Peter asked:

I understand that there is a contemporary refutation of the Humean is/ought 'naturalistic fallacy' which
incorporates ideas from philosophical logic. Could someone please outline simply how it is suggested
that 'ought' can, after all, be derived from 'is'? Thanks.

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You are probably alluding to a well-known article published, I think, In The Philosophical Review
called "How to Derive an 'Ought' from an 'Is.'" by the University of California philosopher, John Searle.
I read it some time ago, so I don't recall the details. Whether you believe it is a refutation of Hume's
view really depends on whether you think it is a successfulrebuttal of that view. I don't remember
finding it persuasive myself, and I don't think many other philosopher have either. Hume thinks that to
derive an "ought" conclusion from any premises, those premises must contain at least one "ought"
premise. On the general principle that in a valid deductive argument, there can be nothing in the
conclusion not contained in the premises, I would say that there can be no refutation of the
naturalistic fallacy, although there have been, and may yet be, many rebuttals.

Kenneth Stern

Hume's point that you cannot derive an "ought" from an "is" is not the naturalistic fallacy. The
naturalistic fallacy is a logical problem described by G.E. Moore aiming to refute arguments that good
is a natural property.

I didn't know that there was a logical way to derive an "ought" from an "is" so I looked in An
Introduction to Ethicsby Geoffrey Thomas and there it was! You would probably find this book helpful
generally. The argument comes from an article by A.N. Prior called "The Autonomy of Ethics" in the
Australasian Journal of Philosophy38 and is probably presented more plausibly than it is here.

The argument is based on material implication. Any proposition 'P' implies the truth of 'P v Q' ('v' is the
logical connective which represents 'or' in the inclusive sense, i.e. 'either P, or Q, or both') because if
'P' is true one disjunct is true. Whenever 'P' is true, 'P v Q' can never be false. Call this the
'v-introduction rule'. If you have 'P v Q' and you add the premise ¬P ('not P') then that logically
implies Q. This is the 'v-elimination rule' or material implication.

Now take a factual descriptive "is" statement, Thomas's example being "she is old and lonely" the
negation of which is also factual and descriptive, i.e. "it is not the case that she is old and lonely". Call
these F and ¬F. Then formulate a normative "ought" statement such as "you ought to help her".
Call this N.

Here is the formalised argument:

*F (premise)

*F v N (v-introduction rule)

*¬F (premise)

*So N

Or in English:

*She is old and lonely (premise)

*She is old and lonely or You ought to help (v-introduction rule)

*It is not the case that she is old and lonely (premise)

*So you ought to help her (v-elimination rule = material implication)

This looks absurd and one reason for this is the logical rule that a self-contradictory statement implies
any other statement. However, the point is that because F is a descriptive statement, F v N must also
be a descriptive statementdespite the fact that F contains an "ought". This is because only a
descriptive statement can imply another descriptive statement. N, "You ought to help her" is no longer
a normative value statement expressing an attitude or imperative. So "ought" becomes a matter of
fact.

Rachel Browne