negation of its antecedent (not P) for the conclusion that the consequent is also negated (not Q). The invalidity of this pattern can be seen clearly using a version of the example above:

P1) If mortgage rates go up (P), house prices will fall (Q).

P2) Mortgage rates have not gone up (not P).

C) House prices will not fall (not Q).

The invalidity here has similar grounds to that of the fallacy of affirming the consequent. There are conditions other than mortgage rates going up that could precipitate a fall in house prices, so the fact that mortgage rates have stayed the same (or decreased) does not give us sufficient grounds for concluding that house prices will not fall; other factors may lead to their falling. Or again: from 'If it is raining then there are clouds' and 'it is not raining', it does not follow that there are no clouds.

Fallacy of deriving ought from is

The Scottish philosopher, David Hume, famously argued that an ought cannot be derived from an is. The claim can be understood in two ways: first, as a claim about motivations to act or refrain from acting. The fact that something is thus-and-so is, argued Hume, insufficient as a reason for thinking that one ought to act in such-and-such a way. The fact that torturing animals causes them suffering is not, according to this argument, sufficient reason to refrain from torturing animals. An additional motivating force - a desire to avoid harm to animals - must also play a role in our motivation to act in such cases. Although an interesting and, indeed, controversial thesis, this way of interpreting Hume's claim is not the one that interests us here.2 Rather we are interested in Hume's claim understood as the claim that a prescriptive conclusion cannot be validly derived from purely descriptive premises, such an inference is fallacious. Thus the fallacy of deriving an ought from an is occurs when a prescriptive conclusion - a conclusion making a claim about something that should or ought to be done or avoided or believed or not believed - is deduced solely on the basis of descriptive - fact-stating - premises. Inferences

2 For a detailed discussion of this debate see J.L. Mackie, Ethics: Inventing Right and Wrong (Harmondsworth: Penguin, 1977).

from descriptive to prescriptive propositions are considered fallacious because the fact that something happens to be the case, or happens not to be the case, is insufficient grounds for concluding that it ought or ought not to be the case. If we want to make a valid argument for a prescriptive conclusion, we must always do so from premises at least one of which is prescriptive. Thus the following commits the fallacy of deriving ought from is:

How can anyone claim that the monarchy should be abolished?

The monarchy as we know it has been central to British life for nearly a thousand years, arguably longer.

Although it is not expressed as such, the conclusion of this argument is really a prescriptive one - that the British monarchy should be retained - but the conclusion is arrived at purely on the basis of the premise that it exists, and has done so for a long time. As such, the argument is plainly invalid:

P1 ) The British monarchy has existed for nearly a thousand years.

C) The British monarchy should be retained.

In this particular case we can make the argument valid by adding a prescriptive premise as follows:

P1 ) The British monarchy has existed for nearly a thousand years.

P2) Anything that has existed for nearly a thousand years should be retained.

C) The British monarchy should be retained.

But the argument is clearly unsound: poverty has existed for at least a thousand years, but it is surely false to claim that it should be retained.

A pattern of argument that occurs frequently in the context of reasoning about problem-solving and policy making can easily fall into

Rhetorical ploys and fallacies

the trap of committing this fallacy. Suppose someone attempting to find a solution to the problem of global warming were to argue:

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