisfying that condition (so P(x)↔x∈{x:P(x)}), but this led directly to Russell's Paradox. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: How rarely any philosophers state this problem clearly (as Brown does here). This is incredibly important for our understanding of how we classify the world. I'm tempted to just ignore Russell, and treat sets in a natural and sensible way. |
| 9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
| Full Idea: In current set theory Russell's Paradox is avoided by saying that a condition can only be defined on already existing sets. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: A response to Idea 9613. This leaves us with no account of how sets are created, so we have the modern notion that absolutely any grouping of daft things is a perfectly good set. The logicians seem to have hijacked common sense. |
| 9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
| Full Idea: The modern 'iterative' concept of a set starts with the empty set φ (or unsetted individuals), then uses set-forming operations (characterized by the axioms) to build up ever more complex sets. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: The only sets in our system will be those we can construct, rather than anything accepted intuitively. It is more about building an elaborate machine that works than about giving a good model of reality. |
| 9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
| Full Idea: Neither a flock of birds nor a pack of wolves is strictly a set, since a flock can fly south, and a pack can be on the prowl, whereas sets go nowhere and menace no one. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 7) | |
| A reaction: To say that the pack menaced you would presumably be to commit the fallacy of composition. Doesn't the number 64 have properties which its set-theoretic elements (whatever we decide they are) will lack? |
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| Full Idea: The law of excluded middle says if a proposition is false, then its negation is true | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 1) | |
| A reaction: Surely that is the best statement of the law? How do you write that down? ¬(P)→¬P? No, because it is a semantic claim, not a syntactic claim, so a truth table captures it. Semantic claims are bigger than syntactic claims. |
| 9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
| Full Idea: The three views one could adopt concerning axioms are that they are self-evident truths, or that they are arbitrary stipulations, or that they are fallible attempts to describe how things are. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch.10) | |
| A reaction: Presumably modern platonists like the third version, with others choosing the second, and hardly anyone now having the confidence to embrace the first. |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
| Full Idea: Berry's Paradox refers to 'the least integer not namable in fewer than nineteen syllables' - a paradox because it has just been named in eighteen syllables. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5) | |
| A reaction: Apparently George Boolos used this quirky idea as a basis for a new and more streamlined proof of Gödel's Theorem. Don't tell me you don't find that impressive. |
| 9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
| Full Idea: Mathematics seems to be the one and only place where we humans can be absolutely sure that we got it right. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 1) | |
| A reaction: Apart from death and taxes, that is. Personally I am more certain of the keyboard I am typing on than I am of Pythagoras's Theorem, but the experts seem pretty confident about the number stuff. |
| 9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
| Full Idea: 'There are two apples' can be recast as 'x is an apple and y is an apple, and x isn't y, and if z is an apple it is the same as x or y', which makes no appeal at all to mathematics. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4) | |
| A reaction: He cites this as the basis of Hartry Field's claim that science can be done without numbers. The logic is ∃x∃y∀z(Ax&Ay&(x¬=y)&(Az→z=x∨z=y)). |
| 9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
| Full Idea: The number π is not only irrational, but it is also (unlike √2) a 'transcendental' number, because it is not the solution of an algebraic equation. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch.10) | |
| A reaction: So is that a superficial property, or a profound one? Answers on a post card. |
| 9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
| Full Idea: Mathematics hooks onto the world by providing representations in the form of structurally similar models. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4) | |
| A reaction: This is Brown's conclusion. It needs notions of mapping, one-to-one correspondence, and similarity. I like the idea of a 'model', as used in both logic and mathematics, and children's hobbies. The mind is a model-making machine. |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| Full Idea: I'm tempted to say that mathematics is so rich that there are indefinitely many ways to prove anything - verbal/symbolic derivations and pictures are just two. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 9) | |
