Tuesday, 6 April 2010

In Defence of Hume’s Guillotine

It may, of course, be a false memory but I remember one clear sign that the last Conservative government had “lost it”. Minister after minister would be interviewed on television and repeat the mantra that they needed to better explain their policies. They saw growing opposition not as a sign that they should re-think their policies but that their policies were sound and anyone would support them if they were just communicated correctly. The idea that they were simply wrong never seemed to occur to them.

Sam Harris gave an eighteen minute “TED” talk entitled “Science can answer moral questions” and ran into some pretty forthright opposition. Much of this opposition Harris seemed to lay at the difficulty in properly explaining himself in the time available:

“18 minutes is not a lot of time in which to present a detailed argument” (Harris, 2010)

Listening to the talk I saw little that extra detail would add. My opposition, and the opposition of others, was guaranteed by the title. We subscribe to Hume’s Guillotine, the old maxim that you cannot derive an ought statement from an is statement. Harris mentioned the Guillotine in the opening minutes of the speech

“it’s often thought that there is no description of the way the world is that can tell us how the world out to be”.

Absent some pretty clear and interesting arguments that Hume’s Guillotine was wrong (and there were none such in the talk) it is clear that any moral system based on deriving ought from is would be wrong. No amount of explanation, no more clarity, would add to that. Harris had not fallen foul of a time limit but of a basic logical error. I am a little jealous of the pithy way Sean Carroll put it:

“Attempts to derive ought from is are like attempts to reach an odd number by adding together even numbers. If someone claims that they’ve done it, you don’t have to check their math; you know that they’ve made a mistake. (Carroll, 2010)”

Harris is of the opinion that not only is Hume’s Guillotine “clearly wrong” (the talk) but that there is something wrong in holding to it:

“Many of my critics piously cite Hume’s is/ought distinction as though it were well known to be the last word on the subject of morality until the end of time. Indeed, Carroll appears to think that Hume’s lazy analysis of facts and values is so compelling that he elevates it to the status of mathematical truth”

To be fair to Harris many people adopt Hume’s Guillotine unargued for. It is time that we examined the Guillotine, which I shall do below. We will not find it to be a “mathematical truth”, but will see that it is a logical one.

The claim made by Hume’s Guillotine

“In every system of morality, which I have hitherto met with, I have always remark'd, that the author proceeds for some time in the ordinary ways of reasoning, and establishes the being of a God, or makes observations concerning human affairs; when all of a sudden I am surpriz'd to find, that instead of the usual copulations of propositions, is, and is not, I meet with no proposition that is not connected with an ought, or an ought not. This change is imperceptible; but is however, of the last consequence. For as this ought, or ought not, expresses some new relation or affirmation, 'tis necessary that it shou'd be observ'd and explain'd; and at the same time that a reason should be given; for what seems altogether inconceivable, how this new relation can be a deduction from others, which are entirely different from it.”
(Hume, 1739)

The key claim is that some reason should be given for the introduction of an ought statement, a reason that cannot be given by however long a chain of is statements. It is not the claim that there are no moral facts, it is the claim that if there are moral facts then these do not derive from non-moral facts. It is not the claim that part of a moral argument cannot be formed of non-moral facts, that is statements cannot help in our formulation of ought statements. It is the claim that if we conclude “ought…” then we must have “ought…” somewhere in our premises: that there is a reason for “ought” and that is another “ought”.

The form of arguments

(By “arguments” I do not mean some disagreement or row. For “argument” I adopt the Monty Python definition: “a connected series of statements to establish a definite proposition”)

All arguments can be represented in the following form:

1. Premises
2. Conclusion

Arguments are generally split into deductive and inductive arguments with deductive arguments thought to be conclusive, whilst inductive arguments non-conclusive.

A deductive argument is one where, if the premises are accepted, the conclusion cannot be denied without contradiction. The old example is:

1. (Premise) All men are mortal
2. (Premise) Socrates is a man
3. (Conclusion) Socrates is mortal

If one were to deny Socrates’ mortality then, to maintain consistency, one would either have to deny than Socrates was a man (and thus deny the second premise) or claim the existence of at least one non-mortal man (and thus deny the first premise).

Non-conclusive arguments are termed inductive. The premises are held to be indicative of the conclusion, lend some support to the conclusion, make the conclusion more likely or whatever but the conclusion can still be denied without contradiction. Whilst we may conclude that “all ravens are black” because all the many hitherto seen ravens have been black there is no contradiction in believing that purple ravens may exist somewhere, have existed or will come to exist.

