84 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] |
13689 | 'Theorems' are formulas provable from no premises at all [Sider] |
13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
13711 | System B introduces iterated modalities [Sider] |
13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider] |
13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider] |
13714 | We can treat modal worlds as different times [Sider] |
13720 | Converse Barcan Formula: □∀αφ→∀α□φ [Sider] |
13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider] |
13723 | System B is needed to prove the Barcan Formula [Sider] |
13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
13680 | Maybe logical consequence is a primitive notion [Sider] |
13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider] |
13700 | A 'total' function must always produce an output for a given domain [Sider] |
13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
13688 | Good axioms should be indisputable logical truths [Sider] |
13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
13685 | Natural deduction helpfully allows reasoning with assumptions [Sider] |
13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |
13697 | Valuations in PC assign truth values to formulas relative to variable assignments [Sider] |
13684 | The semantical notion of a logical truth is validity, being true in all interpretations [Sider] |
13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider] |
13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider] |
13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider] |
13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
13683 | A relation is a feature of multiple objects taken together [Sider] |
13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
13709 | Logical truths must be necessary if anything is [Sider] |
13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider] |
13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider] |
13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider] |
20223 | Epistemology is excessively atomic, by focusing on justification instead of understanding [Zagzebski] |
20188 | Modern epistemology is too atomistic, and neglects 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] |
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] |
20210 | A reliable process is no use without the virtues to make use of them [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] |
20207 | Every moral virtue requires a degree of intelligence [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] |
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] |
6613 | The natural kinds are objects, processes and properties/relations [Ellis] |
6616 | Least action is not a causal law, but a 'global law', describing a global essence [Ellis] |
6615 | A species requires a genus, and its essence includes the essence of the genus [Ellis] |
6614 | A hierarchy of natural kinds is elaborate ontology, but needed to explain natural laws [Ellis] |
6612 | Without general principles, we couldn't predict the behaviour of dispositional properties [Ellis] |