for philosophy.
That said, there is a group of common misconceptions about logic1—that it is cold, unemotional, contrary to feelings, and separate from matters of ethics and value—which keep people from fully recognizing the importance of logic, analytic philosophy, and philosophy generally. Just as we tried to connect analytic philosophy of language to moral improvement and recipes for living one’s life, by looking at its history in the previous chapter, we will connect logic to such practical matters by looking at the history of logic and how it has been connected to ethical matters.
Returning to public skepticism of philosophy, questions about where the intellectual, institutional, and social structure of philosophy will be in 25, 50, 100, and 500 years have all been asked a number of times for a number of reasons. From my perspective, the most pressing of these have to do with how we will be able to undermine the racist, sexist, homophobic, classist, and otherwise oppressive biases that the discipline has inherited from being a part of an extremely oppressive society. Other important inquiries brought up in this regard include how we will deal with shrinking budgets, increasing temporary employment, anti-intellectualism in the broader culture, etc. Among the most important questions asked for a variety of these reasons are:
[Q1] What justifies our spending public money on philosophy?
[Q2] What does philosophy give back to the world?
[Q3] What will philosophy give back to the world in the future?
[Q4] How can philosophy better itself as a community and institution?
The main goal of this chapter is to discuss why I think partial answers to these questions and the future of analytic philosophy lies (or should lay) in logic and ethics coming together to a much greater extent than they do now. In order to achieve this goal, I will enlist help from the following sources:
(1) a certain picture of the development of the modern formal logical revolution, which has come to make Kant’s words infamous2 and which gives good reason to think that there has been a natural, historical progression toward logic and ethics coming together more
(2) which will be discussed through specific works from several prominent actors in this story (n.b. Ruth Barcan Marcus, A. N. Prior, and John Corcoran) that show a great deal of potential for important work to come out of connecting logic and ethics and
(3) several examples that show the untapped potential of dedicated attention to nondeductive logics in understanding prejudice and bigotry.
These will be the topics taken up in the subsequent sections of the chapter, before a final section considering a particularly relevant objection from feminists to whom I hope to be an ally.
§2.2 The History of Logic from 1847 to the Present
When trying to determine the trajectory that any discipline is going to take in the future, it is almost always prudent to investigate the path taken during the period just traversed.3 Given that we are coming out of nothing short of a complete logical revolution, this is certainly true of the discipline of logic. For this reason, I will present a broad-strokes picture of the history of this logical revolution. Given how incomplete I will be in this context, it should be clear that this picture will be largely programmatic and will partly be based on what I see to be important for determining where logic will and should go from here. With this in mind, I take the history of the modern logical revolution to be a five-phased story, which looks something like the following:
[P1] Boole and De Morgan bring mathematical methods to the study of logical problems. This gives 1847 a particularly important place in the history of logic.
[P2] Formal systems of sentential logic are formulated, refined, and mastered. Beginning a trend that will be followed in the next two phases, its syntax is first mastered, then its semantics.
[P3] Formal systems of quantificational logic are formulated, refined, and mastered. Its syntax is relatively well understood by the time of Frege (1879). Its semantics is worked out in impressive detail in the 1930s, with the most important work coming from Tarski and Gödel.
[P4] Formal systems of modal logic are formulated, refined, and mastered. Its syntax is developed by Lewis and Marcus and the semantics is understood well enough to have completeness proofs and applications to natural language by Kripke (1963) and Kripke (1980).
[P5] From the time of Kripke’s 1970 lectures, which would become Naming and Necessity up to today, the story of the development of logic becomes a much more disjointed and partitioned one.
With this outline in place, a bit more about each of these phases is in order.
P1: The Mathematization of Logic
Hans-Johann Glock begins his history of analytic philosophy with a section entitled “First Glimmerings: Mathematics and Logic” (Glock 2008, 26). In this section, Glock looks at the ways in which logico-philosophical problems in the foundations of mathematics surrounding algebra, geometry, analysis, and set theory set the stage for increased connections between mathematics and logic. I too believe this is a suitable place to start and, like Glock, that, with the exception of anticipations by Bolzano that have been unfortunately ignored for some time, the new logic begins in Boole’s mathematization of logic (Glock 2008, 27–28). Boole’s logical contributions begin in 1847 with his Mathematical Analysis of Logic, the same year as Augustus De Morgan’s Formal Logic: Or, The Calculus of Inference. Both of them followed up on these works with further significant contributions in Boole’s The Laws of Thought (1854) and De Morgan’s Syllabus of a Proposed System of Logic (1860). Their individual contributions have been noted many times over by historians and logicians much more competent than myself (Kneale & Kneale 1962, Patton 2018, Terzian 2017). So, I will not rehearse these moves here. We should simply note that what is most important about their work from my general perspective is the bringing of mathematical methods to bear on questions in logic. This is what would ultimately allow logicism to play the role it did at the outset of the explicit movement of analytic philosophy. Though, for example, Aristotle had wanted to explain the knowledge gained in doing mathematics with his system of logic, the two had developed somewhat independently up until the nineteenth century. Boole and De Morgan changed this drastically and forever.4
This mathematization of the study of logic has been most significant for the methods and tools of clarity, precision, and objectivity that have been brought along with it. Most notable here are the uses of algebraic methods and notation, algorithmic procedures, axiomatic structures, recursive definitions, and set-theoretic frameworks.5 Obviously, nothing even slightly resembling modern formal logic could exist without just the members of this short list. Foreshadowing the rest of our sketch of the history of the modern logical revolution, the use of algebra brought with it the modern logician’s lexicon of variable letters, operator symbols, and function-notation. Concern with, and understanding of, algorithms culminates in the famous theorems of decidability and computability of Turing, Church, and others. The use of the axiomatic method in logic has led to the development of modern proof theories, with their bifurcation of axioms and rules of inference. Recursion theory has allowed us to give finitely expressible specifications of the infinity of grammatical constructions in our logical systems (and a means by which to wrangle the theories of their semantics in a finitely expressible way). And, finally, the set-theoretic universe has provided a domain in which to do respectably rigorous semantic work, something whose possibility was doubted even into the twentieth century (e.g., Wittgenstein 1922, Carnap 1934). Thus, the importance of the bringing together of mathematics and logic can simply not be overstated. Likewise, I hope the next revolution in logic will be brought about by the bringing together of logic and ethics.
P2: Sentential Logic
The
