Another puzzle on logic and obligation

Yesterday, I showed that axiom commonly called ‘ought implies can’ (OIC), if applied to logical reasoning itself, implies that a good part of what are considered logically valid deductions in logic various logics, including the standard formalization of deontic logic itself, would have to be rejected. Today, I’ll discuss a different principle – that obligation implies contingency – and draw another counterintuitive conclusion from it.

If you’re not sold on the axiom, I offer the following argument. For any obligation, the weight of that obligation is only given in experience via the possibility of its absence: in other words, one can only feel obliged to bring about something if it is possible for that thing not to be. Consequently, if there were obligation to bring about what is necessary, it could never be given in experience. While an obligation does not be require its being recognized as such, it at least presupposes the possibility that it be recognized. No such possibility exists in the case of necessities. Therefore, it must be that

(O~□) OA → ¬□A,

which is equivalent to

(O~) OA → ¬A

Given (OIC), this gives us

(OI𝒞) OA → (A ¬A)

We can then define a contingency operator 𝒞 such that

(𝒞) 𝒞A A ¬A

This allows us to rewrite OI𝒞 as follows:


Now, apply this reflexively, as before, to the case of logical reasoning itself. The implication is that for any claim A and agent x, if x is obliged to infer A, x‘s actually inferring must itself be a contingent act.

Now there are two ways to understand this statement, depending on whether we understand reasoning to include in its domain reasoning that can be engaged in, but isn’t, or instead to refer to an act of reasoning actually engaged in. On the less controversial reading, Ought-implies-contingency means that x could simply not engage in a given reasoning process: perhaps our logician has chosen instead to spend the afternoon bingeing on Taylor Swift songs. But on the stronger reading, it means that x, while engaging, could fail to get it. The latter, if correct, would imply something about the kinds of beings to whom logic actually applies, viz. that logic doesn’t apply to ideal reasoners. Consequently, even leaving aside the problem of circular definition, a correct set of inferences or axioms would not be able to be defined by appealing to the kinds of inferences ideal reasoners would make.

A puzzle concerning logic and obligation

The standard axiom for deontic logic, (D), reads as follows:

(D) OA → PA

Where ‘OA’ is read as ‘A is obligatory’, and ‘P’ is read as ‘A is permissible’.

An equally well known principle, albeit more controversial, is that obligation implies possibility.

(OIC) OA → A

The principle the axiom captures is often referred to simply as ‘ought implies can’.

1 The problem

Logic itself, on at least one conception, is a normative discipline: it is about inferences we ought to make.

Applying (OIC) to the subject matter of logic conceived as such, the principle states: any axiom of the correct logical system is one capable of being inferred by the reasoners to whom the obligation to reason so applies.

A problem with this is that as is well known, some axioms of just about any propositional modal logic are infinite in length: for instance, □((p v ¬p) & (q v ¬q) & (r v ¬r)…) i.e. the conjunction of excluded middle for each propositional parameter in the language. If you reject excluded middle, then you can substitute some other example to make the same point (or not!).  The problem, then, is that deontic logic, applied to the domain of logic as such, requires those obligated to reason so to be capable of completing infinitely long chains of reasoning.

Thus, applying a claim of deontic logic reflexively to logical reasoning implies that most theorems of most logics, including those of standard deontic logic, should be rejected.

On economic growth and commodification, 1

There are (at least) two ways in which the growth rate of an economy may be increased.

The first is through an increase in the production of goods or services purchased, as occurred, for instance, when goods like automobiles, phones, computers, etc. first came to market.

The second is through an increase in  accounting of goods that previously existed, but weren’t previously accounted for – that is a movement of goods from non-inclusion in a market to inclusion in it. Letting other things be equal (and because of opportunity costs they usually aren’t), a person who purchases herself a meal rather than cook one, for instance, does not bring about an increase in the production of goods, but only trades in a non-market good, the time and labor used to make her own meal, for a market one, and leads to that good being accounted for. Likewise, if we imagine we line up all the parents of underage children in a given city in a circle, and suppose each parent pays the parent to the right of them the same rate – $20 an hour, say – to watch their children, the real value of services produced would not be greater than they would be in a situation where everyone watched their own children. But since the labor in the latter situation isn’t accounted for in market relations, the former situation would lead to an increase in the nominal value of goods and services relative to the latter. Something similar occurs when a previously illegal good is legalized.

