42 ideas
| 21489 | Super-ordinate disciplines give laws or principles; subordinate disciplines give concrete cases [Peirce, by Atkin] |
| 10528 | Definitions concern how we should speak, not how things are [Fine,K] |
| 19095 | Pragmatic 'truth' is a term to cover the many varied aims of enquiry [Peirce, by Misak] |
| 19097 | Peirce did not think a belief was true if it was useful [Peirce, by Misak] |
| 21494 | If truth is the end of enquiry, what if it never ends, or ends prematurely? [Atkin on Peirce] |
| 9672 | Free logic is one of the few first-order non-classical logics [Priest,G] |
| 9697 | X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G] |
| 9685 | <a,b&62; is a set whose members occur in the order shown [Priest,G] |
| 9675 | a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G] |
| 9674 | {x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G] |
| 9673 | {a1, a2, ...an} indicates that a set comprising just those objects [Priest,G] |
| 9677 | Φ indicates the empty set, which has no members [Priest,G] |
| 9676 | {a} is the 'singleton' set of a (not the object a itself) [Priest,G] |
| 9679 | X⊂Y means set X is a 'proper subset' of set Y [Priest,G] |
| 9678 | X⊆Y means set X is a 'subset' of set Y [Priest,G] |
| 9681 | X = Y means the set X equals the set Y [Priest,G] |
| 9683 | X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G] |
| 9682 | X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G] |
| 9684 | Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G] |
| 9694 | The 'relative complement' is things in the second set not in the first [Priest,G] |
| 9693 | The 'intersection' of two sets is a set of the things that are in both sets [Priest,G] |
| 9692 | The 'union' of two sets is a set containing all the things in either of the sets [Priest,G] |
| 9698 | The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G] |
| 9688 | A 'singleton' is a set with only one member [Priest,G] |
| 9687 | A 'member' of a set is one of the objects in the set [Priest,G] |
| 9695 | An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G] |
| 9696 | A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets [Priest,G] |
| 9686 | A 'set' is a collection of objects [Priest,G] |
| 9689 | The 'empty set' or 'null set' has no members [Priest,G] |
| 9690 | A set is a 'subset' of another set if all of its members are in that set [Priest,G] |
| 9691 | A 'proper subset' is smaller than the containing set [Priest,G] |
| 9680 | The empty set Φ is a subset of every set (including itself) [Priest,G] |
| 21493 | Pure mathematics deals only with hypotheses, of which the reality does not matter [Peirce] |
| 19102 | Bivalence is a regulative assumption of enquiry - not a law of logic [Peirce, by Misak] |
| 10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
| 10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
| 10352 | The real is the idea in which the community ultimately settles down [Peirce] |
| 13498 | Peirce and others began the mapping out of relations [Peirce, by Hart,WD] |
| 21491 | Peirce's later realism about possibilities and generalities went beyond logical positivism [Peirce, by Atkin] |
| 16376 | The possible can only be general, and the force of actuality is needed to produce a particular [Peirce] |
| 19107 | Inquiry is not standing on bedrock facts, but standing in hope on a shifting bog [Peirce] |
| 10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |