Symbolic Logic - Chapter 3 - The Predicate Calculus 1
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24 terms
Terms | Definitions |
|---|---|
 The propositional calculus reveals validity when this depends on propositional structure alone. (T/F) | True. |
| What do lower case letters represent in the predicate calculus? | They represent proper names. |
| What do upper-case letters represent in the predicate calculus? | They represent property-expressions or predicates. |
| What are upper-case letters called in the predicate calculus? | They are called predicate letters. |
| What are lower-case letters called in the predicate calculus? (93) | They are called proper names. |
| How does one write that m does not have G? (93) | -Gm |
| How do we say that m has property F? (93) | We juxtapose the symbols 'F' and 'm' in that order, we write: Fm |
| What do we obtain from "all robins are migrants" or "every robin is a migrant"? (94) | We obtain everything with the property of being a robin has the property of being a migrant. It can be written as: Everything with F has G. |
| To what do we naturally abbreviate 'x has F'? (95) | Fx |
| How do we write 'for any x'? (95) | We enclose 'x' in brackets. |
| How do we write 'For any x, if x has F then x has G'? (95) | (x)(Fx -> Gx) |
| How do we write 'nothing with F has G'? (95) | (x)(Fx -> -Gx) For any x, if x has the property of F, then it does not have the property of G. |
| How do we write 'nothing with F has both G and H'? (95) | (x)(Fx -> -(Gx & Hx)) |
| The device of universal quantifier enables us to render into logical notation many sentences that contain what such words? (95) | 'All', 'every', 'any', 'everything', 'no', 'none', and/or 'nothing'. |
| What is (3x)? (96) | It is the existential quantifier. |
| What does (3x) represent? (97) | There is an x such that.. An object x can be found which... |
| How do we write 'some felons are German'? | (3x)(Fx & Gx) |
| If F means felon and G means German, how do we read: (3x)(Fx & Gx)? (97) | There exists some object that is both a felon and a German. |
| How can one write 'something with F has not G', such as 'some Frenchmen are not generous'? (97) | (3x)(Fx & -Gx) |
| How might we summarize the task of translation into the quantifier-notation? (97) | 1) Render into a sentence about properties, and employ predicate-letters for these properties. 2) Introduce variables 3) Introduce propositional calculus connectives and quantifiers. |
| A predicate-letter followed by one name expresses a ___________. A predicate-letter followed by two names expresses a ___________. (98) | Property, Relation |
| If we give 'Pmn' the interpretation 'm is a parent of n', how can we express 'Prince Charles has a parent', where n is Prince Charles? (98) | (3x)Pxn This translates to: "There exists an 'x', that is a parent of Prince Charles." (I'm a bit confused as to why the book does not use 'm', but rather 'x'.) |
| If we give 'Pmn' the interpretation of 'm is a parent of n', and Prince Philip is represented by m, how can we write 'Prince Philip has a child'? (99) | (3x)(Pmx) This translates to: "There exists an 'x' of which Prince Philip is a parent." |
| If Pmn reads as 'm is a parent of n', what is the difference in reading (3x)Pnx in contrast with (3x)Pxn if 'n' represents Prince Charles? (99) | The first reads: there exists an 'x' of which Prince Charles is a parent. The second reads: there exists an 'x' of which Prince Charles is a son, or there exists an 'x' of which 'x' is a parent of Prince Charles. |
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