Fallacy

43 Non Sequitur
False conversion is one kind of non sequitur. Any sentence offered as a consequence of any other is a non sequitur unless, it is j_con-sequence. All invalid arguments, therefore, involve a non sequitur since they at least implicitly assert that the conclusion follows when in fact it does not. As false conversion, the undistributed middle, and the like, can be readily explained on their own grounds, the term "non sequitur" is usually reserved for the widely irrelevant rather than the ordinary invalid conclusions.
In the course of an extended discussion, conclusions are often immediately put to use as premises for further developments. Sometimes these premises are converted, reformulated, corrected, extended. Often it is difficult to judge whether a given sentence is intended as a valid reworking of one of these temporary conclusions or as a new premise which the speaker introduces in the hope that it will be unexceptionable. The ambiguity of usage for such connectives as "so," "therefore," "thus," "hence," contributes to the difficulty, since these terms, taken literally, promise that the sentence to follow will be strictly entailed. But in practice they often serve as mere rhetorical flourishes, smoothing the way and expressing a feeling that what comes after is somehow relevant even if the speaker would not wish to maintain that it is a valid consequence of what has preceded.
It is a hair-splitting pedantry to accuse a speaker of non sequitur when a reasonable recasting of the forms of his language would more clearly express his probable intention and show his argument to be valid. Just as there is no point in supplying for every suppressed premise in an enthymeme some far-fetched proposition that will make the argument invalid, so there is no need to take every "therefore" as a warrant that the sentence which follows in time will also follow in logic. It may express a closely related fact known to be true on other grounds and suitable to serve as a new premise. There are enough veritable non sequiturs in ordinary disputation, exhibiting a real confusion, on which to exercise ingenuity.
EXAMPLE COMMENT
A lecturer in modern history: "All the skill and discipline of Hitler's mechanized forces went down before the forces of communism and democracy which Der Fiihrer had disparaged and despised. 'Degenerate' democracy grasped control of sea and air; 'inefficient' communism inspired its soldiers with the stubborn resolve that fought on to victory in the rubble of Stalingrad. Thus it was fascism that proved inferior." The lecturer makes the sort of non sequitur which is most commonly encountered, that is, a conclusion not patently preposterous and yet far from supported by the premises, The tremendous efforts through which the British Empire, USA, USSR and their allies achieved victory in World War II do seem to show that both democracy and communism are capable of producing substantial military results. To say that the inferiority of fascism was thereby demonstrated is to assert a non sequitur, since the factors of relative resources, manpower and space preclude this as the necessary conclusion drawn from the fact of defeat.
A country boy, tiring of small-town life, argues that there is something "courageous and beautiful" about living an "irregular" life in "bohemian" surroundings. "All men who live thus," he exclaims, "have a touch of poetry in their souls. They are not to be judged and censored by ordinary morality." When pressed for his reasons, he says, "Why, many artists live scandalous lives, and we are the richer for itl" Many is not all. Even if it were, the "all men" sentence would not follow. There are other non sequiturs in this little effusion.
From a scrap-book: "Every reasonable man will want to regulate his life according to moral principles. Yet we all are tempted to make exceptions in our own cases. Therefore, we ought to make allowances for the lapses of others." A marginal case. The three propositions probably are true in a fairly evident sense, and they are closely related to the same subject. The "therefore" makes them sound like a syllogism instead of a complex observation on life. But what follows "therefore" is no consequence in logic of what precedes. At the very least this is bad writing.
"I know what you are thinking about," said Tweedledum; "but it isn't so, nohow."
"Contrariwise," continued Tweedledee, "If it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic."
Tweedledee's comment is perfectly true -- it is indeed logic -- but like many other things said to Alice in Looking-glass Land, though miraculously cogent, it is totally irrelevant.

EXAMPLE	COMMENT
A lecturer in modern history: "All the skill and discipline of Hitler's mechanized forces went down before the forces of communism and democracy which Der Fiihrer had disparaged and despised. 'Degenerate' democracy grasped control of sea and air; 'inefficient' communism inspired its soldiers with the stubborn resolve that fought on to victory in the rubble of Stalingrad. Thus it was fascism that proved inferior."	The lecturer makes the sort of non sequitur which is most commonly encountered, that is, a conclusion not patently preposterous and yet far from supported by the premises, The tremendous efforts through which the British Empire, USA, USSR and their allies achieved victory in World War II do seem to show that both democracy and communism are capable of producing substantial military results. To say that the inferiority of fascism was thereby demonstrated is to assert a non sequitur, since the factors of relative resources, manpower and space preclude this as the necessary conclusion drawn from the fact of defeat.
A country boy, tiring of small-town life, argues that there is something "courageous and beautiful" about living an "irregular" life in "bohemian" surroundings. "All men who live thus," he exclaims, "have a touch of poetry in their souls. They are not to be judged and censored by ordinary morality." When pressed for his reasons, he says, "Why, many artists live scandalous lives, and we are the richer for itl"	Many is not all. Even if it were, the "all men" sentence would not follow. There are other non sequiturs in this little effusion.
From a scrap-book: "Every reasonable man will want to regulate his life according to moral principles. Yet we all are tempted to make exceptions in our own cases. Therefore, we ought to make allowances for the lapses of others."	A marginal case. The three propositions probably are true in a fairly evident sense, and they are closely related to the same subject. The "therefore" makes them sound like a syllogism instead of a complex observation on life. But what follows "therefore" is no consequence in logic of what precedes. At the very least this is bad writing.
"I know what you are thinking about," said Tweedledum; "but it isn't so, nohow." "Contrariwise," continued Tweedledee, "If it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic."	Tweedledee's comment is perfectly true -- it is indeed logic -- but like many other things said to Alice in Looking-glass Land, though miraculously cogent, it is totally irrelevant.