This glossary created by Norman Swartz
October 1997. Revised 2010. | |

Glossary of terms in Chapter One of Possible Worlds: An Introduction to Logic and Its Philosophyby Raymond Bradley and Norman Swartz, Copyright © 2010. | |

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**counterfactual**- in contradistinction to the (actual) facts
**conceivable**- to be imaginable (in the sense of having a mental image)
**A is a necessary condition for B**- B does not occur (/is not true /does not exist) unless A
occurs (/is true /exists). (Example: Having four sides is a
necessary condition for something's being square.) (See
"The Concepts of
*Necessary*and*Sufficient Conditions*".) **A is a sufficient condition for B**- A's occurrence (/truth /existence) guarantees B's occurrence
(/truth /existence). (Example: Being blue is a sufficient
condition for being colored.) (See
"The Concepts of
*Necessary*and*Sufficient Conditions*".) **circularity**- explaining (defining) P in terms of Q,
**and**explaining (defining) Q in terms of P **psychologism**- any theory of logic which makes logic a function of human psychology
**the actual world**- the entire – past, present and future – universe
**physically possible world**- any possible world which has the same natural laws as the actual world
**objects; things; individuals; items; particulars; logical subjects**- whatever exists in at least one possible world
**property**- a characteristic or a feature of an item. (Items are said to 'instance' or 'exemplify' properties. Thus, if Mr. Clean is bald, we may say that the item, Mr. Clean, instances or exemplifies the property of baldness. Note, however, that he does not do so in the actual world.)
**concrete object**- an item which has a position in space and time (e.g. the Eiffel Tower; the pain in my back; the noise when you drop a book)
**abstract object**- an item which does not have a position in space and time but which exists. (Philosophers have nominated such things as numbers, sets, and propositions to this category. The need to posit such entities has been discussed and disputed for at least 2400 years.)
**relations**- (difficult or impossible to define in a non-circular way.
See "circularity".) Examples include such things as
*being older than*,*is the square root of*, and*is consistent with*. **generic term**- pertaining to a whole group or class (example: "color" is a generic term referring to that class which includes redness, blueness, etc.)
**attribute**- a generic term encompassing both "property" and "relation"
**truth-value**- a generic term encompassing both "truth" and "falsity"
**Correspondence Theory of Truth; Realistic Theory of Truth; Simple Theory of Truth**- the theory that a proposition P which ascribes F to
**a**is true if and only if**a**has the property F. (See "Truth".) **Coherence Theory of Truth**- the theory that a proposition P is true if it 'coheres' with
- (i) the majority of our own beliefs, or
- (ii) the majority of the beliefs of our society. (See "Truth".)
**Pragmatist (or Pragmatic) Theory of Truth**- the theory that a proposition P is true if it proves useful or practical to believe it. (See "Truth".)
**actually true**- is true in the actual world
**possibly true**- is true in some (i.e. at least one) possible world
**possibly false**- is false in some (i.e. at least one) possible world
**actually false**- is false in the actual world
**is contingent**- is true in some possible world
**and**is false in some (other) possible world **modal status**- a generic term encompassing "contingency", "necessary truth", and "necessary falsity"
**P is a contradictory of Q**- (i) P is true in all those possible worlds, if any, in which
Q is false;
**and**P is false in all those possible worlds, if any, in which Q is true. - (ii) In each possible world, P and Q have opposite truth-values to one another.
- (iii) There is no possible world in which P and Q are both true;
**and**there is no possible world in which P and Q are both false. **is noncontingent**- is true in all possible worlds
**or**is false in all possible worlds. (Note: this definition is**not**equivalent to "is true or false in all possible worlds". This latter phrase characterizes**every**proposition whatsoever.) **necessarily true proposition**- a proposition which is true in all possible worlds
**disjunctive proposition**- a proposition which asserts of two simpler propositions that one or the other is true. I.e. that at least one of the two simpler propositions is true. (Example: John dented the fender or somebody backed into the car.)
**necessarily false proposition**- a proposition which is false in all possible worlds
**conjunctive proposition**- a proposition which asserts of two simpler propositions that both of them are true. (Example: John dented the fender and his wife had the damage repaired.)
**self-contradictory proposition**- a necessarily false proposition
**sets A and B are mutually exclusive**- no member of set A is a member of set B
**sets A and B are jointly exhaustive of a set C**- every member of set C is either a member of set A or a member of set B or a member of both set A and set B
**modal properties**- properties of propositions arising out of the distribution of the truth-values of the propositions across the members of the set of all possible worlds, viz. possible truth, possible falsity, contingency, noncontingency, necessary truth, and necessary falsity
**modal relations**- relations between propositions arising out of the distribution of the truth-values of pairs of propositions across the members of the set of all possible worlds, e.g. consistency, inconsistency, implication, equivalence
**P is inconsistent with Q**- there is no possible world in which both P and Q are true. (There are two species of inconsistency: contradiction (see above) and contrariety (see below).)
**P is a contrary of Q**- there is no possible world in which both P and Q are true;
**and**there is a possible world in which both P and Q are false. **P is consistent with Q**- there is a possible world in which both P and Q are true
**P implies Q**- (i) Q is true in all those possible worlds, if any, in which P is true
- (ii) there is no possible world in which P is true and Q is false
- (iii) in each of all possible worlds, if P is true then Q is also
**Q follows from P**- P implies Q
**the argument whose premises are A and whose conclusion is B is deductively valid**- (i) the premises A imply the conclusion B
- (ii) there is no possible world in which the premises A are true and the conclusion B is false
*a fortiori*- all the more
**P is equivalent to Q**- (i) P implies Q;
**and**Q implies P - (ii) In each possible world, P and Q have matching truth-values
- (iii) there is no possible world in which P and Q differ in truth-value from one another
**equivalence-class**- (note: this term is given a special, nonstandard meaning in this text) a class of equivalent propositions
**P is a subcontrary of Q**- there is a possible world in which both P and Q are true
(i.e. P and Q are consistent);
**and**there is no possible world in which they are both false. **P is independent of Q**- there is a possible world in which both are true; there is a possible world in which both are false; there is a possible world in which P is true and Q false; and there is a possible world in which P is false and Q is true.
**Laws of Thought**- generic term encompassing the 'laws' of Identity, of The Excluded Middle, and of Noncontradiction
**Law of Identity**- an item is what it is (special case: each proposition P is identical to itself)
**Law of the Excluded Middle**- either an item has a certain attribute or it is not the case that that item has that attribute (special case: there is no 'third' or 'middle' truth-value; i.e. either a proposition P is true or it is not true [i.e. is false].)
**Law of Noncontradiction**- no item both has an attribute and fails to have that attribute (special case: no proposition P is both true and not-true [i.e. false].)
**linguistic theory of necessary truth (/falsity)**- the theory that the truth-values of noncontingent
propositions come about through 'rules of language' (Note: this
theory is
**rejected**in*Possible Worlds*[Chapter 1, Section 7].)
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