| A reaction: Brown has been defending pictures as a form of proof. I wonder how long his list would be, if we challenged him to give more details? Some people have very low standards of proof. |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| Full Idea: The celebrity of the famous proof in 1976 of the four-colour theorem of maps is that a computer played an essential role in the proof. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch.10) | |
| A reaction: The problem concerns the reliability of the computers, but then all the people who check a traditional proof might also be unreliable. Quis custodet custodies? |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
| Full Idea: Maybe all of mathematics can be represented in set theory, but we should not think that mathematics is set theory. Functions can be represented as order pairs, but perhaps that is not what functions really are. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 7) | |
| A reaction: This seems to me to be the correct view of the situation. If 2 is represented as {φ,{φ}}, why is that asymmetrical? The first digit seems to be the senior and original partner, but how could the digits of 2 differ from one another? |
| 9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
| Full Idea: The basic definition of a graph can be given in set-theoretic terms,...but then what could an unlabelled graph be? | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 7) | |
| A reaction: An unlabelled graph will at least need a verbal description for it to have any significance at all. My daily mood-swings look like this.... |
| 9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
| Full Idea: Epistemology is a big worry for structuralists. ..To conjecture that something has a particular structure, we must already have conceived of the idea of the structure itself; we cannot be discovering structures by conjecturing them. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4) | |
| A reaction: This has to be a crucial area of discussion. Do we have our heads full of abstract structures before we look out of the window? Externalism about the mind is important here; mind and world are not utterly distinct things. |
| 9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
| Full Idea: Set theory is at the very heart of mathematics; it may even be all there is to mathematics. The notion of set, however, seems quite contrary to the spirit of structuralism. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4) | |
| A reaction: So much the worse for sets, I say. You can, for example, define ordinality in terms of sets, but that is no good if ordinality is basic to the nature of numbers, rather than a later addition. |
| 9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
| Full Idea: We could not discover irrational numbers by physical measurement. The discovery of the irrationality of the square root of two was an intellectual achievement, not at all connected to sense experience. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 1) | |
| A reaction: Brown declares himself a platonist, and this is clearly a key argument for him, and rather a good one. Hm. I'll get back to you on this one... |
| 9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
| Full Idea: A simple argument makes it clear that all mathematical arguments are abstract: there are infinitely many numbers, but only a finite number of physical entities, so most mathematical objects are non-physical. The best assumption is that they all are. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: This, it seems to me, is where constructivists score well (cf. Idea 9608). I don't have an infinity of bricks to build an infinity of houses, but I can imagine that the bricks just keep coming if I need them. Imagination is what is unbounded. |
| 9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
| Full Idea: Numbers are not 'abstract' (in the old sense, of universals abstracted from particulars), since each of the integers is a unique individual, a particular, not a universal. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: An interesting observation which I have not seen directly stated before. Compare Idea 645. I suspect that numbers should be thought of as higher-order abstractions, which don't behave like normal universals (i.e. they're not distributed). |
| 9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
| Full Idea: Perhaps, instead of objects, numbers are associated with properties of objects. Basing them on objects is strongly empiricist and uses first-order logic, whereas the latter view is somewhat Platonistic, and uses second-order logic. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4) | |
| A reaction: I don't seem to have a view on this. You can count tomatoes, or you can count red objects, or even 'instances of red'. Numbers refer to whatever can be individuated. No individuation, no arithmetic. (It's also Hume v Armstrong on laws on nature). |
| 9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
| Full Idea: Are there mathematical properties which can only be discovered using a particular notation? | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 6) | |
| A reaction: If so, this would seem to be a serious difficulty for platonists. Brown has just been exploring the mathematical theory of knots. |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| Full Idea: For the instinctive nominalist in mathematics, there are no numbers, only numerals. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5) | |
