W&O: §§ Pete Mandik Chairman, Department of Philosophy Coordinator, Cognitive Science Laboratory William Paterson University, New Jersey USA

2 Chapter V: Regimentation “(x)(Ex & Ux)” “(x)(Sx  Px)” What can be gained with translations into a canonical notation like…

3 Sec. 33. Aims and Claims of Regimentation n “Practical temporary departures from ordinary language have recommended themselves at various points….Most of these were fairly representative of the departures that one actually adopts in various pursuits short of symbolic logic…Opportunistic departure from ordinary language …is part of ordinary linguistic behavior….[C]ertain such departures have a…purpose that is decidedly worth noting: simplification of theory. Simplification of theory is a central motive…of the sweeping artificialities of notation in modern logic. …It is the part of strategy to keep theory simple where we can, and then, when we want to apply the theory to particular sentences of ordinary language, to transform those sentences into a “canonical form” adapted to the theory”. Pp

4 Sec 34.Quantifiers and Other Operators n “[W]e can dispense with almost the entire category of indefinite singular terms [by means of paraphrasing along the following lines…] n (1) Everything is an object x such that (if x is an F then…x…), n (2) Something is an object x such that (x is an F and…x…). n Thus all the indefinite singular terms are got down to ‘everything’ and ‘something’…” p. 162

5 Example of regimentation aka translation into a canonical notation n “Snakes are poisonous” becomes… n “Everything is an object x such that if x is a snake then x is poisonous” which in turn becomes… n “(x)(Sx  Px)”

6 Another example n “An elephant sat on a unicycle” becomes… n “Something is an object x such that x is an elephant and x sat on a unicycle” which in turn becomes… n “(x)(Ex & Ux)” n Note that everything is now being said in terms of quantifiers (e.g.””), variables (e.g. “x”), predicates (e.g. “P”), connectives (e.g. “&”), and parentheses (e.g. “)”).

7 Sec. 35 Variables and Referential Opacity “[T]here can be no cross-reference from inside an opaque construction to a ‘such that’ outside. Rephrased for quantification…, this says that no variable inside an opaque construction is bound by an operator outside. You cannot quantify into an opaque construction.” p. 166

8 “When ‘x’ stands inside an opaque construction and ‘(x)’ or ‘(x)’ stands outside, the attitude to take is simply that that occurrence of ‘x’ is then not bound by that occurrence of the quantifier. An example is that last occurrence of ‘x’ in: (1) (x)(x is writing ‘9 > x’). …the final ‘x’ of (1) does not refer back to ‘(x)’, is not bound by ‘(x)’, but does quite other work: it contributes to the quotational name of a three-character open sentence containing specifically the twenty-fourth letter of the alphabet.” p. 166

9 “The case of: (2) (x)(Tom believes that x denounced Catiline) Is similar in that ‘x’ is inside and ‘(x)’ outside an opaque construction …So here again we may say that the ‘(x)’ fails to bind that occurrence of ‘x’. But (2) differs from (1) in that (1) still makes sense while (2) does not. Of course these make sense: (3) (x)(Tom believes x to have denounced Catiline), (4) Tom believes that (x)(x denounced Catiline). But in each of these the ‘x’ is bound by ‘(x)’. In (3), ‘x’ and ‘(x)’ are both outside the opaque construction; in (4) they are both inside.” p

10 Study question: What would be an example of quantifying into an opaque construction and what would be an example of not quantifying into an opaque construction?

11 THE END