Wittgenstein on Logic and Contradiction 

If you’ve had to study analytic philosophy, you’re probably aware of the special status “contradiction” has in the academic field of logic. 

Classical logicians treated contradictions with the principle of explosion: from a contradiction, anything and/or everything follows: If a contradiction is true, then you can say anything is true. And that would ruin everything. Human society would fall into chaos. The philosophers had to do something.

To this end, philosophers in a capacity labeled “logician” spent many hours laboring over supposedly difficult contradictions to resolve like the Liar Paradox (is “this sentence is a lie” a true statement?1??). They found this task hard and and thus constructed elaborate systems of mathematical-looking symbols in attempts to get around the problem.

Some decided they had succeeded. Others that they had failed and embraced a “truth” in pure, actual contradictions and they thus fell into trivialism (‘all propositions of all kinds are true!’), strong paraconsistency (‘contradictions may be true!’), dialetheism (‘some contradictions are true!’), polylogism (‘truth is relative to race, culture, nationality, or class!’) and similarly silly ideas that still amazingly persist in current academic philosophy.

Wittgenstein answers this supposedly difficult “Liar Paradox” and at the same time shows the pointless nature of classical logician’s projects, their obsession with contradictions, and their failed principle of explosion. I’ll let him speak for himself:

Think of the case of the Liar. It is very queer in a way that this should have puzzled anyone — much more extraordinary than you might think… Because the thing works like this: if a man says ‘I am lying’ we say that it follows that he is not lying, from which it follows that he is lying and so on. Well, so what? You can go on like that until you are black in the face. Why not? It doesn’t matter. It is just a useless language-game, and why should anyone be excited? … Suppose I convince Rhees of the paradox of the Liar, and he says, ‘I lie, therefore I do not lie, therefore I lie and I do not lie, therefore we have a contradiction, therefore 2 x 2 = 369.’ Well, we should not call this ‘multiplication,’ that is all.

LFM 21-22

We exclude contradictions from language; we have no clear-cut use for them, and we don’t want to use them.

RPP II §290

To understand how Wittgenstein can see clearly to dismiss these supposed problems, we must recall the central theme of almost all Wittgenstein’s work: natural language and its relation to human thought.

In order to be able to draw a limit to thought, we should have to find both sides of the limit thinkable (i.e. we should have to be able to think what cannot be thought). It will therefore only be in language that the limit can be drawn, and what lies on the other side of the limit will simply be nonsense.

TLP Pref.

Thought can never be of anything illogical, since, if it were, we should have to think illogically. … It used to be said that God could create anything except what would be contrary to the laws of logic. – The truth is that we could not say what an ‘illogical’ world would look like. … It is as impossible to represent in language anything that ‘contradicts logic’ as it is in geometry to represent by its coordinates a figure that contradicts the laws of space or to give the coordinates of a point that does not exist.

TLP 3.03-3.032

The limits of my language mean the limits of my world. … Logic pervades the world: the limits of the world are also its limits. So we cannot say in logic, ‘The world has this in it, and this, but not that.’ For that would appear to presuppose that we were excluding certain possibilities, and this cannot be the case, since it would require that logic should go beyond the limits of the world; for only in that way could it view those limits from the other side as well. We cannot think what we cannot think; so what we cannot think we cannot say either.

TLP 5.6-5.61

In giving explanations I have already to use language full-blown … but then how can these explanations satisfy us? - Well, your very questions were framed in this language; they had to be expressed in this language, if there was anything to ask! One might think: if philosophy speaks of the use of the word “philosophy” there must be a second-order philosophy. But it is not so: it is, rather, like the case of orthography, which deals with the word “orthography” among others without then being second-order.

PI I 120-121

It is the use outside mathematics, and so the meaning of the signs, that makes the sign-game into mathematics.