| A reaction: Maybe. A numeral is a specific sign, sometimes in a specific natural language, so this seems to miss the fact that cardinality etc are features of reality, not just conventions. |
| 9630 | The most brilliant formalist was Hilbert [Brown,JR] |
| Full Idea: In mathematics, the most brilliant formalist of all was Hilbert | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5) | |
| A reaction: He seems to have developed his fully formalist views later in his career. See Mathematics|Basis of Mathematic|Formalism in our thematic section. Kreisel denies that Hilbert was a true formalist. |
| 9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
| Full Idea: Constuctivists link truth with constructive proof, but necessarily lack constructions for many highly desirable results of classical mathematics, making their account of mathematical truth rather implausible. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: The tricky word here is 'desirable', which is an odd criterion for mathematical truth. Nevertheless this sounds like a good objection. How flexible might the concept of a 'construction' be? |
| 9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
| Full Idea: If we define p as '3 if Goldbach's Conjecture is true' and '5 if Goldbach's Conjecture is false', it seems that p must be a prime number, but, amazingly, constructivists would not accept this without a proof of Goldbach's Conjecture. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 8) | |
| A reaction: A very similar argument structure to Schrödinger's Cat. This seems (as Brown implies) to be a devastating knock-down argument, but I'll keep an open mind for now. |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| Full Idea: David's painting of Napoleon (on a white horse) is a 'picture' of Napoleon, and a 'symbol' of leadership, courage, adventure. It manages to be about something concrete and something abstract. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 3) | |
| A reaction: This strikes me as the germ of an extremely important idea - that abstraction is involved in our perception of the concrete, so that they are not two entirely separate realms. Seeing 'as' involves abstraction. |
| 20188 | Modern epistemology is too atomistic, and neglects understanding [Zagzebski] |
| Full Idea: There are complaints that contemporary epistemology is too atomistic, and that the value of understanding has been neglected. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], I 2) | |
| A reaction: This is because of the excessive influence of logic in contemporary analytic philosophy, which has to reduce knowledge to K(Fa), rather than placing it in a human context. |
| 20223 | Epistemology is excessively atomic, by focusing on justification instead of understanding [Zagzebski] |
| Full Idea: The present obsession with justification and the neglect of understanding has resulted in a feature of epistemology already criticised by several epistemologists: its atomism. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 2.2) | |
| A reaction: All analytic philosophy has become excessively atomic, because it relies too heavily on logic for its grounding and rigour. There are other sorts of rigour, such as AI, peer review, programming. Or rigour is an idle dream. |
| 20217 | Truth is valuable, but someone knowing the truth is more valuable [Zagzebski] |
| Full Idea: Of course we value the truth, but the value we place on knowledge is more than the value of the truth we thereby acquire. …It also involves a valuabe relation between the knower and the truth. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 1) | |
| A reaction: Hard to assess this. I take truth to be a successful relationship between a mind and a fact. Knowledge needs something extra, to avoid lucky true beliefs. Does a truth acquire greater and greater value as more people come to know it? Doubtful. |
| 20191 | Some beliefs are fairly voluntary, and others are not at all so [Zagzebski] |
| Full Idea: My position is that beliefs, like acts, arrange themselves on a continuum of degrees of voluntariness, ranging from quite a bit to none at all. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], I 4.2) | |
| A reaction: I'm sure we have no idea how we came to hold many of our beliefs, and if we see a cat, nothing seems to intervene between the seeing and the believing. But if you adopt a religion, believing its full creed is a big subsequent effort. |
| 20222 | Knowledge either aims at a quantity of truths, or a quality of understanding of truths [Zagzebski] |
| Full Idea: Getting knowledge can be a matter either of reaching more truths or of gaining understanding of truths already believed. So it may be a way of increasing either the quality of true belief (cognitive contact with reality) or the quantity. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 2.1) | |
| A reaction: I'm not sure how one would increase understanding of currently believed truths if it didn't involve adding some new truths to the collection. There is only the discovery of connections or structures, but those are new facts. |
| 20225 | For internalists Gettier situations are where internally it is fine, but there is an external mishap [Zagzebski] |
