70 ideas
6814 | Instead of prayer and charity, sinners pursue vain disputes and want their own personal scripture [Mohammed] |
11051 | Frege's logical approach dominates the analytical tradition [Hanna] |
11054 | Scientism says most knowledge comes from the exact sciences [Hanna] |
11070 | 'Denying the antecedent' fallacy: φ→ψ, ¬φ, so ¬ψ [Hanna] |
11071 | 'Affirming the consequent' fallacy: φ→ψ, ψ, so φ [Hanna] |
11088 | We can list at least fourteen informal fallacies [Hanna] |
11059 | Circular arguments are formally valid, though informally inadmissible [Hanna] |
11089 | Formally, composition and division fallacies occur in mereology [Hanna] |
17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
17765 | Propositional language can only relate statements as the same or as different [Walicki] |
17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
11058 | Logic is explanatorily and ontologically dependent on rational animals [Hanna] |
11072 | Logic is personal and variable, but it has a universal core [Hanna] |
11061 | Intensional consequence is based on the content of the concepts [Hanna] |
17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
17754 | Inductive proof depends on the choice of the ordering [Walicki] |
11063 | Logicism struggles because there is no decent theory of analyticity [Hanna] |
11055 | Supervenience can add covariation, upward dependence, and nomological connection [Hanna] |
11083 | A sentence is necessary if it is true in a set of worlds, and nonfalse in the other worlds [Hanna] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
11086 | Metaphysical necessity can be 'weak' (same as logical) and 'strong' (based on essences) [Hanna] |
11084 | Logical necessity is truth in all logically possible worlds, because of laws and concepts [Hanna] |
11085 | Nomological necessity is truth in all logically possible worlds with our laws [Hanna] |
11077 | Intuition includes apriority, clarity, modality, authority, fallibility and no inferences [Hanna] |
11080 | Intuition is more like memory, imagination or understanding, than like perception [Hanna] |
11078 | Intuition is only outside the 'space of reasons' if all reasons are inferential [Hanna] |
11053 | Explanatory reduction is stronger than ontological reduction [Hanna] |
11081 | Imagination grasps abstracta, generates images, and has its own correctness conditions [Hanna] |
11082 | Should we take the 'depictivist' or the 'descriptivist/propositionalist' view of mental imagery? [Hanna] |
11067 | Rational animals have a normative concept of necessity [Hanna] |
11068 | One tradition says talking is the essence of rationality; the other says the essence is logic [Hanna] |
11047 | Hegelian holistic rationality is the capacity to seek coherence [Hanna] |
11048 | Humean Instrumental rationality is the capacity to seek contingent truths [Hanna] |
11046 | Kantian principled rationality is recognition of a priori universal truths [Hanna] |
11045 | Most psychologists are now cognitivists [Hanna] |
6823 | Repay evil with good and your enemies will become friends (though this is hard) [Mohammed] |
6828 | You may break off a treaty if you fear treachery from your ally [Mohammed] |
6826 | Allah rewards those who are devout, sincere, patient, humble, charitable, chaste, and who fast [Mohammed] |
6822 | Those who avenge themselves when wronged incur no guilt [Mohammed] |
6833 | Punish theft in men or women by cutting off their hands [Mohammed] |
6825 | Do not kill except for a just cause [Mohammed] |
6832 | Killing a human, except as just punishment, is like killing all mankind [Mohammed] |
6811 | Allah is lord of creation, compassionate, merciful, king of judgement-day [Mohammed] |
6819 | True believers see that Allah made the night for rest and the day to give light [Mohammed] |
6818 | Allah cannot have begotten a son, as He is self-sufficient [Mohammed] |
6829 | There shall be no compulsion in religion [Mohammed] |
6834 | Unbelievers try to interpret the ambiguous parts of the Koran, simply to create dissension [Mohammed] |
6817 | The Koran is certainly composed by Allah; no one could compose a chapter like it [Mohammed] |
6824 | Do not split into sects, exulting in separate beliefs [Mohammed] |
6821 | I created mankind that it might worship Me [Mohammed] |
6815 | Be patient with unbelievers, and leave them to the judgement of Allah [Mohammed] |
6831 | He that kills a believer by design shall burn in Hell for ever [Mohammed] |
6827 | Make war on the unbelievers until Allah's religion reigns supreme [Mohammed] |
6820 | The righteous shall dwell on couches in gardens, wedded to dark-eyed houris [Mohammed] |
6812 | Heaven will be reclining on couches, eating fruit, attended by virgins [Mohammed] |
6830 | Unbelievers will have their skin repeatedly burned off in hell [Mohammed] |
6816 | The unbelievers shall drink boiling water [Mohammed] |