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While a logical argument is a non sequitur if, and only if, it is invalid, the term "non sequitur" typically refers to those types of invalid arguments which do not constitute formal fallacies covered by particular terms (e.g., affirming the consequent). In other words, in practice, "non sequitur" refers to an unnamed formal fallacy.
An argument that is not valid is said to be "invalid". An example of a valid (and sound) argument is given by the following well-known syllogism: All men are mortal. (True) Socrates is a man. (True) Therefore, Socrates is mortal. (True) What makes this a valid argument is not that it has true premises and a true conclusion.
For example, oxygen is necessary for fire. But one cannot assume that everywhere there is oxygen, there is fire. A condition X is sufficient for Y if X, by itself, is enough to bring about Y. For example, riding the bus is a sufficient mode of transportation to get to work.
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the ...
An example is a probabilistically valid instance of the formally invalid argument form of denying the antecedent or affirming the consequent. [12] Thus, "fallacious arguments usually have the deceptive appearance of being good arguments, [13] because for most fallacious instances of an argument form, a similar but non-fallacious instance can be ...
An argument can be “valid” even if one or more of its premises are false. An argument is sound if it is valid and the premises are true. It is possible to have a deductive argument that is logically valid but is not sound. Fallacious arguments often take that form. The following is an example of an argument that is “valid”, but not ...
Invalid argument. This can be more easily seen by giving a counter-example with the same argument form: Some people are herbivores. Some herbivores are zebras. Therefore, some people are zebras. Invalid argument, as it is possible that the premises be true and the conclusion false.
The resulting argument sounds like the (valid) first example above, but is in fact structured like the invalid second example: Major premise: Nothing is better than eternal happiness. Minor premise: A ham sandwich is better than nothing. Conclusion: A ham sandwich is better than eternal happiness.