| Full Idea: In internalist theories the grounds for justification are accessible to the believer, and Gettier problems arise when there is nothing wrong with the internally accessible aspects of the situation, but there is a mishap inaccessible to the believer. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 3.1) | |
| A reaction: I'm sure we could construct an internal mishap which the believer was unaware of, such as two confusions of the meanings of words cancelling one another out. |
| 20226 | Gettier problems are always possible if justification and truth are not closely linked [Zagzebski] |
| Full Idea: As long as the concept of knowledge closely connects the justification component and the truth component but permits some degree of independence between them, justified true belief will never be sufficient for knowledge. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 3.1) | |
| A reaction: Out of context this sounds like an advertisement for externalism. Or maybe it just says we have to live with Gettier threats. Zagzebski has other strategies. |
| 20228 | We avoid the Gettier problem if the support for the belief entails its truth [Zagzebski] |
| Full Idea: The way to avoid the Gettier problem is to define knowledge in such a way that truth is entailed by the other component(s) of the definition. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 3.1) | |
| A reaction: Thus she defines virtuous justification as being successful, as virtues tend to be. This smacks of cheating. Surely we can be defeated in a virtuous way? If the truth is entailed then of course Gettier can be sent packing. |
| 20227 | Gettier cases arise when good luck cancels out bad luck [Zagzebski] |
| Full Idea: The procedure for generating Gettier cases involves 'double luck': an instance of good luck cancels out an instance of bad luck. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 3.2) | |
| A reaction: You can end up with the right answer in arithmetic if you make two mistakes rather than one. I'm picturing a life of one blundering error after another, which to an outsider seems to be going serenely well. |
| 20194 | Intellectual virtues are forms of moral virtue [Zagzebski] |
| Full Idea: I argue that intellectual virtues are forms of moral virtue. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II Intro) | |
| A reaction: This contrasts with Sosa, who seems to think intellectual virtues are just the most efficient ways of reaching the truth. I like Zabzebski's approach a lot, though we are in a very small minority. I love her book. We have epistemic and moral duties. |
| 20210 | A reliable process is no use without the virtues to make use of them [Zagzebski] |
| Full Idea: It is not enough that a process is reliable; a person will not reliably use such a process without certain virtues. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 4.1.2) | |
| A reaction: This is a point against Sosa's reliabilist account of virtues. Of course, all theories of epistemic justification (or of morality) will fail if people can't be bothered to implement them. |
| 20206 | Intellectual and moral prejudice are the same vice (and there are other examples) [Zagzebski] |
| Full Idea: Maybe the intellectual and the moral forms of prejudice are the same vice, and this may also be true of other traits with shared names, such as humility, autonomy, integrity, perseverance, courage and trustworthiness. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 3.1) | |
| A reaction: I find this claim very persuasive. The virtue of 'integrity' rather obviously embraces groups of both intellectually and morally desirable traits. |
| 20208 | We can name at least thirteen intellectual vices [Zagzebski] |
| Full Idea: Some examples of intellectual vices: pride, negligence, idleness, cowardice, conformity, carelessness, rigidity, prejudice, wishful thinking, closed-mindedness, insensitivity to detail, obtuseness (in seeing relevance), and lack of thoroughness. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 3.1) | |
| A reaction: There are thousands of vices for which we don't have names, like thinking about football when you should be doing metaphysics. The other way round is also a vice too, because football needs concentration. Discontent with your chair is bad too. |
| 20215 | A justified belief emulates the understanding and beliefs of an intellectually virtuous person [Zagzebski] |
| Full Idea: A justified belief is what a person who is motivated by intellectual virtue, and who has the understanding of his cognitive situation a virtuous person would have, might believe in like circumstances. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 6.1) | |
| A reaction: This is a whole-hearted definition of justification in terms of a theory of intellectual virtues. Presumably this would allow robots to have justified beliefs, if they managed to behave the way intellectually virtuous persons would behave. |
| 20187 | Epistemic perfection for reliabilism is a truth-producing machine [Zagzebski] |
| Full Idea: Just as a utility-calculating machine would be the ideal moral agent according to utilitarianism, a truth-producing machine would be the ideal epistemic agent according to reliabilism, | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], I 1.2) | |
| A reaction: Love this one! For consequentialists a successful robot is morally superior to an average human being. The reliabilist dream is just something that churns out truths. But what is the role of these truths in subsequent life? |
