80 ideas
| 20186 | Unlike knowledge, wisdom cannot be misused [Zagzebski] |
| 19694 | Wisdom is the property of a person, not of their cognitive state [Zagzebski, by Whitcomb] |
| 20221 | Precision is only one of the virtues of a good definition [Zagzebski] |
| 20220 | Objection by counterexample is weak, because it only reveals inaccuracies in one theory [Zagzebski] |
| 9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
| 9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
| 9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
| 9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
| 13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |
| 13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn] |
| 9734 | Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn] |
| 9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
| 9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
| 9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn] |
| 13149 | S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn] |
| 13141 | Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn] |
| 13138 | Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn] |
| 13142 | Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn] |
| 13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
| 13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn] |
| 13146 | B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn] |
| 13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn] |
| 9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
| 13137 | Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn] |
| 13140 | Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn] |
| 13139 | Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn] |
| 13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn] |
| 9742 | The system K has no accessibility conditions [Fitting/Mendelsohn] |
| 13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
| 9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9744 | The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9746 | The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn] |
| 9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9748 | System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
| 13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
| 13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
| 13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
| 13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
| 13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 13725 | □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn] |
| 13731 | Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn] |
| 13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
| 20188 | Modern epistemology is too atomistic, and neglects understanding [Zagzebski] |
| 20223 | Epistemology is excessively atomic, by focusing on justification instead of understanding [Zagzebski] |
| 20217 | Truth is valuable, but someone knowing the truth is more valuable [Zagzebski] |
| 20191 | Some beliefs are fairly voluntary, and others are not at all so [Zagzebski] |
| 20222 | Knowledge either aims at a quantity of truths, or a quality of understanding of truths [Zagzebski] |
| 20225 | For internalists Gettier situations are where internally it is fine, but there is an external mishap [Zagzebski] |
| 20226 | Gettier problems are always possible if justification and truth are not closely linked [Zagzebski] |
| 20228 | We avoid the Gettier problem if the support for the belief entails its truth [Zagzebski] |
| 20227 | Gettier cases arise when good luck cancels out bad luck [Zagzebski] |
| 20194 | Intellectual virtues are forms of moral virtue [Zagzebski] |
| 20210 | A reliable process is no use without the virtues to make use of them [Zagzebski] |
| 20206 | Intellectual and moral prejudice are the same vice (and there are other examples) [Zagzebski] |
| 20208 | We can name at least thirteen intellectual vices [Zagzebski] |
| 20215 | A justified belief emulates the understanding and beliefs of an intellectually virtuous person [Zagzebski] |
| 20187 | Epistemic perfection for reliabilism is a truth-producing machine [Zagzebski] |
| 20218 | The self is known as much by its knowledge as by its action [Zagzebski] |
| 20205 | The feeling accompanying curiosity is neither pleasant nor painful [Zagzebski] |
| 20202 | Motives involve desires, but also how the desires connect to our aims [Zagzebski] |
| 20216 | Modern moral theory concerns settling conflicts, rather than human fulfilment [Zagzebski] |
| 20193 | Moral luck means our praise and blame may exceed our control or awareness [Zagzebski] |
| 20199 | Nowadays we doubt the Greek view that the flourishing of individuals and communities are linked [Zagzebski] |
| 20196 | Virtue theory is hopeless if there is no core of agreed universal virtues [Zagzebski] |
| 20200 | A virtue must always have a corresponding vice [Zagzebski] |
| 20201 | Eight marks distingush skills from virtues [Zagzebski, by PG] |
| 20203 | Virtues are deep acquired excellences of persons, which successfully attain desire ends [Zagzebski] |
| 20207 | Every moral virtue requires a degree of intelligence [Zagzebski] |
| 20214 | Virtue theory can have lots of rules, as long as they are grounded in virtues and in facts [Zagzebski] |
| 20213 | We need phronesis to coordinate our virtues [Zagzebski] |
| 20209 | For the virtue of honesty you must be careful with the truth, and not just speak truly [Zagzebski] |
| 20197 | The courage of an evil person is still a quality worth having [Zagzebski] |
| 1868 | The world was made as much for animals as for man [Celsus] |
| 1867 | Christians presented Jesus as a new kind of logos to oppose that of the philosophers [Celsus] |