Logic is everything we know. In some sense.
Ludwig Wittgenstein and logic
Ludwig Wittgenstein’s examinations into the where logic can take us, what its limits are, and what it is dependent upon are found in his Tractatus Logico-Philosophicus. The Tractatus is one of the most important philosophical works of the 20th century, at least in analytic philosophy. By reaching toward the limits of logic, the Tractatus culminated the logical positivism that was moving toward its head in the Edwardian and succeeding eras. Wittgenstein’s own work almost certainly had its origins in his conversations with Bertrand Russell, whose Principia Mathematica hailed a major moment in uniting mathematical logic with philosophy, and analyzing mathematics itself according to the rigors of this logic.
When was Western society any more ready to disrobe itself, to lay bare anything that might be masked, to discard the old and step forward into a brave new world, than the 1890s and early 1900s? It was a jarring time. Even the French Revolution cloaked itself in classical reference, and used the word radical, at least initially, in its most literal sense.
The rise of socialism, fascism, the Progressives; the prostration of religion before critical theory; the destabilization of every Western country’s constitutional self-identity; the final steps toward a factory-dominated economy – nothing was tied to time, and the air was thick with New Ideas.
Wittgenstein was hardly deficient in this attitude, but we must remember that it was not just the New that men were infatuated with, but the Pure. Psychologically, we might say they wanted stability. On their own account, though, it was unadulterated, unmediated, independent, pure Knowledge. Few desired this so strongly as Wittgenstein.
He was not alone, but what makes him unique among the logical positivists (of which he was the most important, and the most logical) was his ability to let go of the notion that he could really know anything as certainly as he wanted. For, the bewilderingly strict logic of the Tractatus leads to the conclusion that the only pure logic rests on the foundation of tautologies. An equation, for example, only has a conclusion when it is set up with an equals sign: 2 + 3 = 5. That is, each side is the same. They are saying the same thing. The only truthful propositions we can make are tautological. A strict opponent of induction, Wittgenstein strove for absolute purity, not the proximal and possible truth of inductive thinking.
Where a Descartes or a Russell or others looked for a rock-solid principle to base all the rest on – a prima causa of the logic itself – Wittgenstein instead saw that there was none. We could make a truly logical language, but the arbitrariness of naming, of defining, would prohibit us from saying anything logical about that original naming. We should note, however, that Wittgenstein refused to call himself a nominalist; while the nominalists said that the only things that existed were our own designations for things, he accepted that there were actually things around us – just that nothing purely logical could be said about them, apart from our naming.
The philosophy of Wittgenstein can be thought of like a donut with a very small hole. At the center is tautology. All examination of the center proceeds itself from the center. The eye cannot see itself. Next, the donut itself is the sum total of logical statements that can be made about the world, and the outer edge is the edge of logic. Beyond is contradiction – what cannot be known by any pure logical connection with the central tautology.
Why did Wittgenstein stop looking for the rock-solid center? His method is based on the idea that logic, and therefore truth, is not about the existence of independent things, but about the relations between things. When we say we know something about something, we talk about it in its relations to other things. If relationships are central to logic and to knowledge, then contradition and tautology are “without sense.” There is no sense to a tautological or contradictory statement because there is no relationship. There is no “it follows that…”.
In Wittgenstein’s verbiage, what is logical is “what can be said.” But by practicing our saying, our language, we can come to understand certain things about the way it works. That is, we have intimations about what the center, the eye, might be – and therefore also what the limits of our logic, and our sense, might be. This is what can be shown but not said.
The divine, or whatever is beyond those limits, thus cannot be known in the same way that we know about the rest of the world. However, feeling those limits is the feeling of mysticism, to Wittgenstein. To search out connections of that feeling would not have sense, as we think of having sense.
A logic less strict than Wittgenstein’s, but more common
But we can see that the mystical/metaphysical possibilities are ultimately related with the tautological source of our logic. An Aristotelian will want to extend his logic of the world to his mysticism, and he will end up with something like St. Thomas. But perhaps someone who thinks like a postmodern conservative will follow Wittgenstein’s logic, in the pure sense, and understand that my logic of the-world-I-see might differ in sense (rather than form) from metaphysical reasoning. The lack of reference is made up for by divine revelation, which must become the stable stake from which we launch out our logic – the center of the donut. But even the choosing of which revelation to follow entails no pure logic. Rather, decision is an act of the will, and commitment is a decision. Even if logic, to Wittgenstein, is inexorable beyond the tautological center, action following from logic is not. It requires will and commitment.
While philosophy, according to the Tractatus, should only transpire according to Wittgenstein’s strict, pure logic, we can see that knowing is much more of a process of testing our logical connections against the world, of making “arbitrary” willful decisions, of resetting our tautological center – a process. For, “what can be shown but not said” is a key indicator to how we should, perhaps, adjust that center, or how the ineffable might actually be related to the material.
One final point
But I have one final point to make here. Defining logic as the relations between things perhaps has an analogy with Wittgenstein’s conception of philosophy, which consists of “what can be said.” That is, knowledge, to Wittgenstein, is restricted to words, and the communication that transpires between people. Knowledge consists in words, and philosophy takes place in conversation. It is inherently a joint project, because our thoughts are illogical which are not verbal, and language is a game that takes place based on agreed-upon definitions. Nonverbal thoughts cannot be said to “relate” in an understandable way to words and their logic.
The religious and mystical pursuit of truth is at least partially personal, though. It involves commitment and therefore will; it also involves personal apprehension.
Mysticism, Wittgenstein could have noted, is never fully effable. If God actually does connect with individual human souls, that relationship will engender a slightly different mysticism, and pursuit of truth, in everyone. It will be partially incommunicable, except by analogy, because experience will never line up for two people completely. This is no radical individualism, but a partial one. What I am saying is that a person’s pursuit of truth is not only a process, but necessarily personal (and therefore subject to moral responsibility). It cannot transpire only within philosophy. The search is mystical, personal, and experiential as well as logical, relational, and communicable. It wavers between induction and deduction. Its inexorable logic is beset by new approximations of the center, and the action of commitment.
How do we “know’? Wittgenstein would insist on reference to how we commonly use terms, and I must insist on it for “knowing.” We are not talking about what would be impossible in the negative (e.g. “It is impossible that God does not exist”), but how people go about discovering a truth that lines up with the reality they experience – a reality that is both personal and transpersonal. And if that kind of knowledge starts to make moral demands, then our search has led us past strict logic, and introduced action, will, and commitment – a knowledge that demands action is one that supercedes pure logic, while using it, and must be called faith.
(Postscript: The Economist’s culture mag countenances questions of logical positivism and knowing religious things. Too bad they did not understand what the relation between the two is.)
Bryan Wandel works in government finance and has studied history, accounting, and religion. He is a member of the editorial board at Humane Pursuits. Bryan’s writing has appeared at Comment Magazine, First Things, and elsewhere.