43 ideas
| 2945 | Most philosophers start with reality and then examine knowledge; Descartes put the study of knowledge first [Lehrer] |
| Full Idea: Some philosophers (e.g Plato) begin with an account of reality, and then appended an account of how we can know it, ..but Descartes turned the tables, insisting that we must first decide what we can know. | |
| From: Keith Lehrer (Theory of Knowledge (2nd edn) [2000], I p.2) |
| 2946 | You cannot demand an analysis of a concept without knowing the purpose of the analysis [Lehrer] |
| Full Idea: An analysis is always relative to some objective. It makes no sense to simply demand an analysis of goodness, knowledge, beauty or truth, without some indication of the purpose of the analysis. | |
| From: Keith Lehrer (Theory of Knowledge (2nd edn) [2000], I p.7) | |
| A reaction: Your dismantling of a car will go better if you know what a car is for, but you can still take it apart in ignorance. |
| 18915 | If facts are the truthmakers, they are not in the world [Engelbretsen] |
| Full Idea: If there are such things as truthmakers (facts), they are not to be found in the world. As Strawson would say to Austin: there is the cat, there is the mat, but where in the world is the fact that the cat is on the mat? | |
| From: George Engelbretsen (Trees, Terms and Truth [2005], 4) | |
| A reaction: He cites Strawson, Quine and Davidson for this point. |
| 18919 | There are no 'falsifying' facts, only an absence of truthmakers [Engelbretsen] |
| Full Idea: A false proposition is not made false by anything like a 'falsifying' fact. A false proposition simply fails to be made true by any fact. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005], 4) | |
| A reaction: Sounds good. In truthmaker theory, one truth-value (T) is 'made', but the other one is not, so there is no symmetry between the two. Better to talk of T and not-T? See ideas on Excluded Middle. |
| 18913 | Traditional term logic struggled to express relations [Engelbretsen] |
| Full Idea: The greatest challenge for traditional term logicians was the proper formulation and treatment of relational expressions. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005]) | |
| A reaction: The modern term logic of Fred Sommers claims to have solved this problem. |
| 18907 | Term logic rests on negated terms or denial, and that propositions are tied pairs [Engelbretsen] |
| Full Idea: That terms can be negated, that such negation is distinguishable from denial, and that propositions can be construed syntactically as predicationally tied pairs of terms, are important for the tree theory of predication, and for term logic. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005], 2) |
| 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) |
| 18912 | Was logic a branch of mathematics, or mathematics a branch of logic? [Engelbretsen] |
| Full Idea: Nineteenth century logicians debated whether logic should be treated simply as a branch of mathematics, and mathematics could be applied to it, or whether mathematics is a branch of logic, with no mathematics used in formulating logic. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005], 3) | |
| A reaction: He cites Boole, De Morgan and Peirce for the first view, and Frege and Russell (and their 'logicism') for the second. The logic for mathematics slowly emerged from doing it, long before it was formalised. Mathematics is the boss? |
| 18905 | Propositions can be analysed as pairs of terms glued together by predication [Engelbretsen] |
| Full Idea: Sommers's 'tree theory' of predication assumes that propositions can be analysed as pairs of terms joined by some kind of predicational glue. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005], 2) | |
| A reaction: This is the basis of Sommers's upgraded Aristotelian logic, known as Term Logic. The idea of reasoning with 'terms', rather than with objects, predicates and quantifiers, seems to me very appealing. I think I reason more about facts than about objects. |
| 18922 | Logical syntax is actually close to surface linguistic form [Engelbretsen] |
| Full Idea: The underlying logical syntax of language is close to the surface syntax of ordinary language. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005], 5) | |
| A reaction: This is the boast of the Term logicians, in opposition to the strained and unnatural logical forms of predicate logic, which therefore don't give a good account of the way ordinary speakers reason. An attractive programme. 'Terms' are the key. |
| 18908 | Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen] |
| Full Idea: Standard logic recognises only one kind of negation: sentential negation. Consequently, negation of a general term/predicate always amounts to negation of the entire sentence. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005], 3) |
| 18917 | Existence and nonexistence are characteristics of the world, not of objects [Engelbretsen] |
| Full Idea: Existence and nonexistence are not primarily properties of individual objects (dogs, unicorns), but of totalities. To say that some object exists is just to say that it is a constituent of the world, which is a characteristic of the world, not the object. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005], 4) | |
| A reaction: This has important implications for the problem of truthmakers for negative existential statements (like 'there are no unicorns'). It is obviously a relative of Armstrong's totality facts that do the job. Not sure about 'a characteristic of'. |
| 18916 | Facts are not in the world - they are properties of the world [Engelbretsen] |
| Full Idea: Facts must be viewed as properties of the world - not as things in the world. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005], 4) | |
| A reaction: Not sure I'm happy with either of these. Do animals grasp facts? If not, are they (as Strawson said) just the truths expressed by true sentences? That is not a clear idea either, given that facts are not the sentences themselves. Facts overlap. |
| 18921 | Individuals are arranged in inclusion categories that match our semantics [Engelbretsen] |
| Full Idea: The natural categories of individuals are arranged in a hierarchy of inclusion relations that is isomorphic with the linguistic semantic structure. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005], 5) | |
| A reaction: This is the conclusion of a summary of modern Term Logic. The claim is that Sommers discerned this structure in our semantics (via the study of 'terms'), and was pleasantly surprised to find that it matched a plausible structure of natural categories. |
| 18918 | Terms denote objects with properties, and statements denote the world with that property [Engelbretsen] |
| Full Idea: In term logic, what a term denotes are the objects having the property it signifies. What a statement denotes is the world, that which has the constitutive property it signifies. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005], 4) |
| 18920 | 'Socrates is wise' denotes a sentence; 'that Socrates is wise' denotes a proposition [Engelbretsen] |
| Full Idea: Whereas 'Socrates is wise' denotes a sentence, 'that Socrates is wise' denotes a proposition. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005], 4) | |
| A reaction: In traditional parlance, 'reported speech' refers to the underlying proposition, because it does not commit to the actual words being used. As a lover of propositions (as mental events, not mysterious abstract objects), I like this. |
| 18906 | Negating a predicate term and denying its unnegated version are quite different [Engelbretsen] |
| Full Idea: There is a crucial distinction in term logic between affirming a negated predicate term of some subject and denying the unnegated version of that term of that same subject. We must distinguish 'X is non-P' from 'X is not P'. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005], 2) | |
| A reaction: The first one affirms something about X, but the second one just blocks off a possible description of X. 'X is non-harmful' and 'X is not harmful' - if X had ceased to exist, the second would be appropriate and the first wouldn't? I'm guessing. |