Remarks on Abduction

I have been thinking about the notion of abduction recently. Not the kidnapping variety, silly. Rather, the kind that begins an inquiry process with a hunch or hypothesis made on the basis of an observation. Charles Sanders Peirce, “may his tribe increase” (i.e., there should be more logicians and more pragmatists) noticed that people often formed hypotheses about the general relationships among things based on a case or observation. While valid deductive reasoning establishes conclusions with certainty and valid inductive reasoning establishes conclusions with probability, abductive reasoning does not establish a conclusion at all. Rather, it suggests a hypothesis that might be further investigated. One might argue that while Arthur Conan Doyle had Doctor Watson say to Sherlock Holmes on many occasions, “brilliant deduction, Sherlock,” what Watson should have said was “insightful abduction, Sherlock.” There is a fair amount of controversy with regard to abduction and its relationship to other forms of inference. I cannot claim to understand all sides of the various critiques of the various forms of abduction. I refer interested readers (i.e., those bored with these ruminations) to the Stanford Encyclopedia of Philosophy entry on abduction – see http://plato.stanford.edu/entries/abduction/. One can also find an excellent entry on Charles Sanders Peirce in the encyclopedia – see http://plato.stanford.edu/entries/peirce/#dia.

My interest in abduction is somewhat different and focuses on what might be called a naturalistic account of epistemology – how people come to know and understand things. In “Questions Concerning Faculties Claimed for Man” (yes, silly, it applies to women, as well; see https://books.google.com/books?id=YHkqP2JHJ_IC&pg=RA1-PA103#v=onepage&q&f=false), Peirce questions capabilities assumed to be inherent in humans: (a) intuition, (b) intuitive self consciousness, (c) intuitive ability to distinguish subjective elements of different kinds of cognition, (d) introspective ability, (e) the ability to think without signs, (f) whether a sign said to be of something incognizable can have any meaning, and (g) whether there is any cognition not determined by previous cognition. Peirce’s exploration of these questions led him to conclude that (1) there is no power of introspection – knowledge of the internal world posited by introspections comes to one by hypothetical reasoning (probably of the abductive variety) about external facts or observations; (2) there is no power of intuition – rather, mental actions have the form of inference (even though the inference itself may not be stated or made explicit); (3) no thinking without signs (i.e.,  interpretation requires the use and manipulation of signs – spoiler alert – more on this soon); and (4) we cannot know what we cannot know (i.e., there is no reason to believe that there are unknowable things).

That last conclusion reminds me of Wittgenstein’s closing remark in the Tractatus Logico-Philosophicus – “7. What we cannot speak about we must pass over in silence.” Others have noted similarities between Peirce and Wittgenstein, although those similarities might be construed as incidental rather than deeply significant. There is Peirce’s works on mathematical logic and Wittgenstein's derivation of two-valued logic (a.k.a., Boolean algebra) in a footnote in  the Tractatus, for example. It seems that both Peirce and Wittgenstein (and others) saw a connection between the laws of mathematical logic and the laws governing human thought and reasoning. I personally see a connection of sorts that binds both to what I earlier called a naturalistic epistemology. Peirce’s extension of thinking beyond the strict confines of mathematical logic came in the form of his notion of abduction – the idea that people often form an hypothesis based on limited observations and then may go on to explore that hypothesis. Wittgenstein’s extension beyond the strict confines of mathematical logic came in the form of language games that proceed according to rules (typically implicit and dynamic) determined by a community of speakers. Ironically, while Peirce is often cited by many constructivists, he argued that introspection and intuition should not be regarded as the basis of human knowledge. On the contrary, while Wittgenstein is often cited by many constructivists as an objectivist, it is Wittgenstein who argued that we create internal representations to make sense of things we experience (Remark 2.1 in the Tractatus) and who developed the notion of language games in Philosophical Investigations in recognition that we engage in discourse with others based on those internal representations (which are not directly observable or knowable). In spite of those ironies, both eventually came to consider what people actually do in the process of coming to form beliefs and understand experiences. If one accepts that general conclusion, then both can be regarded as naturalistic epistemologists.

What brought me to think again about Peirce was a game I sometimes play with my educational technology graduate students and conference audiences. The game is called “Name that Technology.” First I describe a technology (defined as the disciplined application of knowledge to achieve a valued purpose) and then ask who invented it, when, and what it was called. The examples are designed to be very difficult (hardly anyone ever gets even one right) and to remind people that there is a long history to educational technology that precedes the Cloud, the Internet, Social Computing, and Wearable Devices (well, it is true that I used to wear a slide rule clipped to my belt – fastest calculator West of the Pecos was I).  The technology I describe is this: “All digital devices could be constructed using a single logic gate based on a system demonstrated by a philosopher. Who was that philosopher, what was the logic gate, and when did that finding get published?” The answer is Charles Sanders Peirce, of course. It was in 1880 or 1881 in a paper entitled “A Boolean Algebra with One Constant” and that constant (the logic gate) was NOR – the logical operator that is true (or on or 1) only when both operands are false (or off or 0). Yes, one can build a computer using only NOR gates, although it might involve an extremely large number of NOR gates (life is full of trade-offs – I once traded an authenticated Sami knife dated back to the 1930s for a Pentax SLR Spotmatic camera and lenses, the non-digital variety, so there were no logic gates involved).

Peirce also demonstrated that there was a second universal logic gate or single Boolean operator that could generate all of first order, two-valued logic – namely, the NAND gate, which is true (on) only when both operands are false (off). Wittgenstein’s treatment of first order, two-valued logic (a.k.a., Boolean algebra) involves four basic operators: IF-THEN, NOT, AND, OR.

There is yet another similarity to be found in the writings of Peirce and Wittgenstein. As noted previously, Peirce argued that there is no thinking without signs. Wittgenstein says at Remark 5.6 in the Tractatus that “the limits of my language mean the limits of my world.” Signs and symbols are part and parcel of language – without language … without signs … one cannot imagine thought.

Having been drowned (I mean trained) in skepticism, I should point out that those remarks by Peirce and Wittgenstein involve a certain leap – not a leap of faith, but a leap of meaning. From “I cannot imagine X” to “there can be no X” involves a leap beyond the evidence. It amounts to an inverse (or possibly perverse) principle that I hereby dub NABDUCTION (recalling the NOR and NAND gate discussion). Having survived as a skeptical inquirer for more than 40 years, I hereby reject NABDUCTION in all of its various forms. One can suspect that there is no X based on one’s inability to imagine X, but then there are a couple of humbling reminders to consider. First, we are limited beings – most of us, anyway … those of us not running for political office, anyway. Second, there is David Hume’s interesting observation in An Enquiry Concerning Human Understanding that deductive reasoning provides no new information about the world whereas non-deductive reasoning (inductive reasoning and presumably abductive reasoning as well, although Peirce had not then been born) rests on the principle that the future will resemble the past … but that principle cannot be established by either inductive or deductive reasoning. Of course pragmatists and naturalistic epistemologists wiggle out of Hume’s conundrum, but it remains a reminder that we are, after all, limited beings, however much we like to wiggle. The best wigglers, by the way, are politicians who have unearthed a new definition of truth: what is true is simply what they are telling, which is in many cases what people are buying. Your homework, should you accept this assignment, is to compare and contrast the politician’s definition of truth with that of Ruth who tells Naomi, according to non-political accounts, “where you shall go, I will go.” In that latter case, the truth showed itself in the following – something observable … not something intuited nor established by introspection.