A key to Churchland’s symbolic sentences
Churchland states a number of examples of lawlike generalizations of physical and psychological theory using a compact symbolic notation. Here are his examples (using his numbering) restated in a less compact way:
(1) For each particle x, each value f of force, and each value m of mass, if x has mass m and x suffers a net force of f, then x accelerates at f / m
(2) For each person x and proposition p, if x fears that p is true, then x desires that p is not true
(3) For each person x and proposition p, if x hopes that p is true and x discovers that p is true, then x is pleased that p is true
(4) For each person x and propositions p and q, if x believes that p is true and x believes that if p is true then q is true, then, barring confusion, distraction, etc., x believes that q is true
(5) For each person x and propositions p and q, if x desires that p is true and x believes that if q is true then p will be true and x is able to bring it about that q is true, then, barring conflicting desires or preferred strategies, x brings it about that q is true
(6) For each volume x of gas, each value P of pressure, each value V of volume, and each quantity µ, if x has pressure P and x has volume V and x has a quantity µ, then, barring very high pressure or density, x has a temperature of PV / µR
(7) For each person x and proposition p, if x desires with all his heart that p is true and x learns that p is not true, then, barring unusual strength of character, x is shattered that p is not true
Meanings of the symbols Churchland uses:
Symbol | English Meaning |
A & B | A and B |
~ A | it’s not the case that A |
A ⊃ B | if A then B |
(x) … x … | everything, x, is such that … x … |