48 ideas
| 1848 | We are coerced into assent to a truth by reason's violence [Aquinas] |
| Full Idea: We are coerced into assent to a truth by reason's violence. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.10) |
| 1858 | The mind is compelled by necessary truths, but not by contingent truths [Aquinas] |
| Full Idea: Mind is compelled by necessary truths that can't be regarded as false, but not by contingent ones that might be false. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 12) |
| 1852 | For the mind Good is one truth among many, and Truth is one good among many [Aquinas] |
| Full Idea: Good itself as taken in by mind is one truth among others, and truth itself as goal of mind's activity is one good among others. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply) |
| 9672 | Free logic is one of the few first-order non-classical logics [Priest,G] |
| Full Idea: Free logic is an unusual example of a non-classical logic which is first-order. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], Pref) |
| 9697 | X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G] |
| Full Idea: X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets, the set of all the n-tuples with its first member in X1, its second in X2, and so on. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.0) |
| 9685 | <a,b&62; is a set whose members occur in the order shown [Priest,G] |
| Full Idea: <a,b> is a set whose members occur in the order shown; <x1,x2,x3, ..xn> is an 'n-tuple' ordered set. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10) |
| 9675 | a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G] |
| Full Idea: a ∈ X means that a is a member of the set X, that is, a is one of the objects in X. a ∉ X indicates that a is not in X. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
| 9674 | {x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G] |
| Full Idea: {x; A(x)} indicates a set of objects which satisfy the condition A(x). | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
| 9673 | {a1, a2, ...an} indicates that a set comprising just those objects [Priest,G] |
| Full Idea: {a1, a2, ...an} indicates that the set comprises of just those objects. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
| 9677 | Φ indicates the empty set, which has no members [Priest,G] |
| Full Idea: Φ indicates the empty set, which has no members | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4) |
| 9676 | {a} is the 'singleton' set of a (not the object a itself) [Priest,G] |
| Full Idea: {a} is the 'singleton' set of a, not to be confused with the object a itself. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4) |
| 9679 | X⊂Y means set X is a 'proper subset' of set Y [Priest,G] |
| Full Idea: X⊂Y means set X is a 'proper subset' of set Y (if and only if all of its members are members of Y, but some things in Y are not in X) | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
| 9678 | X⊆Y means set X is a 'subset' of set Y [Priest,G] |
| Full Idea: X⊆Y means set X is a 'subset' of set Y (if and only if all of its members are members of Y). | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
| 9681 | X = Y means the set X equals the set Y [Priest,G] |
| Full Idea: X = Y means the set X equals the set Y, which means they have the same members (i.e. X⊆Y and Y⊆X). | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
| 9683 | X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G] |
| Full Idea: X ∩ Y indicates the 'intersection' of sets X and Y, which is a set containing just those things that are in both X and Y. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
| 9682 | X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G] |
| Full Idea: X ∪ Y indicates the 'union' of sets X and Y, which is a set containing just those things that are in X or Y (or both). | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
| 9684 | Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G] |
| Full Idea: Y - X indicates the 'relative complement' of X with respect to Y, that is, all the things in Y that are not in X. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
| 9694 | The 'relative complement' is things in the second set not in the first [Priest,G] |
| Full Idea: The 'relative complement' of one set with respect to another is the things in the second set that aren't in the first. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
| 9693 | The 'intersection' of two sets is a set of the things that are in both sets [Priest,G] |
| Full Idea: The 'intersection' of two sets is a set containing the things that are in both sets. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
| 9692 | The 'union' of two sets is a set containing all the things in either of the sets [Priest,G] |
| Full Idea: The 'union' of two sets is a set containing all the things in either of the sets | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
| 9698 | The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G] |
| Full Idea: The 'induction clause' says that whenever one constructs more complex formulas out of formulas that have the property P, the resulting formulas will also have that property. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.2) |
| 9688 | A 'singleton' is a set with only one member [Priest,G] |
| Full Idea: A 'singleton' is a set with only one member. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4) |
| 9687 | A 'member' of a set is one of the objects in the set [Priest,G] |
| Full Idea: A 'member' of a set is one of the objects in the set. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
| 9695 | An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G] |
| Full Idea: An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10) |
| 9696 | A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets [Priest,G] |
| Full Idea: A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10) |
| 9686 | A 'set' is a collection of objects [Priest,G] |
| Full Idea: A 'set' is a collection of objects. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
| 9689 | The 'empty set' or 'null set' has no members [Priest,G] |
| Full Idea: The 'empty set' or 'null set' is a set with no members. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4) |
| 9690 | A set is a 'subset' of another set if all of its members are in that set [Priest,G] |
| Full Idea: A set is a 'subset' of another set if all of its members are in that set. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
| 9691 | A 'proper subset' is smaller than the containing set [Priest,G] |
| Full Idea: A set is a 'proper subset' of another set if some things in the large set are not in the smaller set | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
| 9680 | The empty set Φ is a subset of every set (including itself) [Priest,G] |
| Full Idea: The empty set Φ is a subset of every set (including itself). | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