RFM 5.2

As the Wittgensteinian linguist Noam Chomsky put it:

Factual beliefs and common-sense expectations also play a role in determining that a thing is categorizable and hence namable. Consider Wittgenstein’s disappearing chair. In his terms, we have no “rules saying whether one may use the word ‘chair’ to include this kind of thing” (PI, p.38). Or to put it differently, we keep certain factual assumptions about the behavior of objects fixed when we categorize them and thus take them as eligible for naming or description.

Chomsky. Reflections on Language (1975)

An actual, literal contradiction as such violates the presuppositions—the factual assumptions about the behavior of objects—of any language meant to be taken literally. If a language game does not presuppose non-contradiction, it is useless if meant to be taken literally. That is all one really needs to say. The claim that “some pure contradictions are literally true” is nonsense. It is itself a performative contradiction. It is nonsense. One does not need to construct elaborate systems of mathematical symbols to figure this out (and doing so doesn’t really help). 

Of course, contradictions can be useful in poetry, as literary devices, in mysticism, in religion or what have you. Furthermore, in programming and mathematics, the principle of explosion is often an impractical way to deal with contradictions (thus weak paraconsistency is sometimes useful). But this is not the issue at hand.

One of the most pernicious misconceptions in cognitive science is the belief in a dichotomy between nature and nurture.

Many psychologists, linguists and social scientists, along with the popular press, continue to treat nature and nurture as combatting ideologies, rather than complementary perspectives. For such people, the idea that something is both “innate” and “learned”, or both “biological” and “cultural”, is an absurdity. Yet most biologists today recognize that understanding behavior requires that we understand the interaction between inborn cognitive processes (e.g. learning and memory) and individual experience. This is particularly true in human behaviour, since the capacities for language and culture are some of the key adaptations of our species, and involve irreducible elements of both biology and environment, of both nature and nurture.

The antidote to “nature versus nurture” thinking is to recognize the existence, and importance, of “instincts to learn”.

This phrase was introduced by Peter Marler, one of the fathers of birdsong research. A young songbird, while still in the nest, eagerly listens to adults of its own species sing. Months later, having fledged, it begins singing itself, and shapes its own initial sonic gropings to the template provided by those stored memories. During this period of “subsong” the bird gradually refines and perfects its own song, until by adulthood it is ready to defend a territory and attract mates with its own, perhaps unique, species-typical song.

Songbird vocal learning is the classic example of an instinct to learn. The songbird’s drive to listen, and to sing, and to shape its song to that which it heard, is all instinctive. The bird needs no tutelage, nor feedback from its parents, to go through these stages. Nonetheless, the actual song that it sings is learned, passed culturally from generation to generation. Birds have local dialects, varying randomly from region to region. If the young bird hears no song, it will produce only an impoverished squawking, not a typical song.

Importantly, this capacity for vocal learning is only true of some birds, like songbirds and parrots. Other bird species, like seagulls, chickens or owls, do not learn their vocalizations: rather, their calls develop reliably in the absence of any acoustic input. The calls of such birds are truly instinctive, rather than learned. But for those birds capable of vocal learning, the song that an adult bird sings is the result of a complex interplay between instinct (to listen, to rehearse, and to perfect) and learning (matching the songs of adults of its species).

It is interesting, and perhaps surprising, to realize that most mammals do not have a capacity for complex vocal learning of this sort. Current research suggests that, aside from humans, only marine mammals (whales, dolphins, seals…), bats, and elephants have this ability. Among primates, humans appear to be the only species that can hear new sounds in the environment, and then reproduce them. Our ability to do this seems to depend on a babbling stage during infancy, a period of vocal playfulness that is as instinctual as the young bird’s subsong. During this stage, we appear to fine tune our vocal control so that, as children, we can hear and reproduce the words and phrases of our adult caregivers.

So is human language an instinct, or learned? The question, presupposing a dichotomy, is intrinsically misleading. Every word that any human speaks, in any of our species’ 6000 languages, has been learned. And yet the capacity to learn that language is a human instinct, something that every normal human child is born with, and that no chimpanzee or gorilla possesses.

