Clearly, the predicate ‘must’ appears, prima facie, to be a stronger predicate that ‘should’. Why is this? It seems to either ‘contain’, as it were, or entail some kind of modality; in this case, one of necessity. Take Kant’s categorical imperative. If we forget, for one moment, what Kant actually wrote on the subject, surely it is the case that he should (!) have written:

Subject S must follow the categorical imperative as it applies to act X.

If Kant had written

Subject S should follow the categorical imperative as it applies to act X.

it would (!) have been a much less demanding or weaker kind than the former version. When we say

S should do X.

what we really mean, I think, is

S should do X given context B and conditions A.

or something of that kind, whereas

S must do X.

does not cry out for such a qualification. We are effectively saying, in the vernacular,

S must do X – no matter what!

Is this not what Kant had in mind when he formulated his categorical imperative? In addition, at a prima facie level, again, it seems to be the case that

should = ought (to)

Even if the above are not identical, either morally or epistemically or whatever, both predicates are still often taken as synonyms or very closely connected predicates. However, in Kant’s case, he did often use the word ‘ought’ but didn’t use, I think, the synonym ‘should’ quite as much, if at all (i.e., in his context of moral duty and human freedom). Thus

S ought to do X.

seems to have a normative or moral resonance which ‘should’ doesn’t have, at least not to such a high degree. Perhaps this is just a question of a contingency or nicety of English grammar or usage and not a conceptual/definitional - let alone a modal - question. However,

Joe ought to be kind to his animals.

has a lesser normative power when expressed as

Joe should be kind to his animals.

So if ‘should’ doesn’t have the same normative burden or power as ‘ought’, it may best fit, say

Joe should not climb Mount Everest in his slippers and pyjamas.

Conversely

Joe ought not to climb Everest in his slippers and pyjamas.

seems to be a little clumsy or even archaic in its use of ‘ought’. Again, the archaic glow around ‘ought’ is also simply a contingent fact about English grammar or usage as well a the conversational implicature of its utterance in a context. For example,

You ought to drink red wine – it’s nicer.

just sounds plain odd, whereas

You should drink red wine - it’s nicer.

sound s like a non-normative and even non-aesthetic recommendation.

In modal terms, ‘must’ seems to bring with it the baggage of some kind of modality. That is,

Subject S must do X in order to bring about A. If S does not do X, then the required consequent, A, will not occur [of necessity].

Here the predicates ‘will’ or ‘will not’ help establish the modal feel of ‘must’ in the context of the just stated (logical) imperative. If we say that something or other ‘will not happen’, a logician can translate this into

S must do act X in order to bring about consequence A. If S does not do X, then, of necessity, consequence A will not, and could not, occur. Thus if S wants A to occur, he must, of necessity, do X.

The problem here is one of using the modal ‘of necessity’, or its English derivations, in what seems to be a future contingent scenario. That is, when we say

S must do X in order to achieve A.

its logical form can be

S must do X at some point in the future if he or she wants to bring about consequence A. 

Of course, just as certain philosophers see problems with assigning  truth-vales to future contingent statements because they believe that an un-instantiated event or action, when expressed linguistically, cannot be the object or subject of a truth-valuational predication; so it may be equally problematic to use modal predicates in future-counterfactuals. However, must-counterfactuals are less problematic than ordinary expressions of future contingents - therefore of their truth-values, or lack thereof. That is, when we say

S must do X.

are we really or actually talking about a future act or event in which S will do X in order to bring about A? Can we look at this must-counterfactuals in another way? Of course! In the evident way suggested by that very term, ‘counterfactual’. Counterfactuals, after all, are not about the future (or the past or present) at all. When we say that

S must do X in order to bring about A.

we are not talking about a future contingent scenario and it modal acceptability. We are talking about an expression that is non-temporal or without  time-index; or, perhaps more correctly, we are talking about a physical act and its physical consequence, not their linguistic expressions, in non-temporal, non-time-indexed terms. As Quine puts it, this modal expression about a particular subject and a particular kind of action which brings about a particular type of situation or condition is really an ‘eternal sentence’ (1970). That is, just as the sentence ‘2 + 2 = 4’ expresses a true proposition that is in no way analysed in terms of its temporal context (it has none), so a must-counterfactual expression is also an ‘eternal sentence’ - or non-temporal expression - which is really about the logical impossibility or possibility of a subject bringing about a specific condition when he or she commits a certain type of act.

Alternatively, we can sneak possible worlds into this discussion in order to get out of our former expression’s seemingly temporal straight-jacket and context. That is, our sentence

S must do X in order to bring about A.

can be expressed in terms of possible worlds, thus:

At every possible world at which conditions of type A have occurred, a possible world inhabitant or counterpart must, of necessity, have carried out an act of type X. At no possible world at which counterparts or non-counterparts have carried out X can it also be the case that consequent A did not follow.

But here again we have sneaked in temporal indicators such as the phrases ‘must have [already] done X’ and ‘did not follow’.. That is, the above is expressed in terms that suggest - or state - that consequence A has already come to pass at this or other possible worlds. And neither does it suggest that the act of type X is still here or elsewhere in transit, as it were.

We can still express ourselves logically in terms that seem not to be contingently and contextually determined and/or time-indexed. For example, we can say

Take any case of volitional act X being instantiated. Take any subject, S, who carries out X. In every conceivable situation in which S does X, consequent A must, of necessity, follow.