A short remark on specialization in professional philosophy

Public discourse on the nature of philosophy and the future of the philosophy profession currently divides into two camps. One pushes for philosophy to somehow be more public, to move away from specialization by reaching out to the masses. The other holds that the future of philosophy is bound to be more specialized, with different kinds of philosophy available for different subfields, categories of individuals, or even different economic sectors.

Behind the latter view is a pair of assumptions about the nature and understanding of wholes: 1) that wholes are sums of their parts, and 2) that consequentially, distinct knowledge of a whole is built up from, and thus presupposes, distinct knowledge of its parts.

Both of these assumptions are false.

Weekly recap,May 12-18, 2019

This week the blog put up three new posts.

On the consequences of capital concentration and its addendum show how a wide variety of contemporary political problems are directly caused or otherwise conditioned by the concentration of capital according to class and location.

What non-cooperative games can tell us about suffering for a cause discusses a simple, real-world example of a non-cooperative game – a traffic jam – and draws from it the broader claim that even the possibility of obtaining the best, most harmonious outcome for any group considered as a whole requires some of its members to suffer gratuitously, so long as the ideal conditions sought after fail to obtain.

What non-cooperative games can tell us about suffering for a cause

The other day, I found myself stuck on the highway in traffic, which was caused by a lane that was blocked so workers could wash graffiti off of an approaching tunnel wall and trim trees reaching over the highway’s guard rail. The natural reaction of many, if not most drivers in this situation was to place themselves in the shorter and/or faster lane, switching back and forth as necessary up to the point where the traffic jam dissipated.

A traffic jam is a very simple, real-world example of what game-theorists call a non-cooperative game: it is an activity, essentially a very slow race, in which multiple participants have a goal, getting to the end of the jam in the fastest way possible.  It is non-cooperative in that under certain conditions, a participant can better secure that goal for themselves by inhibiting others from achieving it. For instance, if the traffic jam is caused, as they often are, by the imposition of a large blinking light followed by traffic cones blocking off a lane, one can drive as far as one can up to the blocked lane, then merge at the last possible moment, cutting others off and slowing down traffic in the process. In doing so, a driver makes his own position better, but makes the jam worse for everyone else.

People behave in non-cooperative ways for a variety of reasons. Some may have a compelling reason for doing so – emergency ambulance drivers, to continue with our example, can initiate a traffic jam in this way. Others are inattentive, e.g. a distracted driver who slows down and rapidly switches lanes to avoid missing an exit. Others may simply be aggressive or selfish. Others engage in non-cooperative behavior as a preventative and punitive measure against the bad behavior of others, e.g. a driver who refuses to let another merge and thereby contributes to the backup in the merging driver’s lane. Still others, recognizing that their own good behavior won’t be enough to change the underlying situation in light of the uncooperative behavior of others, abandon their natural disposition on the grounds of futility.

Given the assumption that others will behave badly in a given situation, one cannot secure one’s own best outcome by behaving in a cooperative way, e.g. by staying in one lane, driving at a slow, constant pace, and letting others merge when they wish, rather than shifting lanes and closing traffic gaps as quickly as possible. Conversely, the only way to secure the best available outcome for everyone is if everyone (or at least the vast majority) behaves cooperatively, and thus refuses to consider their own advantage under changing conditions.

Let us call the best possible outcome, with respect to a given end, for a community as a whole, just. Understood in this way, not reaction to bad behavior, but indifference to it, serves as a precondition of justice.

Furthermore, for a just outcome in the above sense to even be possible requires that some suffer voluntarily so long as ideal conditions don’t obtain. In doing so, those who suffer under such conditions witness to the possibility of harmony among members of the community, a possibility that they themselves may never see realized.

