The previous consideration of Rudolf Carnap’s The Logical Structure of the World, brief as it was, showed that the existence of such structure cannot be argued for. Nor can you get from logical structure—as Carnap sees it, anyway—to its presence in ordinary experience. For in order to avoid the “subjectivity” of grounding science on individual sensations, Carnap comes up with a “structural” account of what he calls “elementary experiences,” which in fact bear little resemblance to what we actually experience of the world. So let us leave Carnap aside and start from such experience—from what phenomenologists call the “life-world”—and ask whether it exhibits logical structure of a very basic type. If it does, then we can say that whatever we make of Carnap’s constructional system and the problems it encounters, our life-world would be a place for logic.
We normally assume, of course, that the “laws of logic” hold in our experience—but what would our world look like if they didn’t? Consider the good old (and gratifyingly simple) law modus ponens:
p implies q; p; therefore, q.[1]
If modus ponens were always invalid, we could instead conclude:
p implies q; p. therefore, not-q.
But this is just a restatement of
p or q
So what we are asking about is a life-world in which modus ponens is only intermittently valid:
p implies q; p; therefore, q or not-q
I suggest that a world in which modus ponens functioned like this would be indistinguishable from the world we live in, where surprises—violations of actual cases of modus ponens—are common:
If x is a swan, x is white.
If x is hydrogen, x has atomic weight 1.00784
When we get such surprises, we normally salvage modus ponens by saying that the specific empirical rules in play—that all swans are white, or that there is no such thing as deuterium—were wrong. It’s our fault, we didn’t get the rules right.
It is, I think, revealing to note the similarities between this and the way some believers excuse God from causing evil. If an earthquake hits Lisbon and between 13,000 and 50,000 people die, the goodness of God is not impugned: either the catastrophe leads to some greater good and so was not really evil (Leibniz), or we caused it by building a city in the wrong place (Rousseau). So with modus ponens: if it doesn’t work in a particular case, it is we, not modus ponens, who are to blame. The religious undertones to this are unmistakable, and call to mind Nietzsche’s dictum somewhere about the “laws” of logic: “No law without a Lawgiver.”
If the logical structure of the world cannot be argued for or shown from experience, it seems that it must be an assumption—and since it is an action-guiding assumption, a matter of faith. In the case of someone like Carnap, that faith is clearly rock-hard; but so was Antigone’s faith in the eternal laws that commanded her to bury her brother.
Immutable unwritten laws of heaven
They were not born today or yesterday
They die not; and no one knoweth whence they spring (Antigone, Loeb, lines 454-457
The alternative to construing logic in this crypto-theological way is to say that modus ponens, and a fortiori other rules of logic, are only approximate or probabilistic. With apologies to George Boole, they are rules of thumb, rather than laws of thought. As a convention, modus ponens can govern other conventions (as it does in mathematics); but it does not seem to “capture” our ordinary experience other than probabilistically. There is no firm place for it, no place where it can be counted on to hold, just a series of happy coincidences.
This was the view that Hans Reichenbach, whose thought I explored a bit in my The Philosophy Scare (2016), takes of the laws of nature. The laws of logic, for their part, are for him purely analytic, i. e. tautological, and so place no constraints on reality. They can inform us of nothing but our linguistic conventions. But those conventions are themselves murky and imprecise, which is why “linguistic analysis” became central to philosophy in the 20th Century.[2] So logic is at most a normative account of how we should use words; it certainly does not describe how we do use them. This is a good thing to have, but is a peculiar place to be in.
If logic does not describe (or “capture”) anything about the world, is it of more than grammatical interest? We use language to describe things; but we also use it to formulate orders, suggestions, hints, and so on—it has directive uses. One thing logic can do is provide general directives for structuring, not the life-world in general, but our experience of it as temporal—as having a past and a future which have bearing upon the present.
Consider “A=A,” the “law of identity.” In standard interpretations, this contains two tokens of a single type; while the tokens have different temporal and spatial positions, the type does not, and so is somehow above space and time. Hegel, however, interprets the “law” as temporal (and spatial) through-and-through.[3] Temporalized in this way, it says that A at one time is the same thing as A at another time; and this locution, which expresses an obvious tautology, also shows itself also to be an impossibility: if A=A because they are both A, A ≠ A because, since A is in time, some of its properties change over time. Temporally speaking, identity is never absolute; it is always, at best, what Hegel might call identity-over-difference. In order to be purely self-identical, a temporal being would have to persist wholly unchanged for some period of time. I challenge anyone to adduce an actual experience of something like that.
And so we learn one very general “rule of synthesis” for connecting the past to the present (or two pasts to one another): any A is both identical to and different from previous states of itself. This “dialectical” rule provides us with an abstract heuristic: in seeking to establish connection to some phenomenon of the past which may have produced some later state of the world, we are to look at what in the past resembles the later state of affairs and what does not. To be in the past includes to be given as resembling the present, but not wholly.
It is not like this for beings in the future, for at any time in the future there may be no “A” at all. Talking about any specific future thing—such as A—is not really talking about the future; we are talking, at most, about a sort of ersatz future into which we have projected aspects of the past and/or present. Logic, simply by its abstractness, allows us to avoid such projection, for its emptiness captures that of the future, allowing for something completely new and different to come to pass—as long as that something does not contain contrary qualities at the same time.
In this perspective, the “laws” of logic function, not as unchanging truths detached from time (as philosophers from Plato to David Lewis and beyond have seen them), but as very general rules for bringing together past and future, thereby constituting a present. Here they do yeoman service—less, perhaps, than when they are considered to structure something called “the world;” but more than they deliver as empty tautologies.
[1] I’ll keep this in ordinary language except for the variables.
[2] Linguistic conventions may also actually violate basic conceptions of logic. In his treatise “On the Non-Existent,” as reported by Sextus Empiricus, Gorgias uses the premise that to be is to be somewhere: “that which is nowhere is not.” This defines existence, not as independent of all (or of all other) properties, but as bound up with location. Of course, Gorgias was a sophist; but the point of good sophistry was to advance premises which were, individually, acceptable but which added together produced an unacceptable conclusion. So it seems that Gorgias’ Hellenophonic audience, at least, agreed that to be is to be located somewhere.
[3] G. W. F. Hegel Science of Logic (A. V. Miller, trans.) London: George Allen & Unwin, 1969 pp. 411-417