A few weeks ago, I quoted this line from Russell: "The ethical work of Spinoza, for example, appears to me of the very highest significance, but what is valuable in such work is not any metaphysical theory as to the nature of the world to which it may give rise, nor indeed anything which can be proved or disproved by argument." (On Scientific Method In Philosophy) In commenting on the full passage, I remarked, "Russell systematically defends the beauty and nobility of Spinoza's ethics, but denies it is philosophical for three reasons: (a) Spinoza's metaphysics of substance has been disproved by science. I call such appeal to the authority of science to settle philosophic argument within philosophy, "Newton's Challenge to Philosophy." Russell here echoes eighteenth century Newtonian criticism of Spinoza. Once Spinoza's metaphysics is discredited, (b) Spinoza's ethics is not really founded on or supported by argument, but by feeling (and this is indeed also Russell's view of Bergson) and "maxims." I actually think this reading of Spinoza has a lot going for it (and the significance of maxims is a way in which Spinoza and Smith are connected), but about that some other time. (c) The feeling that Spinoza's ethics promotes is oriented toward practice, and (c*) Russell denies that philosophy is fundamentally concerned with practice, but rather with understanding." In private I wondered why Russell would have thought (b); had he done an analysis of Spinoza's arguments in the Ethics, which (we learn from Monk's biography) he admired greatly, and found them wanting? I doubt he did.
Rather, I suspect Russell remembered chapter 13 (and 14) of Boole's masterpiece, An Investigation of the Laws of Thought (1854). Elsewhere, Russell credits Boole with having discovered "pure mathematics," or formal logic. (Oddly, Boole is not mentioned by Monk; this neglect is emblematic for a more general problem in the way "early analytic" is treated, but about that some other time more.) Boole writes, "The analysis of its [Spinoza's Ethics'--ES] main argument is extremely difficult, owing not to the complexity of the separate propositions which it involves, but to the use of vague definitions, and of axioms which, through a like defect of clearness, it is perplexing to determine whether we ought to accept or to reject. While the reasoning of Dr. Samuel Clarke is in part verbal, that of Spinoza is so in a much greater degree; and perhaps this is the reason why, to some minds, it has appeared to possess a formal cogency, to which in reality it possesses no just claim." (p. 145) What are these remarks doing in a book that regardless of its limitations from a more recent point of view, invents "pure mathematics"?
Sadly, if we remember George Boole (1815–1864) at all it is because we sometimes talk of logical connectives as Boolean operators. Specialists in the history of logic are, of course, aware that he is something like the Copernicus of modern logic (Frege/Russell=Galileo; Tarski/Godel=Newton/Leibniz?), but in reflecting on his masterpiece, I think that Boole -- a self-taught mathematician from modest economic background -- set in motion a way of thinking that have become deeply entrenched within analytic philosophy. Let me illustrate this with a few remarks on chapter 13, where Boole (also) invents what we now call "rational reconstruction" of arguments in the history of philosophy.
The general order which, in the investigations of the following chapter, I design to pursue, is the following. I shall examine what are the actual premises involved in the demonstrations of some of the general propositions of the above treatises [Clarke's Demonstration and Spinoza's Ethics--ES], whether those premises be expressed or implied. By the actual premises I mean whatever propositions are assumed in the course of the argument, without being proved, and are employed as parts of the foundation upon which the final conclusion is built. The premises thus determined, I shall express in the language of symbols, and I shall then deduce from them by the methods developed in the previous chapters of this work, the most important inferences which they involve, in addition to the particular inferences actually drawn by the authors. I shall in some instances modify the premises by the omission of some fact or principle which is contained in them, or by the addition or substitution of some new proposition, and shall determine how by such change the ultimate conclusions are affected. In the pursuit of these objects it will not devolve upon me to inquire, except incidentally, how far the metaphysical principles laid down in these celebrated productions are worthy of confidence, but only to ascertain what conclusions may justly be drawn from given premises; and in doing this, to exemplify the perfect liberty which we possess as concerns both the choice and the order of the elements of the final or concluding propositions, viz., as to determining what elementary propositions are true or false, and what are true or false under given restrictions, or in given combinations. 2. The chief practical difficulty of this inquiry will consist, not in the application of the method to the premises once determined, but in ascertaining what the premises are."
What follows in Boole is an extremely careful analysis of the arguments on both sides of the Clarke-Spinoza dispute (as well as Butler's letters to Clarke). (Sadly, Jonathan Bennett seems to have been unaware of this.) This is extended by a separate analysis ín the following chapter 14 of the linchpin of Clarke's argument against Spinoza. (Recall my piece here.) I have a growing belief that the Clarke-Spinoza dispute is of seminal importance if we want to understand the development of Kant's and Hume's philosophy, but about that more elsewhere. I am unsure to what degree there was still a live debate on this in the middle of the nineteenth century. Here I offer five general comments on the significance of Boole's treatment of the Spinoza-Clarke dispute.
First, the main stated point of Boole's exercise is to illustrate and, perhaps, teach the philosophic power of his technical tool. Even with the limitations of Boole's symbolic logic, the arguments by Clarke and Spinoza do become transparent and clear in a way that may have never before been seen. While early modern philosophers talked about "clear and distinct" knowledge (inspired by mathematical rigor), inspecting ideas always remained a suspect method. In fact, it's from Boole that we learned the ideal how analysis could provide clarity.
Second, rational reconstruction requires good judgment. For, sometimes its practice requires the search for suppressed premises as well as the transformation of explicit premises. The technique can be taught, but I have been unable to find a place where Boole discusses how we can gain mastery of such good judgment.
Third, Boole concludes chapter 13 with the following remark: "It is not possible, I think, to rise from the perusal of the arguments of Clarke and Spinoza without a deep conviction of the futility of all endeavours to establish, entirely `a priori, the existence of an Infinite Being, His attributes, and His relation to the universe. The fundamental principle of all such speculations, viz., that whatever we can clearly conceive, must exist, fails to accomplish its end, even when its truth is admitted." Without mentioning the principle of sufficient reason as such, the implication is clear: the PSR can't even do the work that it has been designed to do. This sets the stage for Russell's rejection of the PSR (in his disputes with Bradley [recall]).
Fourth, Boole thinks that henceforth God's existence can only be argued on the uncertain, inductive and probabilistic grounds. It is no surprise then that he concludes his work with several chapters with the role of probability and statistics in formal epistemology. (There is a historic irony: a few years later Darwin undermines the argument from design.)
Fifth, Boole conceives of his enterprise of developing symbolic logic in moral terms (this is undeniable in the last pages of the book). But above it shows up as a hint by way of the "the perfect liberty which we possess as concerns both the choice and the order of the elements of the final or concluding propositions." In part our freedom consists in logical ordering. I think this anticipates Carnap's voluntarism.