| 22049 | Transcendental idealism aims to explain objectivity through subjectivity [Bowie] |
| Full Idea: The aim of transcendental idealism is to give a basis for objectivity in terms of subjectivity. | |
| From: Andrew Bowie (German Philosophy: a very short introduction [2010], 1) | |
| A reaction: Hume used subjectivity to undermine the findings of objectivity. There was then no return to naive objectivity. Kant's aim then was to thwart global scepticism. Post-Kantians feared that he had failed. |
| 22055 | The Idealists saw the same unexplained spontaneity in Kant's judgements and choices [Bowie] |
| Full Idea: The Idealist saw in Kant that knowledge, which depends on the spontaneity of judgement, and self-determined spontaneous action, can be seen as sharing the same source, which is not accessible to scientific investigation. | |
| From: Andrew Bowie (German Philosophy: a very short introduction [2010]) | |
| A reaction: This is the 'spontaneity' of judgements and choices which was seen as the main idea in Kant. It inspired romantic individualism. The judgements are the rule-based application of concepts. |
| 22054 | German Idealism tried to stop oppositions of appearances/things and receptivity/spontaneity [Bowie] |
| Full Idea: A central aim of German Idealism is to overcome Kant's oppositions between appearances and thing in themselves, and between receptivity and spontaneity. | |
| From: Andrew Bowie (German Philosophy: a very short introduction [2010], 2) | |
| A reaction: I have the impression that there were two strategies: break down the opposition within the self (Fichte), or break down the opposition in the world (Spinozism). |
| 22056 | Crucial to Idealism is the idea of continuity between receptivity and spontaneous judgement [Bowie] |
| Full Idea: A crucial idea for German Idealism (from Hamann) is that apparently passive receptivity and active spontaneity are in fact different degrees of the same 'activity, and the gap between subject and world can be closed. | |
| From: Andrew Bowie (German Philosophy: a very short introduction [2010], 3) | |
| A reaction: The 'passive' bit seems to be Hume's 'impressions', which are Kant's 'intuitions', which need 'spontaneous' interpretation to become experiences. Critics of Kant said this implied a dualism. |
| 1860 | Knowledge may be based on senses, but we needn't sense all our knowledge [Aquinas] |
| Full Idea: All our knowledge comes through our senses, but that doesn't mean that everything we know is sensed. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 18) |
| 1855 | If we saw something as totally and utterly good, we would be compelled to will it [Aquinas] |
| Full Idea: Something apprehended to be good and appropriate in any and every circumstance that could be thought of would compel us to will it. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply) |
| 1856 | Nothing can be willed except what is good, but good is very varied, and so choices are unpredictable [Aquinas] |
| Full Idea: Nothing can be willed except good, but many and various things are good, and you can't conclude from this that wills are compelled to choose this or that one. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 05) |
| 1862 | However habituated you are, given time to ponder you can go against a habit [Aquinas] |
| Full Idea: However habituated you are, given time to ponder you can go against a habit. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 24) |
| 1849 | Since will is a reasoning power, it can entertain opposites, so it is not compelled to embrace one of them [Aquinas] |
| Full Idea: Reasoning powers can entertain opposite objects. Now will is a reasoning power, so will can entertain opposites and is not compelled to embrace one of them. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.x2) |
| 1861 | The will is not compelled to move, even if pleasant things are set before it [Aquinas] |
| Full Idea: The will is not compelled to move, for it doesn't have to want the pleasant things set before it. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 21) |
| 1853 | Because the will moves by examining alternatives, it doesn't compel itself to will [Aquinas] |
| Full Idea: Because will moves itself by deliberation - a kind of investigation which doesn't prove some one way correct but examines the alternatives - will doesn't compel itself to will. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply) |
| 1854 | We must admit that when the will is not willing something, the first movement to will must come from outside the will [Aquinas] |
| Full Idea: We are forced to admit that, in any will that is not always willing, the very first movement to will must come from outside, stimulating the will to start willing. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply) | |
| A reaction: cf Nietzsche |
| 1847 | The will must aim at happiness, but can choose the means [Aquinas] |
| Full Idea: The will is compelled by its ultimate goal (to achieve happiness), but not by the means to achieve it. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.07) |
| 1857 | We don't have to will even perfect good, because we can choose not to think of it [Aquinas] |
| Full Idea: The will can avoid actually willing something by avoiding thinking of it, since mental activity is subject to will. In this respect we aren't compelled to will even total happiness, which is the only perfect good. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 07) |
| 1846 | The will can only want what it thinks is good [Aquinas] |
| Full Idea: Will's object is what is good, and so it cannot will anything but what is good. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.06) |
| 1850 | Without free will not only is ethical action meaningless, but also planning, commanding, praising and blaming [Aquinas] |
| Full Idea: If we are not free to will in any way, but are compelled, everything that makes up ethics vanishes: pondering action, exhorting, commanding, punishing, praising, condemning. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply) | |
| A reaction: If doesn't require some magical 'free will' to avoid compulsions. All that is needed is freedom to enact your own willing, rather than someone else's. |
| 1851 | Good applies to goals, just as truth applies to ideas in the mind [Aquinas] |
| Full Idea: Good applies to all goals, just as truth applies to all forms mind takes in. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply) | |
| A reaction: In danger of being tautological, if good is understood as no more than the goal of actions. It seems perfectly possibly to pursue a wicked end, and perhaps feel guilty about it. |
| 1859 | Even a sufficient cause doesn't compel its effect, because interference could interrupt the process [Aquinas] |
| Full Idea: Even a sufficient cause doesn't always compel its effect, since it can sometimes be interfered with so that its effect doesn't happen | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 15) |