The "logical necessity of obligations" puzzle

[Mighara Sovmadhi]

So there is this puzzle in deontic logic, the logic of the concepts of permission, prohibition, obligation, etc. and the puzzle concerns the fact that the primordial deontic functions are interpreted as postulating the existence of an obligation that is always necessary, i.e. if deontic logic mathematically exists forever, then so does this primordial duty, as it were. But without agency there would be no duty, hence the puzzle: it "surely" does not seem as if there are always necessarily agents, does it?

Well, one quasi-solution to the problem (this is all taken from the Stanford Encyclopedia of Philosophy article on the topic) is to say that the eternal duty is to make sure the Law of Non-Contradiction morally obtains. This is vacuously satisfied since no being can violate said Law. And "surely" a vacuous solution to a pure logical problem fits the abstraction of the case, no? Well, what if no?

On the face of it, "the power to make sure the Law of Non-contradiction perfectly holds," sounds absurd, for this is the one delimitation of omnipotence, that the divine nature can do anything consistent with this principle, and so this principle is the only internal limit on the divine nature's abilities---but not to the detriment of the divine glory, mind you. However, as the case may be, if we postulate the eternal duty as similar to safeguarding the laws of logic, then we have to postulate an agency commensurate with this task. But it is only something with power akin to what many would describe as divine, that would be up to said task. Now, this doesn't immediately lead to particular theism, or even monotheism at all, maybe. The physical postulate would just be that some unknown number, possibly one, possibly infinite, of physical agents, also has the property of necessarily existing somehow, empowered to the safeguarding of whatever Law needs to be upheld and protected. However, the eternal aspect of the duty in question does strongly weigh the interpretation in favor of the perhaps greater simplicity of assuming a singular transcendental agent, on this level. Or at least it paints an aesthetic argument to said effect, maybe.

[Avatar]

Uh, no obligations are always necessary?

--A

[Mighara Sovmadhi]

Well, it's an incredibly obscure obligation that's in question. Has something to do with the pure use of the OB operator in SDL (Standard Deontic Logic) and some weird quantification principle for existence in formal logic. Like, the relevant axiom for the relevant operator only has a sufficient semantic grounding if it "ranges over" an existent entity who can meet the abstract obligation encoded into the axiom, or some such thing. So this obligation, whatever it is, is supposed to in fact necessarily exist, inasmuch as it is supposed that the laws of logic are eternal truths or suchlike forces. But then the entity or set of entities that SDL thus "ranges over" will also exist eternally, which is the puzzle as it doesn't seem in fact that we just have to assume that some such entity exists (unless, perhaps of course, we were theists?).

[Avatar]

Sounds like sophistry to me.

--A

[Mighara Sovmadhi]

Here's the puzzle from the SEP article:

Consider

(1)Consider

(1) Nothing is obligatory.
A natural representation of this in the language of SDL would be:

(1') ~OBq, for all q.
We noted above that OB-NEC entails OB-N: :: OBT; but given (1'), we get ~OBT, and thus a contradiction. SDL seems to imply that it is a truth of logic that something is always obligatory. But it seems that what (1) expresses, an absence of obligations, is possible. For example, consider a time when no rational agents existed in the universe. Why should we think that any obligations existed then?

von Wright 1951 notes that since the denial of ~OBT is provably equivalent to PET (given the traditional definitional scheme and OB-RE), and since both OBT and PET are odd, we should opt for a "principle of contingency," which says that OBT and ~PET are both logically contingent. von Wright 1963 argues that OBT (and PET) do not express real prescriptions (pp.152-4). Follesdal and Hilpinen 1971 suggests that excluding OB-N only excludes "empty normative systems" (i.e., normative systems with no obligations), and perhaps not even that, since no one can fail to fulfill OBT anyway, so why worry (p.13; cf. Prior 1958) However, since it is dubious that anyone can bring it about that T, it would seem to be equally dubious that anyone can "fulfill" OBT, and thus matters are not so simple. al-Hibri 1978 discusses various early takes on this problem, rejects OB-N, and later develops a deontic logic without it. Jones and Porn 1985 explicitly rejects OB-N for "ought" in the system developed there, where the concern is with what people ought to do. If we are reading OB as simply "it ought to be the case that", it is not clear that there is anything counterintuitive about OBT (now read as, essentially, "it ought to be that contradictions are false"), but there is also no longer any obvious connection to what is obligatory or permissible for that reading, or to what people ought to do.

The theistic inference does not seem to be suggested, either historically or by the author of the article, so though such an inference might be sophistry, I would not be inclined to describe the existence of the puzzle itself as inferred invalidly.

[Avatar]

I'm not sure I understand. Nothing is obligatory, in and of itself.

Any implied obligation springs from subjective moral constructs. Except things like breathing of course, but that's only obligatory if you wish to live, for example.

--A

[Mighara Sovmadhi]

OBT reads "it is obligatory that T," where "T" is the law of non-contradiction or something similar. Of course it might be something of a reducto of objectivistic(al!) ideas about morality, that they would require such a bizarre obligation.

[Vraith]

I'm not sure I understand. Nothing is obligatory, in and of itself.