| 20218 | The self is known as much by its knowledge as by its action [Zagzebski] |
| Full Idea: It seems to me that the concept of the self is constituted as much by what we know as by what we do. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], III 1) | |
| A reaction: People take pride in what they know, which indicates that it is of central importance to a person's nature. Hard to evaluate ideas such as this. |
| 20205 | The feeling accompanying curiosity is neither pleasant nor painful [Zagzebski] |
| Full Idea: Most feelings are experienced as pleasant or painful, but it is not evident that they all are; curiosity may be one that is not. [note: 'curiosity' may not be the name of a feeling, but a feeling typically accompanies it] | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 3.1) | |
| A reaction: If a machine generates a sliding scale from pain to pleasure, is there a neutral feeling at the midpoint, or does all feeling briefly vanish there? Not sure. |
| 9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
| Full Idea: The current usage of 'abstract' simply means outside space and time, not concrete, not physical. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: This is in contrast to Idea 9609 (the older notion of being abstracted). It seems odd that our ancestors had a theory about where such ideas came from, but modern thinkers have no theory at all. Blame Frege for that. |
| 9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
| Full Idea: The older sense of 'abstract' applies to universals, where a universal like 'redness' is abstracted from red particulars; it is the one associated with the many. In mathematics, the notion of 'group' or 'vector space' perhaps fits this pattern. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: I am currently investigating whether this 'older' concept is in fact dead. It seems to me that it is needed, as part of cognitive science, and as the crucial link between a materialist metaphysic and the world of ideas. |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| Full Idea: In addition to the sense and reference of term, there is the 'computational' role. The name '2' has a sense (successor of 1) and a reference (the number 2). But the word 'two' has little computational power, Roman 'II' is better, and '2' is a marvel. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 6) | |
| A reaction: Very interesting, and the point might transfer to natural languages. Synonymous terms carry with them not just different expressive powers, but the capacity to play different roles (e.g. slang and formal terms, gob and mouth). |
| 20202 | Motives involve desires, but also how the desires connect to our aims [Zagzebski] |
| Full Idea: A motive does have an aspect of desire, but it includes something about why a state of affairs is desired, and that includes something about the way my emotions are tied to my aim. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 2.6) | |
| A reaction: It is standard usage that a 'motive' involves some movement towards achieving the desire, and not merely having the desire. I'd quite like to stand on top of Everest, but have absolutely no motivation to try to achieve it. |
| 20216 | Modern moral theory concerns settling conflicts, rather than human fulfilment [Zagzebski] |
| Full Idea: Modern ethics generally considers morality much less a system for fulfilling human nature than a set of principles for dealing with individuals in conflict. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 7) | |
| A reaction: Historically I associate this move with Hugo Grotius around 1620. He was a great legalist, and eudaimonist virtue ethics gradually turned into jurisprudence. The Enlightenment sought rules for resolving dilemmas. Liberalism makes fulfilment private. |
| 20193 | Moral luck means our praise and blame may exceed our control or awareness [Zagzebski] |
| Full Idea: Because of moral luck, the realm of the morally praiseworthy / blameworthy is not indisputably within one's voluntary control or accessible to one's consciousness. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], I 4.2) | |
| A reaction: [She particularly cites Thomas Nagel for this] It is a fact that we will be blamed (more strongly) when we have moral bad luck, but the question is whether we should be. It seems harsh, but you can't punish someone as if they had had bad luck. |
| 20199 | Nowadays we doubt the Greek view that the flourishing of individuals and communities are linked [Zagzebski] |
| Full Idea: Modern moral philosophers have been considerably more skeptical than were the ancient Greeks about the close association between the flourishing of the individual and that of the community. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 2.2) | |
| A reaction: I presume this is not just a change in fashion, but a reflection of how different the two societies are. In a close community with almost no privacy, flourishing individuals are good citizens. In the isolations of modern liberalism they may be irrelevant. |
| 20196 | Virtue theory is hopeless if there is no core of agreed universal virtues [Zagzebski] |
| Full Idea: An analysis of virtue is hopeless unless we can assume that most of a selected list of traits count as virtues, in a way not strictly culture. ...These would include wisdom, courage, benevolence, justice, honesty, loyalty, integrity, and generosity. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 2.1) | |
