A Naturalistic Conception of the Laws of Logic

The Problem

It is a standard notion in philosophy, going back to Aristotle, that what distinguishes us human beings from other animals is our ability to reason.   Unlike any other animals we know of, we conform to the demands of reason.  There are a few different dimensions to these demands.  First, reasoning is a practice that involves concrete interactions with the world, and along this dimension, it demands that we respond appropriately to the objects and events in the world, as well as to other rational agents, forming the right sorts of beliefs and engaging in the right sorts of actions.  Making the norms of this dimension explicit is the task of normative epistemology and ethics, as I see the disciplines, and making sense of what sorts of things these norms are and how they function is the task of meta-epistemology and meta-ethics.  The demands of reason also have a formal element, demanding that we follow the rules of inference, to infer from the beliefs we do have to what logically follows from them.   It is this latter dimension of reason that I will focus on here.

We can refer to standards of coherence and inference by which proper reasoning is bound as the “laws of logic.”  Construing this category broadly, it includes things like the law of exclude middle and modus ponens.  These laws constitute the principles of rationally forming judgments about the world. To form judgments that violate the laws of logic is to be incoherent or irrational, and so, as rational agents, we cannot help but think and act largely in accordance with these laws of logic.  And yet, anyone trying to explain the laws of logic on a naturalistic worldview seems to face a dilemma:

The first horn of the dilemma arises when we try to say that the laws of logic are dependent on the minds of us rational agents.  At first glance, we might try to think of these laws as human conventions, principles that we decide to adopt in order to foster reasonable agreement.  But this will not do.   If we did just make up the laws of logic, it seems like we would be able to change them, but that’s patently absurd.  There’s a further problem with this suggestion, and that is the fact that the very act of deciding on principles seems to presuppose rules of correct inference by which this decision could even count as a good one.  Suppose then, we try to say that the laws of logic are the result of the human brain.  This too faces difficulties, since it seems to imply that in a possible world where there are no brains, there would be no laws of logic, and this seems wrong.  In a world with no minds, a rock still can’t be something other than a rock; all of the things in this mindless world must still conform to the laws of logic.  In short, to say that these laws are mind-dependent on naturalism seems to imply that they are contingent, that they could be otherwise, and that is an untenable consequence.

On the other hand, if we try to think of the laws of logic as non-contingent, we face a different puzzle.  Even on the most metaphysically liberal naturalistic worldview, one seems to be committed to saying that natural stuff like atoms and molecules are causally responsible for everything else (whatever that “everything else,” if anything, may be).  But logical laws, though they certainly exist, are not the sort of natural stuff that atoms and molecules are.  One easy way to point this out is to point out that they are true.  It is true, for example, that from A and if A then B, B follows, and, while we may say true things about natural stuff like atoms and molecules, atoms and molecules themselves cannot be true or false.  Further, it is difficult to say how these necessary truths could be a direct consequence of the existence of atoms and molecules.  On the naturalistic position, it seems that we don’t get things that can be true or false unless we get agents capable of uttering sentences and thinking thoughts that can be true or false.  But if we make the laws of logic contingent upon thinking and speaking agents, it appears as if we are pushed back into the first horn of the dilemma.

This dilemma has led Christian apologists like Greg Bahnsen, Victor Reppert, and James N. Anderson to think the existence of the laws of logic constitute a powerful argument for theism as opposed to naturalism.  On Christianity, it seems like one can give a satisfying response to both horns of the dilemma.  Like us, God is a rational being capable of conceiving truths and so the nature of logical laws are preserved as the second horn demands, but, unlike us, God is a necessary being and so these laws (the outflow of God’s necessarily perfect mind) must be necessary as well, thus avoiding the first horn of the dilemma.  This is a version of the transcendental argument for the existence of God, and, as far as the standard arguments for theism go, I think this is one of the better ones.  However, while I think this argument may pose an insurmountable challenge to some forms of naturalism, I believe that there is a form of naturalism that can respond to this challenge in an elegant fashion.

My goal here is propose a middle way between the two horns of the dilemma available to the liberal naturalist.  This middle way includes providing an explanation of the rules of rational inference that has both a naturalistic component and a transcendental component.  The naturalistic component shows how these rules are a product of animal rationality that arises out of natural causal processes.  The transcendental component accommodates the obvious truth that these laws would exist even in a possible world with no rational animals at all, since they are the preconditions for any sense to be made of things at all.  The key to understanding this sort of explanation is appreciating the explanatory fecundity of what I call a “causal/conceptual” loop.  Elements in the naturalistic story are proposed as causally prior to the existence of logical laws, but these logical laws are conceptually prior to any of these elements since they are preconditions for the possibility of any explanation at all.

