44 ideas
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 21812 | Being is the product of pure intellect [Plotinus] |
| Full Idea: Intellectual-Principle [Nous] by its intellective act establishes Being. | |
| From: Plotinus (The Enneads [c.245], 5.1.04) | |
| A reaction: This is a surprising view - that there is something which is prior to Being - but I take it to be Plotinus giving primacy to Plato's Form of the Good (a pure ideal), ahead of the One of Parmenides (which is Being). |
| 21817 | The One does not exist, but is the source of all existence [Plotinus] |
| Full Idea: The First is no member of existence, but can be the source of all. | |
| From: Plotinus (The Enneads [c.245], 5.1.07) | |
| A reaction: The First is the One, and this explicitly denies that it has Being. This answers the self-predication problem of Forms. Plato thought the Form of the Beautiful was beautiful, but it can't be (because of the regress). The source of existence can't exist. |
| 21824 | The One is a principle which transcends Being [Plotinus] |
| Full Idea: There exists a principle which transcends Being; this the One. | |
| From: Plotinus (The Enneads [c.245], 5.1.10) | |
| A reaction: The idea that the One transcends Being is the distinctive Plotinus doctrine. He defends the view that this was also the view of Anaxagoras, Empedocles and Plato. |
| 21813 | Number determines individual being [Plotinus] |
| Full Idea: Number is the determinant of individual being. | |
| From: Plotinus (The Enneads [c.245], 5.1.05) | |
| A reaction: You might have thought that number was the consequence of the individualities (or units) within being, but not so. You can't get more platonic than saying that the idealised numbers are the source of the particular units. |
| 18284 | Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper] |
| Full Idea: Whereas particular reality statements are in principle completely verifiable or falsifiable, things are different for general reality statements: they can indeed be conclusively falsified, they can acquire a negative truth value, but not a positive one. | |
| From: Karl Popper (Two Problems of Epistemology [1932], p.256), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 18 'Laws' | |
| A reaction: This sounds like a logician's approach to science, but I prefer to look at coherence, where very little is actually conclusive, and one tinkers with the theory instead. |
| 5506 | If soul was like body, its parts would be separate, without communication [Plotinus] |
| Full Idea: If the soul had the nature of the body, it would have isolated members each unaware of the condition of the other;..there would be a particular soul as a distinct entity to each local experience, so a multiplicity of souls would administer an individual. | |
| From: Plotinus (The Enneads [c.245], 4.2.2), quoted by R Martin / J Barresi - Introduction to 'Personal Identity' p.15 | |
| A reaction: Of course, the modern 'modularity of mind' theory does suggest that we are run by a team, but a central co-ordinator is required, with a full communication network across the modules. |
| 21827 | The movement of Soul is continuous, but we are only aware of the parts of it that are sensed [Plotinus] |
| Full Idea: The Soul maintains its unfailing movement; for not all that passes in the soul is, by that fact, perceptible; we know just as much as impinges on the faculty of the sense. | |
| From: Plotinus (The Enneads [c.245], 5.1.12) | |
| A reaction: This is a straightforward argument in favour of an unconscious aspect to the mind - and a rather good argument too. No one thinks that our minds ever stop working, even in sleep. |
| 21828 | A person is the whole of their soul [Plotinus] |
| Full Idea: Man is not merely a part (the higher part) of the Soul but the total. | |
| From: Plotinus (The Enneads [c.245], 5.1.12) | |
| A reaction: The soul is psuche, which includes the vegetative soul. The higher part is normally taken to be reason. This seems pretty close to John Locke's view of the matter. |
| 21809 | Our soul has the same ideal nature as the oldest god, and is honourable above the body [Plotinus] |
| Full Idea: Our own soul is of that same ideal nature [as the oldest god of them all], so that to consider it, purified, freed from all accruement, is to recognise in ourselves which we have found soul to be, honourable above the body. For what is body but earth? | |
| From: Plotinus (The Enneads [c.245], 5.1.02) | |
| A reaction: The strongest versions of substance dualism are religious in character, because the separateness of the mind elevates us above the grubby physical character of the world. I'm with Nietzsche on this one - this view is actually harmful to us. |
