The limits of means/ end reasoning
'Ought' operates in a variety of contexts outside means/ end (instrumental) reasoning.
Take the case of : 'The train ought to arrive by 21.00hrs'. This means that the probability is that it will arrive by that time. This is a probabilistic prediction unconnected with means/ end reasoning.
Again, 'I ought to be at the meeting tonight but I can't make it'. This means or can mean something like (to add context) : 'I had planned to go to the meeting tonight and a lot of people will be expecting me but I can't go because I have cut my arm'. 'Ought' functions non-instrumentally here. It simply contrasts my previous plans and people's current expectations with what I can - or rather, can't - do. The 'ought' may not be a moral 'ought'; it could be merely the 'ought' of etiquette.
What does Hume exactly say ?
I cannot forbear adding to these reasonings an observation, which
may, perhaps, be found of some importance. 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 way of reasoning, and establishes
the being of a God, or makes observations concerning human affairs;
when 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 imper-
ceptible; 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. But as authors do not commonly use this precaution, I shall
presume to recommend it to the readers; and am persuaded, that this
small attention wou'd subvert all the vulgar systems of morality, and let
us see, that the distinction of vice and virtue is not founded merely on the
relations of objects, nor is perceiv'd by reason. (Treatise III.1.1..0
To understand why Hume believes that 'ought' introduces a 'new relation' you have to set aside means/ end reasoning and wants. They are, excuse my directness, red herrings.
Hume's sting in tail of Treatise III.1.1. is that no moral 'ought' can ever validly be derived from a non-moral 'is'. Or, said another way, a valid argument cannot have both an ethical conclusion and purely non-ethical premises; the non-ethical premises are ought-irrelevant. Or yet again, nothing about what ought or ought not morally to be the case can be deduced from what (as (i) a pure matter of actual or putative empirical fact or (ii.) a conceptual truth : 'a matter of fact' or a 'relation of ideas' in Hume's language) is or isn't the case. A 'new relation' is introduced when we move from 'is' to 'ought'.
As an example :
- The air in New York is high in particulates due to heavy traffic.
Therefore
- Traffic ought to be banned from New York.
The argument is invalid because there is a logical gap between 'is' and 'ought'. Ethical conclusions ('Traffic ought to be banned from New York') cannot validly be derived solely from non-ethical premises ('The air in New York is high in particulates due to heavy traffic'). Any argument like this, which goes straight from an "is" to an "ought", must therefore be invalid. This is Hume's point.
Hume has his own way of transitioning the gap
Hume does not say, believe or imply that moral 'oughts' are not crucially based on empirical facts or conceptual truths - on what 'is' the case. It is just that he does not believe that the transition is one of logical deduction. Moral judgements - judgements about what we morally ought to do - arise causally from emotion, not logically by deduction.
Hume's position is more clearly stated in the Enquiry concerning the Principles of Morals. There are shifts of viewpoint between the Treatise and the Enquiry, so these are not exactly interchangeable texts, but there is enough linkage for our purposes.
Take an issue, whether euthanasia should be legalised under certain conditions, c1 ... cn. This is not something Hume considers but his ethics can deal with it - how satisfactorily is another matter.
Moral judgement has the following genesis.
- We must check all the relevant facts, or as many as it is practicable to check:
... it is often necessary, we find, that much reasoning should precede, that nice distinctions be made, just conclusions drawn, distant comparisons formed, complicated relations examined, and general facts fixed and ascertained.
- We must take a general view:
He must here, therefore, depart from his private and particular situation, and must choose a point of view, common to him with others ...
http://www.gutenberg.org/files/4320/4320-h/4320-h.htm
This means that the requisite moral sentiments will arise only if we detach ourselves from our personal interests and inclinations. Adam Smith captured this perspective of 'a point of view, common to him with others' in his idea of the 'impartial spectator' (Theory of Moral Sentiments, I.i.5.4). Hume talked of 'the principle of humanity': http://www.gutenberg.org/files/4320/4320-h/4320-h.htm.
When these conditions are fulfilled, what causally arises is an emotional reaction, which is all that a moral judgement actually is. We experience 'certain peculiar sentiments of pain and pleasure' as Hume puts it in the Treatise:
https://www.gutenberg.org/files/4705/4705-h/4705-h.htm
These sentiments are 'peculiar', sui generis, unique, unlike any other sentiments or emotions in their specific character. To stress the emotional nature of moral judgement Hume observes that 'Morality ... is more properly felt than judged of':
https://www.gutenberg.org/files/4705/4705-h/4705-h.htm
Conclusion
There is much to probe in Hume's statements about moral judgement and its relation to emotion. I am not concerned to analyse or defend those statements here. The point is that when we note Hume's logical objection to the derivation of 'ought' from 'is' and his causal account of the emotional origin of moral judgement, we have left means/ end reasoning and wants far behind.
Logical endnote
It is in fact possible logically to deduce a moral 'ought' from a non-moral 'is'. This can be done as A.N. Prior showed by or-introduction :
'Coffee-drinking is common in the United States; therefore either coffee-drinking is common in the United States or you ought to lend me $100.'
For an assessment of Prior-style manoeuvres, see Campbell Brown, 'Minding the Is-Ought Gap', Journal of Philosophical Logic, Vol. 43, No. 1 (February 2014), pp. 53-69.
References
Campbell Brown, 'Minding the Is-Ought Gap', Journal of Philosophical Logic, Vol. 43, No. 1 (February 2014), pp. 53-69.
J. Harrison, Hume's Moral Epistemology', Published by Oxford University Press (1976)
ISBN 10: 0198750374 ISBN 13: 9780198750376.
Geoffrey Thomas, An Introduction to Ethics, Published by Gerald Duckworth and Co Ltd (1997), Pp.53-8.
ISBN 10: 0715624318 ISBN 13: 9780715624319.