I’ll start with the naturalistic story.  I will then show how a transcendental picture allows us to fill the explanatory gaps left behind.

A Four Billion Year Long Story

Let’s start at the beginning.  About four billion years ago on planet Earth, perhaps in a hot spring or ocean vent, strings of nucleotides started bonding together through a purely chemical catalytic process.  This kept happening in random assortment, creating millions and millions nucleotide strands until, eventually, a pretty neat strand came about.  It was a ribonucleic acid (RNA) strand with the strange property of self-replication.  Though this RNA strand had the property of self-replication, it didn’t always replicate itself perfectly.  Sometimes the replica was slightly different than the original, and in some of these cases, the slightly different replica ended up with a more efficient property of self-replication.  In this latter case, we ended up with more of these more efficient self-replicators, replicating themselves.   And so began Darwinian evolution, the means to produce biological complexity out of a purely causal chemical process.

At some pretty early point in the evolutionary timeline, this process brings about organisms towards which we can adopt what Daniel Dennett calls the intentional stance.  That is, we can interpret these organisms as things acting in accord with beliefs and goals.  There’s no sharp line in the evolutionary timeline from when we can’t productively adopt the intentional stance towards an organism and when we can, but it seems like a safe bet to say that, we can adopt the intentional stance to something like a paramecium with some success.  When a predator attacks a paramecium, it seems as if the paramecium is trying to get away, as if it doesn’t want to be eaten.  In fact, it’s nearly impossible to not see its behavior in these goal-oriented terms.  Now, it doesn’t really want not to be eaten, or really believe that its predator a potential harm to it.  Of course not; it’s a paramecium!  But we can attribute these intentional states to it, and make sense of its behavior accordingly.

In order to treat the paramecium as having these intentional states, we have to treat it as a basically rational organism, as following the laws of logic.   Dennett says,

one gets nowhere with the assumption that entity x has beliefs p, q, r . . . unless one also supposes that x believes what follows from p, q, r . . . ; otherwise there is no way of ruling out the prediction that x will, in the face of beliefs p, q, r . . . do something utterly stupid, and, if we cannot rule out that prediction, we will have acquired no predictive power at all.

Here, we have the first glimpses of what I’ll call primitive rationality.  Now, the paramecium isn’t really rational, in the sense that we’re rational.  But we have to think of it as rational, in order to think of it as having beliefs and intentions.   And when we do this, we can make sense of its behavior, and we can predict how it will behave when it is thrown into various circumstances, even without knowing anything about its internal biology.

There’s a reason why we can think of the paramecium as rational with some success.  The sorts of behaviors that evolve by the process of natural selection are the once that make it such that the paramecium survives and reproduces, and when these behaviors inevitably evolve, it will seem as if the paramecium is itself trying to survive and reproduce.  Of course, it doesn’t really have a concept of self or death, but it acts as if it does, and if it didn’t act in that way, it wouldn’t be able to pass its genes on to make more things like it.  That’s the reason why evolution has made it the way it is.  When we make a claim like this, we’re adopting another stance, what Dennett calls the design stance, towards the paramecium, treating at as something that was made with particular goals in mind.  And now we’re also adopting intentional stance to evolution as the “designer,” the thing that makes organisms with the “goal” of survival and reproduction “in mind.”  Of course, evolution doesn’t really design anything; this attribution of intentions to it, as well, is merely instrumental.   And yet, this instrumental attribution is the only way we can explain, in an informative way, why it’s possible to instrumentally attribute rationality to the paramecium.

It’s not too hard to see how we can get a paramecium out of the fundamental laws of physics.  And we can see this paramecium as exhibiting primitive rationality, “choosing” its actions in accord with its goals in a way consistent with the laws of logic.   But of course, we haven’t solved the problem of naturalistically explaining the laws of logic yet, since all we’ve gotten is something that can be attributed rational behavior.  We haven’t gotten to the rules of rational judgement themselves yet.  We’ve only gotten a thing that can be seen as following these rules, and we still have no clue as to how these rules actually got there such that they could be followed.