| 21825 | The soul is outside of all of space, and has no connection to the bodily order [Plotinus] |
| Full Idea: We may not seek any point in space in which to seat the soul; it must be set outside of all space; its distinct quality, its separateness, its immateriality, demand that it be a thing alone, untouched by all of the bodily order. | |
| From: Plotinus (The Enneads [c.245], 5.1.10) | |
| A reaction: You can't get more dualist than that. He doesn't seem bothered about the interaction problem. He likens such influence to the radiation of the sun, rather than to physical movement. |
| 21826 | The Soul reasons about the Right, so there must be some permanent Right about which it reasons [Plotinus] |
| Full Idea: Since there is a Soul which reasons upon the right and good - for reasoning is an enquiry into the rightness and goodness of this rather than that - there must exist some pemanent Right, the source and foundation of this reasoning in our soul. | |
| From: Plotinus (The Enneads [c.245], 5.1.11) | |
| A reaction: This is pretty close the Kant's concept of 'the moral order within me', and Plotinus even sees it as rational. Presumably this right is 'permanent' because the revelatlons of reason about it are necessary truths. |
| 6922 | Ecstasy is for the neo-Platonist the highest psychological state of man [Plotinus, by Feuerbach] |
| Full Idea: Ecstasy or rapture is for the neo-Platonist the highest psychological state of man. | |
| From: report of Plotinus (The Enneads [c.245]) by Ludwig Feuerbach - Principles of Philosophy of the Future §29 | |
| A reaction: See Bernini's statue of St Theresa. Personally I find this very unappealing because of its utter irrationality, but what is the 'highest' human psychological state? Doing mental arithmetic? Doing what is morally right? Dignity under pressure? |
| 21815 | Because the One is immobile, it must create by radiation, light the sun producing light [Plotinus] |
| Full Idea: Given this immobility of the Supreme ...what happened then? It must be a circumradiation, which may be compared to the brilliant light encircling the sun and ceaselessly generating from that unchanging substance, | |
| From: Plotinus (The Enneads [c.245], 5.1.06) | |
| A reaction: This is the answer given to the problem raised in Idea 21814. The sun produces energy, without apparent movement. Not an answer that will satisfy a physicist, but an interesting answer. |
| 21816 | Soul is the logos of Nous, just as Nous is the logos of the One [Plotinus] |
| Full Idea: The soul is an utterance [logos] and act of the Intellectual-Principle [Nous], as that is an utterance and act of the One. | |
| From: Plotinus (The Enneads [c.245], 5.1.06) | |
| A reaction: Being only comes into the picture at the secondary Nous stage. Nous is the closest to the modern concept of God. |
| 21814 | How can multiple existence arise from the unified One? [Plotinus] |
| Full Idea: The problem endlessly debated is how, from such a unity as we have declared the One to be, does anything at all come into substantial existence, any multiplicity, dyad or number? | |
| From: Plotinus (The Enneads [c.245], 5.1.06) | |
| A reaction: This was precisely Aristotle's objection to the One of Parmenides, and especially the problem of the source of movement (which Plotinus also notices). |
| 21808 | Soul is author of all of life, and of the stars, and it gives them law and movement [Plotinus] |
| Full Idea: Soul is the author of all living things, ...it has breathed life into them all, whatever is nourished by earth and sea, the divine stars in the sky; ...it is the principle distinct from all of these to which it gives law and movement and life. | |
| From: Plotinus (The Enneads [c.245], 5.1.02) | |
| A reaction: This seems to derive from Anaxagoras, who is mentioned by Plotinus. The soul he refers to his not the same as our concept of God. Note the word 'law', which I am guessing is nomos. Not, I think, modern laws of nature, but closer to guidelines. |
| 21811 | Even the soul is secondary to the Intellectual-Principle [Nous], of which soul is an utterance [Plotinus] |
| Full Idea: Soul, for all the worth we have shown to belong to it, is yet a secondary, an image of the Intellectual-Principle [Nous]; reason uttered is an image of reason stored within the soul, and similarly soul is an utterance of the Intellectual-Principle. | |
| From: Plotinus (The Enneads [c.245], 5.1.03) | |
| A reaction: It then turns out that Nous is secondary to the One, so there is a hierarchy of Being (which only enters at the Nous stage). |