Any implied obligation springs from subjective moral constructs. Except things like breathing of course, but that's only obligatory if you wish to live, for example.

--A

Breathing is an obligation? Funny.
Most obligations don't even arise from moral constructs, though. We may translate them into moral forms, but that's not why/how they are born.
Why should I keep my word?
Because the body of human culture [and human survival itself] works better when people do.
Why do we punish people who don't keep their word?
Because they make that body sick or weak...threatening survival.
The whole mess evolves and becomes complicated because we are complex---have such a wide range of needs, desires, and particular contexts...creating conflicts within ourselves and with others.

I don't think a logical necessity of obligation exists. Only practical/pragmatic necessity.
Some things can only be meaningful in the abstract by destroying/stripping away meaning in practice.

[Avatar]

Of course breathing is obligatory, if you want to carry on living.

--A

[Mighara Sovmadhi]

I think that's just one way the word "obligatory" is used. Just like we might say "there's nothing you just have to do, you only have to do things if you are doing something else."

Does this confuse two senses of "have to"? Much has been made of the similarity between the "modal hexagon" and the "deontic hexagon" in formal logic.* However, plenty of interesting locutions in natural language have been analyzed in this context, such as show that deontic logic operates on some sort of principles weirdly different from those of plain modal logic. When we say "I have to" or "I must" as a modal assertion, we are just describing what is automatically true if something else more general is true. For example, if I say, "I have to go to the moon if I am going to set up a base there," well, sure that's true, but in a cause-and-effect sort of way or whatever. So when I say, "I just have to go to the moon," and leave it at that, well, that's the point. Not everything we do is in order to accomplish something else. That would be absurd on a number of levels, maybe all of them. So it is possible for us to do things for their very own sake. Now, since deontic modality is irreducible as such to alethic modality, it does not seem as though it follows from the fact that "obligatory/have to" is used in an iffish way, that this is the only use of such terms/phrases, wherefore the argument that nothing is obligatory by itself because we say things otherwise sometimes doesn't go through, since the inference is a limited participation in the vernacular.

*Also, the most substantial work in deontic logic of which I am aware, i.e. Paul McNamara's, posits a very different "shape" for the pure diagram of the operators in the logic. It's an octodecagon or something, not a hexagon. So moral information is apparently possibly much more complex than plain modal information. In fact, let's say we even tried to abandon speaking of things as "just obligated by themselves." Now, the language still speaks of the concept of "going beyond the call of duty," which is also known as supererogation, and as far as the history of such words goes, this ties in with the word "obligation," which is after all then paired with the concept of duty. No one rightly says, "It is my duty to do such-and-such, only if I am doing something else." Not that there are no such duties, but rather it is natural to think of duties we have---also called "responsibilities" sometimes---that we just have. And anyway, McNamara's graph basically asserts the supererogation operator as an aspect of what makes his polygon end up so much more complex than the original modal one.

[Vraith]

Of course breathing is obligatory, if you want to carry on living.

--A

Yea...I don't like that usage of "obligation." It seems to dilute/distort the meaning, making it a synonym for necessary. Breathing---or a similar process that performs the same function---is necessary for all living things to live. Obligation exists only when you have agents.

[Avatar]

I agree really. I only added into that earlier post so that nobody would say "But you're obliged to keep on breathing..."

--A

[Mighara Sovmadhi]

It's still an interesting question, and it's one Kant fiddles with so much in his moral writings. For him, moral reasoning is practical reasoning of a special kind. We can rather easily tell that we are using reason to guide our actions when we infer means from ends and apply such information. Thus far, we can think of rational activity. However, rationalists liked to press the idea that reason is not just a faculty of conclusions but contained special premises, and not just vague laws like noncontradiction but substantial claims. Kant argued that reason is the faculty of asking questions to infinity, and so the only substantive or non-vague axioms it supplies take the form of problems to solve. But the assertion of the problem is not the assertion of an infinite object that solves the problem---this discrepancy is where transcendental illusion creeps in.

But anyway, then, in theoretical reason, empiricism is the use of sense-perceptions to supply the premises of reasoning. In Mill even noncontradiction comes from a distinct experience, that of the basic operations of the empirically-recognized faculty of belief and disbelief. But then in practical reason empiricism is using sensations of desire, which are like imperative sentences ("Go eat! Go to sleep! Stop touching the hot surface!"), to supply the premises of reasoning about imperatives.

And here, then, the idea of "have to" as having meaning only in relation to "if" becomes stark. For it is again fairly clear that imperative inferences are valid, at least in natural language. Consider:

• 1. Go to the store.
  2. To go to the store, it is necessary to take the road.
  C. Therefore, take the road.

What Kant tries to prove, then, though fail he may have, is that there is an imperative "sentence," if you will, encoded into pure reason. Since he takes the erotetic road on this score, he assimilates the concept of a moral "ought" to the notion of the a priori synthesis of the concept of pure rational action, with finite sentient nature. As he puts it, what I ought to do is what I would do if the only source of inputs into my action-function were reason. This is a rather peculiar analysis and of course G. E. Moore essentially rejects it in his (in)famous Principia Ethica, but unless you're sympathetic to that cause...

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