How conclusive arguments work

In the Socrates example we begin with a generalisation: “all men are mortal”. This statement has consequences, lots of them. It means that Plato is mortal, Aristotle is mortal, Cratylus and Xenophanes are mortal. It means that anything of which we can say “is a man” is mortal.

The second premise, “Socrates is a man”, picks out just one of those consequences. We could have picked out any of the other consequences, that about Plato or Aristotle or any of the others. The key issue is that we would be picking out a consequence of “all men are mortal”, a consequence that (to be picked out) must already be there. Before we make the specific statement that Socrates is mortal we have already said it in general.

Kant calls this picking out of consequence that is already there “analytic”:

“(I)f I say: “All bodies are extended,” then this is an analytic judgement. For I do not need to go outside the concept that I combine with the word “body” in order to find that extension is connected with it” (Kant, 1998, p. 130)

The conclusion to a conclusive argument contains no more than is contained in the premises of the argument.


Now all arguments on which we rely are, in a certain way, conclusive. That “certain way” is that we conclude. As a consequence, in principle, a logically conclusive argument can be reconstructed for any accepted proposition.

It is important not to confuse “conclusive” with “shown to be true”. If we conclude incorrectly then we still conclude and there are still reasons why we conclude how we did. “Conclusive” should not even be confused with “rational” or “reasonable”. If we come to an entirely unreasonable conclusion we do so because, well, we are being entirely unreasonable. We still have reasons why we conclude as we do even if they are not thought to be particularly good reasons.

If, for example, I conclude that “the pixies are after me” you might think me insane. “Insane” would be a reason put forward to explain my, otherwise odd, conclusion. Only insane people think that pixies are “after them” when everything else is normal and, given a few ancillary facts, certain types of insanity will lead one to believe in malevolent pixies. Here is the argument:

1. Pixie-type insanity
2. Ancillary facts
3. (Conclusion) The pixies are after me

The “pixie-type insanity” I have imagined above has as part of its consequences a range of situations where the sufferer (me) would become convinced that pixies were after him. The ancillary facts pick out one of those situations: situations that, as with individual mortal men, are already there. We need not go “outside the concept” of “pixie-type insanity” to find the conclusion.

On non-insanity inspired arguments, Kant expands his “containing” concept:

“in synthetic judgements I must have in addition to the concept of the subject something else (X) on which the understanding depends…(i)n the case of empirical judgements of experience there is no difficulty here. For this X is the complete experience of the object that I think through some concept A.(Kant, 1998, p. 131)”

When saying something about the world (“synthetic judgements”) requires us to go “outside” the concepts we hold. The concepts we hold do not “contain” descriptions of the world. To remain conclusive the arguments we put forward must have something about the world (the “X”) added to our premises. It is the fact that, from Hume’s arguments against induction, this X is contains more than we can possibly derive from empirical data that motivates the entire Critique of Pure Reason: where do the extra premises come from?

Whether or not Kant is successful in overcoming “Hume’s problem” (of induction) or, indeed whether Hume’ arguments against induction are sound, we can see the problem behind the critique: what reasons do we have for concluding on the basis of seemingly inconclusive arguments. How do we make the arguments conclusive?

The same issue faces us with “all ravens are black”. The evidence we have is not conclusive, it is compatible with a number of different propositions. Yet we do conclude. Somewhere, buried in our heads, must be another principle which, together with the arguments we put forward, entails “all ravens are black”.

Back to Hume’s Guillotine


1. All arguments are conclusive
2. The conclusion of a conclusive argument is “contained” in its premises
3. A conclusion that expresses a “should” has a premise that expresses a “should”

---Edit---12th April 2010

Dave Lull has sent me a number of links to another blogger's detailed examination of the is/ought distinction in Hume:

Reading Hume on Ought and Is

On Ought and Is, II

Hume on Ought and Is, Part I: Background

Hume on Ought and Is, Part II: The Argument

Hume on Ought and Is, Part III:

Is-Ought Muddles

Blackford and Is/Ought

Works Cited
Carroll, S. (2010, 03 24). The Moral Equivalent of the Parallel Postulate. Retrieved 04 05, 2010, from Discover: http://blogs.discovermagazine.com/cosmicvariance/2010/03/24/the-moral-equivalent-of-the-parallel-postulate/
Harris, S. (2010, March 29). Moral confusion in the name of science. Retrieved April 5, 2010, from Project Reason: http://www.project-reason.org/newsfeed/item/moral_confusion_in_the_name_of_science3/
Hume, D. (1739). A Treatise of Human Nature. London: John Noon.
Kant, I. (. (1998). Critique of Pure Reason. Cambridge: Cambridge University Press.

No comments: