My purpose here is to present a formal framework for the relationship between intuitions and concrete particular judgements in moral cases and the general theories which are supposed to capture them. This framework is to give that relationship a suitable interpretation in intuitionistic (or constructivist) logic, with which I hope to give an interesting way to articulate the difference between theoretical and anti-theoretical approaches to ethics. On this interpretation, the propositions to be evaluated are particular moral judgements, and they are evaluated in terms of whether they are endorsed by the general theory in question. What the particular judgements or the theory are is unimportant for my present purposes, since what I am after here is to make a general point about the way these things might relate.

The feature of intuitionistic logic which interests me here is that it gives a way to articulate how theories might only imperfectly account for the particular cases they are supposed to address. On intuitionistic logic, a theory is gradually constructed over successive stages of reasoning, where there are conclusions you can reach at later stages which would be unwarranted at earlier ones. In the paradigmatic interpretation, concerning mathematical reasoning, propositions ~~stand for mathematical theorems~~ are mathematical propositions, and to assert a proposition is to claim that there is a mathematical proof of it (and asserting a negation means that there is a proof that the ~~theorem~~ proposition can't be true). The theorems proved at stage n can then be used to prove further theorems at stage n+1 which could not be proved or disproved with the resources of stage n-1. Of particular interest here is that intuitionistic logic allows for a final stage of reasoning, where there exists either a proof or disproof for every theorem. At this final stage intuitionistic logic is equivalent to classical logic (for instance, the law of excluded middle then holds, and, more importantly, the logic becomes complete,

*but only at the final stage*).My claim here is that theoretical approaches to ethics are ones where, if we give a suitable a intuitionistic interpretation to the field of particular judgements and the general theory, the approach asserts that there is some (actual or possible) final stage of theory construction where every particular judgement is comprehensively captured in the theory. Anti-theoretical approaches deny this. The interpretation would be as follows: there is some theory

*T*at stage*s*which validate inferences to certain moral judgements (A,B,C, etc.) – this is meant as a straightforward analogy to the mathematical case. This allows for an interesting contrast between approaches which allow for a final stage of theory construction, and ones that don't. If we were at the final stage of our theory*T*(let's call it*T*_{Ω}), then the content and import of every particular judgement would be accounted for by*T*. In contrast, if we aren't (and might never be) at*T*_{Ω}, then there remains some particular judgement on the strength of which*T*can be modified, and needs to be if*T*is to be a comprehensive guide to our moral lives. This seems to me to be equivalent to the anti-theoretical claim in ethics: that there is no systematisation of our ethical practice which can hope to capture the variety and complexity of that practice, but that there will always be a remainder which is not accounted for in the theory.My claim is very limited – I am not proposing something like a logic in which to couch our moral reasoning. But, even in the limited role as a way to make an important distinction, my proposal here has its virtues. Casting the developing of an ethical theory as a series of constructive stages matches very well with the view, for instance, of our understanding of ethics as an expanding circle of moral concern, where as we develop our moral sensibilities we see duties to things we hadn't considered important earlier. It also is a natural ally of something like the reflective equilibrium to approach to moral reasoning, where we have a to-and-fro between general theories and particular moral judgements, each being revised on the strength of the other. But intuitionistic logic is not the same as reflective equilibrium: for one thing, the latter isn't a logic; another, more troubling point is that intuitionistic logic doesn't allow for the type of oscillation between different versions of particular claims that reflective equilibrium requires.

What I mean is that, once we reach some stage

*T*_{n}where moral claims A, B and C are validated (given comprehensive and convincing support by*T*), then at no*T*after*T*_{n }will A, B and C fail to be validated. Reflective equilibrium isn't like that: up until the final equilibrium is reached, everything is up for modification. This leads to what I see as the greatest problem for my proposal: interpreting particular moral claims in the way we do theorems in mathematics might not be very convincing, especially because we are often very willing to give up particular judgements or intuitions which seemed certain to us earlier.I have two replies to this worry, one ambitious and another more modest. The ambitious reply would try to dodge this problem by being very careful about what the scope of the particular moral claims are. Instead of having a proposition A like 'intentionally killing another human being is always wrong', which we might believe to a greater or lesser extent given variations in our background theories and our moral theory as a whole, we can see the pronouncements at earlier stages of

