University:
Harvard University
Course:
PHIL S-12 | Deductive Logic
Academic year:

2024
Views:

307

Pages:

2
Author:

Edgar Rowe

SYMBOLIC LOGIC LOGICAL PROPERTIES OF SENTENCES AND SENTENCE FORMS When we talk about the logical properties of a sentence (or sentence form) we are referring to the possible truth values of that sentence (or sentence form). For example, if we say that a certain sentence must always be true, no matter what is going on in the world, we are identifying the logical properties of that sentence. 1. Children are children, after all. INDIVIDUAL SENTENCES Any individual sentence can be either (1) satisfiable (in which case it is either contingent or tautological) or (2) contradictory. A sentence is satisfiable if it is possible for it to be true (in other words, it is not a sentence that must be false). A sentence is contingent if it is possible for it to be true or false (in other words, it is neither necessarily true or necessarily false). 1. It is over 40 degrees Farenheit in downtown San Fransisco today. A sentence is tautological if and only if it must be true. 2. A rose is a rose is a rose. 3. Either I will make it home for Christmas day or I will not. A sentence is contradictory if it is impossible for it to be true. 4. Henry does and does not have one pierced ear. EXAMPLE 5. Either I will go to Starbucks or I will not go to Starbucks. SENTENCE FORMS Sentence forms (that is, formulas that consist of sentence parts (and, maybe, sentence connectives) and thus represent many possible individual sentences) have logical properties, just like individual sentences. A sentence form is satisfiable if it is either contingent or tautological. A sentence form is contingent if it is possible for it to be true or false (in other words, there is nothing in its form that makes it necessarily true or necessarily false). Any atomic sentence (represented by one sentence letter) must be contingent. For example, if r represents an atomic sentence, it must be contingent. 1. r 2. p&q A sentence form is tautological if and only its form causes it to be necessarily true. 3. q V ~q A sentence form is contradictory if its form makes it impossible for it to be true. 4. p & ~p EXAMPLES 5. p  ~p 6. p  (p & q) 7. (f & r)  t 8. (f & g)  k 9. s & r & (t  ~m) 10. m V (~p V ~q)

Symbolic Logic: Logical Properties of Sentences and Sentence Forms

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