Lastly, call the harmony of a community, with respect to its natural and chosen ends, consequent on the self-abnegation of its members, its culture.

Voluntary suffering under unjust conditions, then, would serve as a both a witness to and a condition for the very possibility of a common culture.

On the consequences of capital concentration, addendum

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In a previous post, I showed how a wide variety of problems, from rural poverty to data mining, are consequent on or otherwise conditioned as responses to the problem of the concentration of capital resources both geographically and by class. Here, I’ll add a few further points that I neglected to mention in the previous post.

As capital concentration increases and capital itself improves, the number of laborers necessary to secure sufficient societal goods decreases. Hence competition among laborers becomes greater. One way this manifests itself is in a tendency for individuals whose production under earlier conditions had been within the context of household business or even outside of sphere of monetary economic activity, to enter (or re-enter) that sphere, particularly women, children, and the elderly. As a result, households, previously themselves diversified units of production, get drawn into the same kind of iterative non-cooperative game that we earlier saw befall businessmen in their competition for the accumulation of capital, and localities, states, and nations in their competition to secure sources both of revenue for their operations and of labor for their citizens. In short, women and, where legal, children, enter the labor force. Initially, this secures a competitive advantage for two-income households. But in the aggregate, this not only increases the supply of labor, leading to a corresponding decrease in its value; it also undermines the rationale of the household as itself a stable unit for production. Inasmuch as marriage was previously understood as a precondition for the well-being and stable operation of households, the need for marriage in this form is undermined, the absolute rate of marriages decreases, and the rationale for marriage itself, if it is to continue playing any important societal role, must shift, as it has in our society to romantic love. Initially, this leads to the possibility of expanding marriage to those who were excluded by the previous definition, e.g. homosexuals, the divorced, groups of individuals, or blood relatives (the exact groups to whom the institution is expanded will differ from society to society, but the underlying rationale is the same). Ultimately, as it becomes clear that marriage is not a prerequisite for romantic love, the institution itself loses its distinction and meaning.

In societies where public discomfort prevents children from working, they do not remain unaffected by effects of capital concentration. Instead, where the education of children was previously informal and conducted by households and local communities (generally as one activity among others), it later becomes the dominant focus of childhood, aimed at a) inculcating attitudes conducive to working conditions that prevent households from serving as economic units and drains societies of the power and opportunity to bring people together and b) providing the basic skills necessary to secure future advantage as skilled laborers in a capitalist economy. Today, these two aims take the form of a) cultivating an understanding of social relations themselves on the model of market relations, i.e. as transactions between consenting individuals free from natural ties, and b) an emphasis on skills in science, technology, engineering, and mechanics (STEM).

Lastly, as individuals are increasingly bereft of not only capital, but of property more broadly, this comes to affect not only the material conditions of life but also the attitudes and psychology of those thus affected. Bereft of the opportunities to meaningfully participate in productive activity that they can call their own, the economic activity of those lacking capital becomes increasingly concentrated on consumption. This brings with it a general slackening of attitudes of self-denial, such as those previously cultivated by religious belief towards the partaking of sex, food, and sleep. Second, it allows opportunities for consumption themselves to become a source of community substituting for kinds of social relations that economic conditions no longer support. This can take the form of associating only with those who have similar consumption habits (e.g. dining at luxury restaurants), or even of the creation of cultural icons and events (e.g. superhero movies, the Super Bowl) as substitutes for religious and other forms of community. As people increasingly identify themselves with what it is they consume, consumer attitudes are increasingly extended to things not previously thought of as consumer goods (e.g. gender, race). Likewise, if forms left over from a fading culture associate consumption with different types of individuals to different degrees (e.g. teenagers more than adults, women more than men, the wealthy more than the poor), those attitudes will be correspondingly more manifest in a society among those classes more associated with consumption, at least until the underlying logic of capital itself extinguishes the material conditions requisite for those attitudes to be sustained.