*T*to be on propositions like B = 'intentionally killing of a human being without special societal sanction is always wrong' and C = 'there is some appropriate societal sanction which would allow for the intentional killing of another human being', where*T*_{1}might validate B but not C, whereas*T*_{2}might also validate C's negation (if our moral theory ended up being a pacifist one, for instance). Having finer-grained judgements of this type makes it far more believable that we can at some stage of the reasoning set some of them in stone (at least regarding the further development of*T*). The more modest reply, in contrast, would be to point out that the distinction I'm trying to make between theory and anti-theory holds even if there are just two or three stages of reasoning, where when we go to*T*_{Ω }we settle almost every moral question in one bound. This is not a fantastic state of affairs, since if we take many defenders of various theories at their word, when we carefully and conscientiously apply the theory in question, we at least have a procedure for answering any moral question (difficult to apply as it might be).There is a further worry, about whether the claim that a theoretical approach to ethics would entail asserting that there is some final stage for the theory in question is too strong a claim – it at least seems to assert the existence of a complete decision procedure which either asserts or denies any possible particular moral judgement, which many people who see themselves as opposing moral anti-theory would also deny. But I will leave that question unanswered at the moment.

1) Theorems are things that have been proved, so 'there exists either a proof or disproof for every theorem' probably should read '...every proposition'.

ReplyDelete2) Intuitionistic logic can't settle every claim as being true or false. i.e. 'p or not-p'.

3) To prove every proposition that can be proved requires at least a countable number of iterations. This makes it impractical for humans to reach a sensible fixed-point where the set of proven theorems is stable.

Intuitionistic logic is (loosely) just classical without excluded middle. It's not he beast you are looking for. It sounds like you want some sort of belief-revision system, or a non-monotonic logic. If you want to read up on belief revision, start with AGM - its the industry standard. It's got problems, but its better to start with the mainstream views.

ReplyDeleteEthics is mainly about gut-feel, and what seems right to people, plus figuring out justifications for their reactions. The main type of logic to paddle in the shallow end of this kind of reasoning is deontic logic, and its all bollocks (the logic, that is). I suggest that you keep fancy logics out of post-facto justification - humans are much better at ethics, in the sense of being more ethical, when they don't think through the logical consequences of their justifications, which are generally quite separate from the basis for their intuitions.

ReplyDeleteReflective equilibrium can be modelled with Adaptive logics, which are a class of logics also usually modelled by stages. Each stage changes the judgements on previous stages, sometimes making some previous claims unfounded. Some claims have the status of being derivable, no matter what future stages might occur. Others seem to stay true, but aren't provably so, and others change back and forth once, twice, or even unprovably often. The range of behaviours available varies based on the the flavour of logic within the adaptive logic framework, but if you are going to draw an analogy with some type of logic, again this may be more suitable than intuitionistic logic.

ReplyDeletePlease leave NJ alone. Brouwer doesn't deserve this.

ReplyDeleteThanks for the comments, Andrew.

ReplyDeletePointing out the sloppy wording around 'theorems' is exactly the kind of thing I dreaded a logician might find. Also thanks for the pointer to adaptive logics -- I'll investigate whether that works as well (and I can already see that you're right that they fit reflective equilibrium very well). I'm encouraged by it also working in stages, like intuitionistic/constructive logic. I have also wondered whether a non-monotonic logic might be what I'm after, like you suggested.

But I want to come to the defense of what I'm doing. I'm certainly not hoping to provide a logic for moral reasoning -- I share your opinion of deontic logic, and I'm not optimistic about something else coming along to plug the gaps. What I'm trying to do is to wheel in an interesting feature of intuitionistic logic in order to articulate an important point in meta-ethics.

Most ethicists disagree with you when you say that ethics is about gut-feel. At the very least, there is almost certainly some type of rational constraints to be put on what we feel, and we not only can but must reason from our moral judgements. That means they have propositional content, and it means we can do at least

somelogic with them. Not a lot, probably, butsome(the Frege-Geach problem for expressivism is a good example of this point). Michael Dummett is someone who has done a lot of interesting work on relating features of intuitionistic logic in particular to ethics (though I don't know of where he's done what I've tried to do here -- it's possible he has, intimidatingly productive as he is).The prevailing tradition in normative ethics is to try and provide fully systematised theories for our moral judgements. Many prominent ethicists, like Philip Pettit, believe that you are simply not to be taken seriously unless you are arguing for some such system. But increasingly many people disagree (Jonathan Dancy is the best known, our own Christine Swanton is a good example as well). What I tried to do here is give a nice clear way to split ethical theory from anti-theory, making use of this interesting feature of the logic.

So, on that point, I'm not after belief-revision: I'm after the contrast between complete and incomplete systems. I'm attracted by intuitionistic logic because it provides that contrast, which is what you get when you move from some non-final to the final stage of construction. The final stage is equivalent to classical logic, meaning that it can decide every proposition, and all the other (enormously optimistic) things a complete moral theory is supposed to do (in fact, like I said, I worry whether this is too strong a claim). Denying a final stage of reasoning is a nice way to articulate an anti-theoretic position, tohugh, and I find that

veryencouraging.So, I'm not convinced that I need to give this up. I'd love it if you had another go, though.