| A reaction: This requirement needs there to be a single core to human nature, right across the species. If we are infinitely flexible (as existentialists imply) then the virtues will have matching flexibility, and so will be parochial and excessively relative. |
| 20200 | A virtue must always have a corresponding vice [Zagzebski] |
| Full Idea: It is important for the nature of virtue that it have a corresponding vice (or two, in the doctrine of the mean). Claustrophobia is not a vice not only because it is involuntary, but also because there is no corresponding virtue. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 2.3) | |
| A reaction: Presumably attaining a virtue is an achievement, so we would expect a label for failure in the same field of endeavour. The failure is not purely negative, because bad things ensue if the virtue is not present. |
| 20201 | Eight marks distingush skills from virtues [Zagzebski, by PG] |
| Full Idea: The difference between skills and virtues is that virtues must be enacted, are always desirable, can't be forgotten, and can be simulated, whereas skills are very specific, involve a technique, lack contraries, and lack intrinsic value. | |
| From: report of Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 2.4) by PG - Db (ideas) | |
| A reaction: [my summary of her II 2.4 discussion of the differences] She observes that Aristotle made insufficient effort to distinguish the two. It may be obscure to say that virtues go 'deeper' than skills, but we all know what is meant. 'Skills serve virtues'. |
| 20203 | Virtues are deep acquired excellences of persons, which successfully attain desire ends [Zagzebski] |
| Full Idea: A virtue can be defined as 'a deep and enduring acquired excellence of a person, involving a characteristic motivation to produce a certain desired end and reliable success in bringing about that end'. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 2.7) | |
| A reaction: She puts this in bold, and it is the culminating definition of a long discussion. It rather obviously fails to say anything about the nature of the end that is desired. Learning the telephone book off by heart seems to fit the definition. |
| 20207 | Every moral virtue requires a degree of intelligence [Zagzebski] |
| Full Idea: Being reasonably intelligent within a certain area of life is part of having almost any moral virtue. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 3.1) | |
| A reaction: The fact that this bars persons of very limited intelligence from acquiring the Aristotelian virtues is one of the attractions of the Christian enjoinder to merely achieve 'love'. Anyone can have a warm heart. So is virtue elitist? |
| 20214 | Virtue theory can have lots of rules, as long as they are grounded in virtues and in facts [Zagzebski] |
| Full Idea: A pure virtue theory can have as many rules as you like as long as they are understood as grounded in the virtuous motivations and understanding of the nonmoral facts that virtuous agents possess. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 6.1) | |
| A reaction: It is important, I think, to see that a virtue theorist does not have to be a particularist. |
| 20213 | We need phronesis to coordinate our virtues [Zagzebski] |
| Full Idea: We need phronesis (practical wisdom) to coordinate the various virtues into a single line of action or line of thought leading up to an act or to a belief. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 5.2) | |
| A reaction: If I have a conflicting virtue and vice in a single situation, something must make sure that the virtue dominates. That sounds more like Kant's 'good will' than like phronesis. |
| 20209 | For the virtue of honesty you must be careful with the truth, and not just speak truly [Zagzebski] |
| Full Idea: It is not sufficient for honesty that a person tells whatever she happens to believe is the truth. An honest person is careful with the truth. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 3.2) | |
| A reaction: Not sure about that. It matches what Aristotle says about courage, which also needs practical reason [phronesis]. But being sensitive and careful with truth seems to need other virtues. If total honesty is not a virtue, then is honesty a virtue at all? |
| 20197 | The courage of an evil person is still a quality worth having [Zagzebski] |
| Full Idea: In the case of a courageous Nazi soldier, my position is that a virtue is worth having even in those cases in which it makes a person worse overall. | |
| From: Linda Trinkaus Zagzebski (Virtues of the Mind [1996], II 2.2) | |
| A reaction: A brave claim, which seems right. If a nasty Nazi reforms, they will at least have one good quality which can be put to constructive use. |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| Full Idea: There seem to be no actual infinites in the physical realm. Given the correctness of atomism, there are no infinitely small things, no infinite divisibility. And General Relativity says that the universe is only finitely large. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5) | |
| A reaction: If time was infinite, you could travel round in a circle forever. An atom has size, so it has a left, middle and right to it. Etc. They seem to be physical, so we will count those too. |