So let’s fast forward a bit until we get some mammals.  Around 160 million years ago, our ancestors were small rat-like mammals (let’s just call them rats for simplicity).  These rats appear to have all sorts of beliefs about the surroundings they are in, about what sorts of things are food and what sorts of things are predators, and they seem to be relatively smart in their going about the world.  Now, what sort of rationality do these rats have?  Is it simply the same sort of “primitive rationality” that we saw in the paramecium?  If it is, it seems quite a bit less primitive.  It’s much harder thinking of the rat’s apparent rationality as a purely instrumental rationality attribution.  It seems as if the rat really is acting in accord with a will, with intentions and beliefs.  But how could that possibly be the case?  What other stuff happened between then and now?  Well, there was a billion years of evolution.   There was a billion years of back and forth between the “primitive rationality” that we attributed purely instrumentally to the paramecium and the “design motives” that we attributed purely instrumentally to the evolutionary process.  And, through this back and forth, animals came about that are truly purposive.   This is to say that we cannot regard thinking of rats as having reasons as merely a convenient shortcut, since now, if we did, without thinking of them as having reasons, we would be missing something.

There’s no clear-cut line between the paramecium and the rat which says at this point, we’d really be missing something if we didn’t think of these organism as genuinely purposive.  But since it seems that we can view the paramecium’s primitive rationality as “merely instrumental” and we cannot regard the rat’s in the same manner, this transition must occur.  Now, of course, these rats don’t sit around reflecting on their purposes.  But it’d be a mistake to think that, because of this lack of reflection, they don’t have any purposes at all.  They have what Dennett calls “unrepresented reasons.”  And the norms to which they conform are what Robert Brandom calls “implicit norms” of rationality.  But the story can’t end here.  We’re still in the dark about how these norms came about.  So far we know that the evolutionary process still causes animals to follow these norms, but we still don’t know what sorts of these things these norms themselves are, or how they came about.  So let’s fast forward even further.

Now we come to the great apes, our most recent ancestors, and here my story hinges on some empirical work in comparative psychology primarily by Michael Tomasello and his lab.  Apes are highly social in a sense that did not exist in animals before them.  Of course, the rats just discussed might appear to be follow rules in acting around other rats, in mating, in competing for territory, and so on, but there isn’t a particularly strong community-based social structure among the rats.   In the ape’s community, the primitive social norms that might be interpreted in the rat’s behavior have gotten quite a bit more complex.   We find a relatively rich normative social infrastructure, and within this infrastructure there are various communicative gestures that apes employ with the intention of instigating some action in another ape.

And then, in the context of this social infrastructure, something strange happens:  collective intentionality develops.  According to Tomasello, for this to happen, we must learn the trick of recursive mindreading.  He has us consider a case in which you’re at a bar, and you point to your empty glass to signal that you want more whisky.  By pointing at your empty class, the bartender reads your intentions, knowing what you want, and knowing that you want a drink.  Further, you, know that the bartender will know what you want.  And even further, the bartender knows that you know that he knows what you want.  This recursivity terminates in shared intentionality, a shared goal-oriented perspective on the world.  As far as we know, we’re the only living species that has learned this trick, and, accordingly, the only one that has this sort of perspective.

With the advent of collective intentionality, these rules of rationality that we’ve been privately following for millions of years now become our rules, and for the first time in history, animals understand each other enough to hold one another accountable when they fail to live up to them.  Now, of course, when I say that they “hold one another accountable,” this is not in the sense that we hold one another accountable by taking one another to court or something like that.  What I mean is that they are able to implicitly understand the concept of a normative transgression.  And, in holding each other accountable we can come to understand ourselves as being accountable.  To understand ourselves as accountable is to understand ourselves as bound by these norms.  Here then, marks the switch from implicit rule-following to explicit rule-following, from unrepresented reasons to represented ones.  In Proverbs it says, “The fear of the Lord is the beginning of wisdom,” but perhaps what it should have said is “The fear of messing up is the beginning all wisdom.”  Explicit understanding of ourselves the world in which we inhabit arises out of the awareness of the responsibility we take on for violating our shared norms of reason.

Once we explicitly understand ourselves as norm-bound agents, we can try to formally articulate the norms by which we are all bound.  And thus, the rules of rationality end up being articulated as the laws of logic and systematized by the discipline of formal logic.  We get principles things that look like this, (P∨∼P), and rules for manipulating these principles that look like this, {P,(P→Q)}⊦Q.  These are our explicit interpretations of the rules of rationality that we’ve all been implicitly following for millions of years.

