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It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [4] [1] or sometimes zeroth-order logic. [ b ] [ 6 ] [ 7 ] [ 8 ] Sometimes, it is called first-order propositional logic [ 9 ] to contrast it with System F , but it should not be confused with first-order logic .
A rule of inference is a scheme of drawing conclusions that depends only on the logical form of the premises and the conclusion but not on their specific content. [39] [40] The most-discussed rule of inference is the modus ponens. It has the following form: p; if p then q; therefore q. This scheme is deductively valid no matter what p and q ...
One solution of the nine dots puzzle. It is possible to mark off the nine dots in four lines. [13] To do so, one goes outside the confines of the square area defined by the nine dots themselves. The phrase thinking outside the box, used by management consultants in the 1970s and 1980s, is a restatement of the solution strategy. According to ...
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems ; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms ...
The fifth and sixth examples are meaningful declarative sentences, but are not statements but rather matters of opinion or taste. Whether or not the sentence "Pegasus exists." is a statement is a subject of debate among philosophers. Bertrand Russell held that it is a (false) statement. [citation needed] Strawson held it is not a statement at all.
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises ...
Identify which statements are premises, sub-conclusions, and the main conclusion. Provide missing, implied conclusions and implied premises. (This is optional depending on the purpose of the argument map.) Put the statements into boxes and draw a line between any boxes that are linked. Indicate support from premise(s) to (sub)conclusion with ...