(I must admit I have no idea what you mean with: "Please leave NJ alone. Brouwer doesn't deserve this.")

Thanks for clarifying. Classical reasoning in any system at least as complex as arithmetic is also incomplete, and I'd take moral reasoning to be as least as self-reflexive and complex as arithmetic, although that is a loose statment and really just an analogy. Int logic doesn't allow reasoning by cases, and various other limits that might seem odd in moral reasoning, so if you can steer away from that particular system and towards the complete/incomplete distinction, you might be better served.

ReplyDeleteI agree with your comments about most ethicists believing that ethics is more than gut feel, but take it as no more than a sociological observation, as I don't regards most ethicists as particularly expert on how humans make ethical decisions. I laugh openly, long, and loud, at the position taken by Pettit etc, if it is supposed to be a description of how humans reason, and question its usefulness otherwise ('how humans ought to reason to be ethical' is defining ought with ought, and I'd need a foundation below that).

NJ is the abbreviation for the natural deduction system for Int logic that is taught at AKL in Stage II, where I thought you may have been exposed. Brouwer is of course the father of constructivism and Int logic, and a wonderful mathematician. I would think that he would take Int logic as expressing a theoretic rather than anti-theoretic position, and disappove of it being applied to ethics. He wouldn't think much of 90% of Dummett's [ab]use of Int logic either.

One last note. Many writings applying Godel's incompleteness theorem to non-logical or mathematical matters are crap, as they take the result to be more deep and meaningful than a technical limitation of a recursive approach to reasoning with peano axioms. Most others draw airy-fairy analogies to make some spurious point. It may appear that I have recommended the latter course of action. I have not, merely given reasons why it would be no worse, and possibly better than continuing with your Int logic analogy. This hopefully will give you pause for thought. Analogies to technical properties of logic are no better than analogies to technical properties of car engines - discussing the delay lag of a particular brand of turbo may be an analogy for the time taken to make a decision, but in general its a poor analogy, and why choose an Evo VIII?. Be careful not to borrow some 'authority of rigour' from logic. It will sound phony to those who understand any logic, even if it impresses the ignorant.

This doesn't mean that you can't make a nice descriptive or evocative analogy; some people have succeeded, but many more people have not.

Thanks for clarifying. Classical reasoning in any system at least as complex as arithmetic is also incomplete, and I'd take moral reasoning to be as least as self-reflexive and complex as arithmetic, although that is a loose statment and really just an analogy. Int logic doesn't allow reasoning by cases, and various other limits that might seem odd in moral reasoning, so if you can steer away from that particular system and towards the complete/incomplete distinction, you might be better served.

ReplyDeleteI agree with your comments about most ethicists believing that ethics is more than gut feel, but take it as no more than a sociological observation, as I don't regards most ethicists as particularly expert on how humans make ethical decisions. I laugh openly, long, and loud, at the position taken by Pettit etc, if it is supposed to be a description of how humans reason, and question its usefulness otherwise ('how humans ought to reason to be ethical' is defining ought with ought, and I'd need a foundation below that).

NJ is the abbreviation for the natural deduction system for Int logic that is taught at AKL in Stage II, where I thought you may have been exposed. Brouwer is of course the father of constructivism and Int logic, and a wonderful mathematician. I would think that he would take Int logic as expressing a theoretic rather than anti-theoretic position, and disappove of it being applied to ethics. He wouldn't think much of 90% of Dummett's [ab]use of Int logic either.

One last note. Many writings applying Godel's incompleteness theorem to non-logical or mathematical matters are crap, as they take the result to be more deep and meaningful than a technical limitation of a recursive approach to reasoning with peano axioms. Most others draw airy-fairy analogies to make some spurious point. It may appear that I have recommended the latter course of action. I have not, merely given reasons why it would be no worse, and possibly better than continuing with your Int logic analogy. This hopefully will give you pause for thought. Analogies to technical properties of logic are no better than analogies to technical properties of car engines - discussing the delay lag of a particular brand of turbo may be an analogy for the time taken to make a decision, but in general its a poor analogy, and why choose an Evo VIII?. Be careful not to borrow some 'authority of rigour' from logic. It will sound phony to those who understand any logic, even if it impresses the ignorant.

ReplyDeleteThis doesn't mean that you can't make a nice descriptive or evocative analogy; some people have succeeded, but many more people have not.

Oops. Comments duplicated, as blogspot claimed my comment was too long to save, then saved it while I was cutting it into two. My comments are barely worth reading once; don't read them twice!

ReplyDelete