39 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 5806 | Belief is the power of metarepresentation [Dretske] |
| Full Idea: Belief is the power of metarepresentation. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2.3) | |
| A reaction: Hm. I have always defined belief as 'commitment to truth', and this definition leaves out both parts. Where is the commitment? If hope is another metarepresentation, how does it differ from belief? I imagine things, not believing them to be true. |
| 5801 | A mouse hearing a piano played does not believe it, because it lacks concepts and understanding [Dretske] |
| Full Idea: A mouse can see and hear a piano being played, but believing is something else; it requires the concept of a piano, and understanding. Mice who hear pianos being played do not believe pianos are being played. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §1.3) | |
| A reaction: Are we to say that when a mouse hears a piano it has no beliefs at all? Might not a belief involve images, so that a mouse calls up appropriate images from previous experiences, which are in a grey area on the edge of belief? |
| 5802 | Representations are in the head, but their content is not, as stories don't exist in their books [Dretske] |
| Full Idea: Representations are in the head, but their content is not; in this sense, the mind isn't in the head any more than stories (i.e. story contents) are in books. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §1.6) | |
| A reaction: This is the final consequence of Putnam's idea that meanings ain't in the head. Intentionality is an extraordinary bridge between the brain and the external world. The ontology of stories, and musical compositions, is one philosophy's deepest problems. |
| 5809 | Some activities are performed better without consciousness of them [Dretske] |
| Full Idea: Some tasks (playing the piano, speaking foreign languages, playing fast sports) are best performed when the agent is largely unconscious of the details. | |
| From: Fred Dretske (Naturalizing the Mind [1997], Ch.4 n16) | |
| A reaction: A significant point, but it supports the evolutionary view, which is that what matters is success, and consciousness will switch on or off, whichever promotes the activity best. |
| 5808 | Qualia are just the properties objects are represented as having [Dretske] |
| Full Idea: The Representational Thesis of mind identifies the qualities of experience - qualia - with the properties objects are represented as having. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §3.2) | |
| A reaction: This seems to challenge the distinction between primary and secondary qualities, of which I am very fond. Is 'looks beautiful' a property of an object? Is the feeling of anger a property of an object? Qualia are properties of brains? |
| 5807 | Introspection is the same as the experience one is introspecting [Dretske] |
| Full Idea: Introspection has no phenomenology or, if it does, it always has the same phenomenology as the experience one is introspecting. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2.4) | |
| A reaction: There is a difference between looking at a tree, and being aware of yourself looking at a tree. You can be faintly depressed, and then become aware that you are faintly depressed. He is nearly right. |
| 5803 | In a representational theory of mind, introspection is displaced perception [Dretske] |
| Full Idea: On a representational theory of the mind, introspection becomes an instance of displaced perception - knowledge of internal (mental) facts via an awareness of external (physical) objects. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2) | |
| A reaction: This sounds close to a behaviourist (e.g. Ryle) account of introspection, via observing one's own behaviour. The word 'displaced' is an easy one, concealing a multitude of questions. |
| 5805 | Introspection does not involve looking inwards [Dretske] |
| Full Idea: The 'problem' of introspection evaporates once one understands that it is not a process in which one looks inward. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2) | |
| A reaction: I take it that when we introspect we look at the contents of thoughts, which are representations of the external world, on the whole. But surely only the connections of those contents with memories can be seen inwardly? |
| 5804 | A representational theory of the mind is an externalist theory of the mind [Dretske] |
| Full Idea: A representational theory of the mind is an externalist theory of the mind. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2) | |
| A reaction: Presumably brain events bring the world into the mind, so the world must be mentioned in explaining the mind. Maybe 'externalism' sounds grand, but is stating the boringly obvious. Explanations of mind need no mention of external particulars. |
| 5800 | All mental facts are representation, which consists of informational functions [Dretske] |
| Full Idea: My thesis is that all mental facts are representational facts, and that all representational facts are facts about informational functions. | |
| From: Fred Dretske (Naturalizing the Mind [1997], Prol) | |
| A reaction: The first half of the thesis seems a bit difficult to disagree with, but that a fact is 'represented' may not be the essence of that fact. The biggest mystery is the content, not its representation. And everything is 'information' about everything else. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |