THE LOGICAL CHOICE
Sentential/propositional logic and predicate logic are two of my passions. I became interested in logic during my undergraduate studies in philosophy. I won't get into the nitty-gritty here, but if you're wondering what my business card means, I'll offer a brief explanation below of what the card denotes.
As you may have guessed, the logical equation that ultimately denotes my existence is on the upper half of the card, whereas the English translation of the logic is on the lower half. Though I wrote the equation, the validity of the statement was verified by an old philosophy professor (who is a logician).
Ǝx is an existential quantifier; it asserts that something exists if all of the conditions within the parenthesis ( ) are true. Everything in ( ) provides a set of conditions and general propositions, which are described by predicates that have certain truth values.
Each upper-case letter (predicate) represents a sentence that has a certain truth value, which can be either true or false. The variables attached to those predicates (either x or y) act as container into which the predicates are grouped and apply to the quantifiers, which bind that section of the sentence to the quantifier itself. Those being, Ǝx, the existential quantifier ("there is an x such that."), and Ɐy, the universal quantifier ("for all of"). The variables attached to these quantifiers act as placeholders for phrases, and the symbols in-between govern the validity and truth value of such statements.
The upward caret sign ^ is the symbol for "and," whereas the downward caret sign ⌄ is the symbol for "or." The diamond sign is the symbol I used to represent a conditional (if __, then __), which is commonly represented by the arrow sign, → . And finally, this thing ~ is the symbol for "not." Though the language seems complicated at first, it's really no different than learning that a green light means go and a red light means stop.
If any of the predicate statements are false, then Ǝx does not exist. If all conditions are satisfied and their truth value is positive, then Ǝx exists. In short, my business card verifies my existence and denotes that I am looking for work.
Try to guess the English translation of the sentence below. (The answer will be at the bottom of the page.)
P → Q
P = Paul goes to the store.
Q = Quincy stays at home.
If Paul goes to the store, then Quincy stays at home.