Terms to master

Kristen had a wise request the other day. She asked for a list of logical terms that students should know. I'm going to restrict this list to terms (and phrases) related to propositional logic.  Here ya go:

Valid
Invalid
Truth-value
Negation
Conjunction
Conjunct
Disjunction
Disjunct
Conditional
Antecedent
Consequent
Biconditional
Rules of Implication: MP, MT, HS, CD, ADD, SIMP, CONJ, DS
Rules of Equivalence: TRANS, IMPL, EQUIV, DM, DN, TAUT, EXP, DIST, COM, ASSOC
     What is the difference between an implication rule and an equivalence rule?
Conditional Proof
Indirect Proof
Simple Proposition
Complex Proposition
Truth Table


Comments

Post a Comment

Popular posts from this blog

Exportation: Some Explanations

Let me try to explain the exportation rule a few more times. Here's the rule (I am using the triple bar to symbolize logical equivalence and the arrow to symbolize conditionals): (p & q) -> r  ≡ p -> (q -> r) Explanation 1: Look at the left side of the triple bar. It tells us that if p and q are true, then r is true. Look at the right side of the triple bar. It tells us that if p is true, then if q is true, then r is true. Even in plain English that sounds nearly identical.  Explanation 2: Look at the left side of the triple bar. It tells us, according to the meaning of conditionals, that if p is false then the whole conditional is true. Look at the right side of the triple bar. It tells us that if p is false the whole conditional is true (just remind yourself of the truth-table for p -> q). Explanation 3: Look at the left side of the triple bar. It tells us that if q is false the whole conditional is true. Look at the right side of the...
Read more

Predicates in search of nouns

According to standard categorical logic, statements of the form All S are P must have some sort of noun-phrase in the predicate.  Thus ‘All dogs are mammals’ is fine, but ‘All dogs are four-legged’ is not.  Why is this a requirement? Standard categorical logic is based on Aristotelian logic and inherits some of Aristotle’s assumptions. So one reason for the noun-requirement is that given Aristotelian metaphysics predicates without nouns are incomplete. To understand why, we first need to keep in mind that  predicates (parts of language) correspond to  properties (parts of the extra-linguistic—that is, non-linguistic—world).  Predicates without nouns are incomplete because, according to Aristotle,  properties  must inhere in objects in order to exist.  There are no free-floating properties—properties without some subject that they attach to.  Thus, statements like ‘All dogs are four-legged’ while grammatic...
Read more

Relations and Multiple Quantifiers in Predicate Logic

Thus far we have been using only one-place predicates. These are predicates that only require one name (put differently, these are properties that only require one object) to complete them. For example, _____ is red = Rx _____ is heavy = Hx _____ is a wife = Wx ( ∃ x)Rx is true if and only if there is at least one thing in the universe that is red. ( ∃ x)Hx is true iff there is at least one thing in the universe that is heavy, and so on. (x)Rx is true iff everything in the universe is red, and so on.  But, as we all know, there are predicates that are more than one place. In other words, there are predicates that require more than one name to complete them (put differently, there are properties-- better-called relations--that require more than one object). For example ____ is heavier than ____ = Hxy ____ is taller than ____ =  Txy ____ loves ____ = Lxy ____ is between ____, _____ = Bxyz (∃ x) (∃y )Hxy is true iff there is something ...
Read more