The instinct to learn language is, indeed, innate (meaning simply that it reliably develops in our species), even though every language is learned. As Darwin put it in Descent of Man, “language is an art, like brewing or baking; but … certainly is not a true instinct, for every language has to be learnt. It differs, however, widely from all ordinary arts, for man has an instinctive tendency to speak, as we see in the babble of our young children; whilst no child has an instinctive tendency to brew, bake, or write.”

And what of culture? For many, human culture seems the very antithesis of “instinct”. And yet it must be true that language plays a key role in every human culture. Language is the primary medium for the passing on of historically-accumulated knowledge, tastes, biases and styles that makes each of our human tribes and nations its own unique and precious entity. And if human language is best conceived of as an instinct to learn, why not culture itself?

The past decade has seen a remarkable unveiling of our human genetic and neural makeup, and the coming decade promises even more remarkable breakthroughs. Each of us six billion humans is genetically unique (with the fascinating exception of identical twins). For each of us, our unique genetic makeup influences, but does not determine, what we are.

If we are to grapple earnestly and effectively with the reality of human biology and genetics, we will need to jettison outmoded dichotomies like the traditional distinction between nature and nurture. In their place, we will need to embrace the reality of the many instincts to learn (language, music, dance, culture…) that make us human.

~ W. Tecumseh Fitch, “An Insinct to Learn” (Department of Cognitive Biology, University of Vienna)

 jauxelin asked:

I’m just wondering - in a way that is non-judgmental and assumes I’m simply uninformed - why does logic matter?

Good question. Asking why logic matters is similar to asking why language matters. Language is not an end in itself, but it’s necessary for articulation and communication. What is called “logic” is the common structure of human language (sometimes called “universal grammar” or “natural language semantics” or “natural metalanguage”) and therefore the common structure of human thought. Some common structure of thought is the precondition for communication, i.e. necessary for you understanding what I am saying.

(also, in the terms of biology, logic is what homo sapiens evolved for the purpose of dealing usefully with the world around them. Logic is derivable from evolutionary theory itself as William Cooper showed in The Evolution of Reason: Logic as a Branch of Biology.)

The very question of “why logic matters” presupposes logic. For example, the law of non-contradiction: In asking your question, I assume you are not asking “why logic doesn’t matter” and you’re not telling me that you are “judgmental,” and you’re talking about yourself and not someone else, and so on.

In a way, though, logic doesn’t “matter” at all. You don’t really need to care or worry about logic and you certainly don’t need to care about the formal systems of logic devised by logicians. Some people are just interested in the subject, like linguists are interested in language or music theorists are interested in music. You use logic all the time every day without realizing it, just like we learn language as babies without thinking about it. It comes natural. Children naturally understand that there is something wrong with contradictions and something right with valid syllogisms and so forth. You are not uninformed. You already know all you need to know. Wittgenstein put this nicely in the TLP:

Thought can never be of anything illogical, since, if it were, we should have to think illogically. It used to be said that God could create anything except what would be contrary to the laws of logic. The truth is that we could not say what an ‘illogical’ world would look like. … It is as impossible to represent in language anything that “contradicts logic” as it is in geometry to represent by its coordinates a figure that contradicts the laws of space or to give the coordinates of a point that does not exist.

(Tractatus Logico-Philosophicus 3.03-3.032)

Logic pervades the world: the limits of the world are also its limits. So we cannot say in logic, ‘The world has this in it, and this, but not that.’ For that would appear to presuppose that we were excluding certain possibilities, and this cannot be the case, since it would require that logic should go beyond the limits of the world; for only in that way could it view those limits from the other side as well. We cannot think what we cannot think; so what we cannot think we cannot say either.

(Tractatus Logico-Philosophicus 5.6-5.61)

However, sometimes we confuse ourselves or don’t consistently follow the structure of our thought. This is when we engage in logical fallacies or talk nonsense… which itself doesn’t necessarily matter unless you are trying to demonstrate something to someone else (like in an argument, debate, technical discussion, etc.). If you are trying to demonstrate something to someone else, and your argument violates the structure of thought common to both of you, there is a problem. That is when logic really “matters.”