36 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) |
| 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) |
| 16422 | The necessity of a proposition concerns reality, not our words or concepts [Stalnaker] |
| Full Idea: The necessity or contingency of a proposition has nothing to do with our concepts or the meanings of our words. The possibilities would have been the same even if we had never conceived of them. | |
| From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 1) | |
| A reaction: This sounds in need of qualification, since some of the propositions will be explicitly about words and concepts. Still, I like this idea. |
| 16423 | Conceptual possibilities are metaphysical possibilities we can conceive of [Stalnaker] |
| Full Idea: Conceptual possibilities are just (metaphysical) possibilities that we can conceive of. | |
| From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 1) |
| 16421 | Critics say there are just an a priori necessary part, and an a posteriori contingent part [Stalnaker] |
| Full Idea: Critics say there are no irreducible a posteriori truths. They can be factored into a part that is necessary, but knowable a priori through conceptual analysis, and a part knowable only a posteriori, but contingent. 2-D semantics makes this precise. | |
| From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 1) | |
| A reaction: [Critics are Sidelle, Jackson and Chalmers] Interesting. If gold is necessarily atomic number 79, or it wouldn't be gold, that sounds like an analytic truth about gold. Discovering the 79 wasn't a discovery of a necessity. Stalnaker rejects this idea. |
| 16429 | A 'centred' world is an ordered triple of world, individual and time [Stalnaker] |
| Full Idea: A 'centred' possible world is an ordered triple consisting of a possible world, an individual in the domain of that world, and a time. | |
| From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 2) |
| 16428 | Meanings aren't in the head, but that is because they are abstract [Stalnaker] |
| Full Idea: Meanings ain't in the head. Putnam's famous slogan actually fits Frege's anti-psychologism better than it fits Purnam's and Burge's anti-individualism. The point is that intensions of any kind are abstract objects. | |
| From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 2) | |
| A reaction: If intensions are abstract, that leaves (for me) the question of what they are abstracted from. I take it that there are specific brain events that are being abstractly characterised. What do we call those? |
| 16432 | One view says the causal story is built into the description that is the name's content [Stalnaker] |
| Full Idea: In 'causal descriptivism' the causal story is built into the description that is the content of the name (and also incorporates a rigidifying operator to ensure that the descriptions that names abbreviate have wide scope). | |
| From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 5) | |
| A reaction: Not very controversial, I would say, since virtually every fact about the world has a 'causal story' built into it. Must we insist on rigidity in order to have wide scope? |
| 16430 | Two-D says that a posteriori is primary and contingent, and the necessity is the secondary intension [Stalnaker] |
| Full Idea: Two-dimensionalism says the necessity of a statement is constituted by the fact that the secondary intensions is a necessary proposition, and their a posteriori character is constituted by the fact that the associated primary intension is contingent. | |
| From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 2) | |
| A reaction: This view is found in Sidelle 1989, and then formalised by Jackson and Chalmers. I like metaphysical necessity, but I have some sympathy with the approach. The question must always be 'where does this necessity derive from'? |
| 16431 | In one view, the secondary intension is metasemantic, about how the thinker relates to the content [Stalnaker] |
| Full Idea: On the metasemantic interpretation of the two-dimensional framework, the second dimension is used to represent the metasemantic facts about the relation between a thinker or speaker and the contents of her thoughts or utterances. | |
| From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 4) | |
| A reaction: I'm struggling to think what facts there might be about the relation between myself and the contents of my thoughts. I'm more or less constituted by my thoughts. |
| 19399 | Prime matter is nothing when it is at rest [Leibniz] |
| Full Idea: Primary matter is nothing if considered at rest. | |
| From: Gottfried Leibniz (Aristotle and Descartes on Matter [1671], p.90) | |
| A reaction: This goes with Leibniz's Idea 13393, that activity is the hallmark of existence. No one seems to have been able to make good sense of prime matter, and it plays little role in Aristotle's writings. |