In other words, as is always the case with logical truths or laws, it is actually irrelevant whether or not some subject, S, has or has not actually committed act X and thus brought about a consequence of type A. It does not matter if this situation has occurred in the past, is occurring now, or will occur in the future. What matters is

If S, or if any S, commits act X, then consequent A will follow from act X as carried out by subject S.

This is a statement of inferential entailment, even though it appears to be instantiated by a physical person and involves physical conditions. It will still work as a logical true if act X has never been done or even if it will never occur in the future. (Though its future non-realisation is itself logically and metaphysically or/and epistemically problematic.) However, perhaps the statement above is better seen as an analytic, rather than solely logical, truth.

We can express all this symbolically, thus:

"a  "c $S      ((Xa ^ SXa) É (SXa É SAc))

[Key: 'a' = 'action'; 'c' = 'condition-consequence'; 'S' = 'subject'; 'Xa' = 'action X'; 'SXa' = 'subject S dos action X'; 'SAc' = 'subject S brings condition-consequence A about'.]

Of course my quantification over subject-based volitional acts and physical events, rather than over objects and properties, is problematic and no doubt logically expressed in ways more complex and detailed than the above.

In addition, in modal logic, instead, we can have

((Xa É ”SXa) É (”SXa É ”SAc))

This formula is a de re, or extensional, expression of our former modal sequence of events. Perhaps a de dicto, or intensional, reading will be more satisfactory (to some). Thus:

” ((Xa É SXa) É (SXa É SAc))

Again, perhaps I should (!) or ought to say that it may be a big mistake to read modal or metaphysical natures into these otherwise ordinary language predicates. This was the fatal mistake committed by nearly every metaphysician before Frege, Wittgenstein, Russell and the logical positivists of the 1920s and in the decades before, at least according to Frege, Wittgenstein, Russell and the logical positivists. That is, should we really say that ‘must’ or ‘will’ has a modal and/or normative nature; and that ‘should’ has only a normative but a non-modal one? Similarly, if someone says

Judgment Day will happen in the very near future.

is the utterer of this really expressing something of a modal nature or status rather than something of an exclusively, say, apocalyptic nature? This is not an argument about that sentence’s modal credentials as a future contingent and/or counterfactual (or not), but simply an argument to say that a subject, in this case at least, may really mean, but not say, that

Judgment Day will happen in the very near future if we don’t get our act together in terms of the world’s and our own massive geo-political problems.

So although I am not arguing that people are never aware of the modal nature or status of many of their predicates or statements, the above is not, or need not be, modally interpreted if it is really an ellipsis for the latter translation just given. However, it may well be, or it could be, the case that

Judgment Day will happen in the very near future.

does indeed have a modal resonance for certain non-philosophers who may utter it; even if such people have never heard the term ‘modal’ or even use the word ‘necessity’ or ‘necessarily’ often, if it all. But even here, if we taken the above as it may actually be spoken by a certain subjects at a certain time within a certain context, rather than as merely inscriptions on the page, then we may again need to rely on our interpretations of such utterances in terms of their Gricean conversational implicature. In that case, one such utterance of the above, perhaps because expressed in a monotonic and coldly logical way, may have a justifiable strictly modal interpretation. However, if spoken by someone with foam running down his chin and shouting the sentence out loud, then a reading of this maniac’s outburst may have no truly modal interpretation at all and thus be solely an expression of, say, what he really wants to happen given this or that (say, growing secularism and hedonism), rather than an admittedly hyperbolic claim that the end is nigh that is nevertheless still partly modal in nature.

There is a danger, of course, of going back to the kind of ‘ordinary language’ philosophy that was in fashion just before and a little time after the Second World War. My position is not necessarily one of tacitly accepting Wittgenstein’s commandment that every philosopher should ‘leave everything as it is’ and, instead, stick to descriptive and analytical linguistic work. In addition, it is not necessarily expressive of a desire to let various metaphysical flies out of the ordinary language fly-bottle in order to enable our perennial philosophical problems to escape by rejecting traditional metaphysics; which had confusedly, apparently, created the problems in the first place. In other words, a modalist can say, in response, that he is not in the least bit interested in everyday usage, or even in purely descriptive linguistic analysis, but instead he is concerned with the modal status and nature of concrete conditions, concrete acts, concrete events and concrete objects or persons which may well be expressed by everyday predicates and in everyday sentences (such as ‘it will, ‘you must’ and ‘one ought to’). When our modalist, qua modalist, says

S must do X in order to achieve A.

he is primarily talking about a physical act, X, a physical consequence, A, and the bodily and mental movements of a physical subject who does X. More clearly

If a human rational subject caries out a volitional act of type X, then this physical occurrence will cause or bring about the physical condition or consequence A.

Perhaps our modalist should never really write about things like Mount Everest, slippers or moral acts like giving money to charity if such examples or formulations of ostensibly modal and metaphysical fact or truth create problems in terms of their strictly linguistic – non-modal – nature and status. Bringing in predicates like our earlier name ‘Joe’, or consequence A’s being John becoming a ‘millionaire’, may only serve to muddy the desired modal waters. If we are categorically not talking about linguistic usage or the specific actions, specific consequences, specific subjects and a specific moral (or non-moral) volitional act and its specific consequences.