If we come across aliens from another galaxy, it’s possible that their explicit interpretations of the rules of rationality might be quite different than ours.  Perhaps they use a form of propositional logic in which the only operator they use is the Sheffer stroke (thinking of logic in this way is perfectly coherent, but rather annoying for our feeble human minds).  In this system they would symbolize the law of excluded middle as (P|P)|((P|P)|(P|P)), and maybe that’s a law that doesn’t immediately click in their minds, just like P→(P→P) doesn’t really click in ours.  Even if this is the case, by virtue of the fact that they are rational beings, they will still be following the same norms of rationality as we are.  Therefore, since a logical system is just an explicit interpretation of the norms of rationality, their logical system will be isomorphic with ours.  And thus, when we say that both we and the aliens will discover the same laws of logic, we are saying that our explicit interpretations of the norms of rationality will be constrained in the same sorts of ways.

Looking Back at the Problem

Now we’re in a position to really answer the question.   Where do these laws of logic come from?  The answer to this question, as I’ve promised, has two sides.  On the first side, they didn’t come from anywhere; these just are the rules of rationality as they can be articulated by explicitly rational beings.  When rational beings came into existence by purely non-rational evolutionary processes, they came into being as following these rules.  And then, at some later point in time they became aware of themselves following these rules, and able to represent them explicitly.

But if our answer stopped here, it wouldn’t be satisfactory, since the nature of these rules of rationality still seems utterly mysterious.   We know the laws of chemistry come from the laws of physics, but no reduction seems possible at all when it comes to the rules of rationality.  So, the other side of the answer is to make a statement, not about nature, but about us.  It is to say that the rules that we interpret animals like rats as conforming to are the rules of rationality as made explicit by us.  When we see there as being implicitly logically-governed behavior in nature, we interpret nature in accordance with the way we understand ourselves as explicitly logical.  We think of the behavior of entities of nature as if they represented their rational behavior like we do, and so we see the paramecium and the rat as conforming to the laws of logic, our way of explicitly representing the norms of rationality.  These things don’t have the slightest clue what the laws of logic are.  But they behave as we do, and that’s how we see them.

We can only make explanatory sense of how we have become explicitly aware of logical laws by showing how we are the result of beings that evolved an implicit awareness of these laws.  And yet, we can only understand our natural ancestors as having implicit grasp of logic once we’ve garnered an explicit grasp of logic.  That’s the only way we can make sense of them as actually following the laws of logic. There’s what we might call a causal/conceptual loop here, in that our ancestors’ having evolved to behave rationally is causally prior to our ability to explicitly grasp and articulate these norms of rationality, but this ability to explicitly articulate rational norms is conceptually prior to understanding our ancestors as behaving rationally.

The reason it is unproblematic for an explanation to conceptually (but not causally) presuppose that laws of logic is that we cannot hope to get out of these laws conceptually, since they just are, to use P.F. Strawson’s phrase, the bounds of sense.  When sense-makers like us naturally evolve this just is the way in which we must make sense of things.  It’s is the essential structure of sense-making, so to speak.  And since explanation is a sense-making enterprise, and any coherent explanation will conform to sense’s bounds—the things we’ve come to describe as the laws of logic.

On this transcendental understanding, when we say that, even in a world where life never came about, the laws of logic would still apply, we are saying something about a possible world as we could make sense of such a world.  Insofar as this latter part is added, it is clearly true that the laws of logic would still apply in a lifeless world (even though there wouldn’t be things that would become aware of them).  If one wants to reject this latter condition, then I can’t say I even know what they’re talking about when they bring up this possible world!  When we talk about any other possible world, we have already made sense of it, making it intelligible, conceiving of it as conforming to the laws of logic.

This is a very Kantian sort of view, and I take the important lesson to be learned from Kant here to be the transcendental nature of certain norms.  Unlike traffic laws, the laws of logic are transcendental in that they are necessary conditions for any sense to be made of things at all.  That’s what makes them different.  The name “Kant,” especially when the word “transcendental” is also mentioned, will ring alarm-bells in the minds of many naturalists.  But I don’t think naturalists need be alarmed here.  Though my story includes a transcendental element, it seems that we can give a perfectly good naturalistic explanation of how it got there.  Of course the explanation of how we’ve come to make sense of things will have to be put in terms of the way we do in fact make sense of things; that’s the causal/conceptual loop that I’ve mentioned. I don’t see how we could get around it, nor do I see why we would want to.

(edited 4/27)