What Is It to Be Rational?

Man, it has been said, is the rational animal. Our doings need not be determined by automaticity or instinct, but can result from deliberative thought. Deliberative thought based on beliefs and evaluations regarding ends can be the determining of actions. Accordingly the full exercise of our human rationality calls for trying to do the best we can manage under the circumstances to meet our genuine needs and our appropriate wants—that is, to realize our best interests.

Does Rationality Have Different Forms or Versions?

Rationality has three different modes, cognitive, evaluative, and practical, depending on whether the issue at hand relates to matter of beliefs, evaluation, or action. And accordingly rationality has three departments concerned, respectively, with its cognitive (epistemic), evaluative (normative), and procedural (practical) dimensions. In each case, we look to the best estimate we can make of

Gödel's Belief in a Leibnizian Conspiracy

Kurt Gödel's 1930s demonstration of the provability incompleteness of axiomatic arithmetic was a monumental achievement in mathematical logic and marked him as “one of the most significant logicians in history.” In the mid-1940s, Kurt Gödel embarked on a systematic study of Leibniz's logic which continued for at least another decade. During this time, I myself was writing my Princeton doctoral dissertation on Leibniz's Cosmology, and we had something of a tug-of-war over the Leibniz material in Firestone Library—each recalling for his own needs material out on loan to the other. (Unfortunately for me, we never made any direct contact.)

Gödel described himself as, unlike Einstein, “following Leibniz rather than Spinoza.” As Gödel studied Leibniz via Louis Couturat's classic La logique de leibniz, he became convinced that resistance to the logico-mathematical Platonic realism of his own position was prefigured in a conspiracy of suppression and silence that had kept Leibniz's similar insights from being properly understood and appreciated. And the more Gödel studied Leibniz, the more keenly he suspected that Leibniz might have anticipated parts of his own work—and especially his demonstration of arithmetic's provabilityincompleteness. Gödel came to this view because he saw Leibniz as a precursor and a kindred spirit whose problematic reception was a foreshadowing of his own difficulties.

But while there is little doubt that Gödel saw Leibniz as a precursor engaged in a kindred inquiry, there remained in his mind questions about the extent of anticipation about findings. Moreover, the matter of motivation remains somewhat obscure. Was he worried that he might have been fully anticipated? (After all, in mathematics all the credit goes to whoever gets there first.) Or was he hopeful of finding that he had succeeded where the great Leibniz had tried and failed? Perhaps we will never know. But either way, Leibniz's work on matters of provability and demonstrative systematization in mathematics was of deep concern to Gödel.

Curiously, Gödel saw Leibniz as a precursor not only in logic and the foundations and epistemology of mathematics but also in metaphysics, the general theory of reality.

Since the inauguration of philosophy among the ancient Greeks, the definitive mission of the enterprise has been to address the “big questions” regarding mankind, the world, and our place in the human and natural scheme of things. The task has been to elucidate how we should understand these matters and what we can and should do to implement this understanding in action.

These issues set the philosophical agenda as cultivated in Greek antiquity, and give rise to a tripartite division of the discipline into logic (the theory of thought), metaphysics (the theory of existence), and ethics (the theory of human conduct). It equipped the agenda of Greek philosophy with such topics as truth, knowledge, mathematics, justice, novelty, reality, and analogous key issues of enduring human concern.

But these fundamental issues were only the starting point. Questions always have presuppositions and these raise further questions. Over time the range of issues or the question-agenda grows substantially larger and becomes changed in matters of emphasis and orientation. Later questions were given out of attempts to grapple with earlier ones. The problem-agenda of a particular thinker or era is bound to reflect the state of knowledge of the day, the climate of opinion of the culture, and the specific connections of individuals. It is bound to be diverse and variable.

The individual philosopher is of course free in the choice of problems, unfettered in his work, and unhampered by any need for agenda balance. With individuals this does not matter. But at the communal level it does. But the wider community bears an obligation to the discipline as a whole and neglects major areas of thematic orientation at its own peril.

The definitive task of the philosophical enterprise is systematic in its constituting mission to provide a comprehensively integrated account of the salient problems. The situation of medicine is not dissimilar here. The individual physical may coordinate in the eye but the medical professor cannot afford to leave the ear out of it. And essentially the same thing holds with regard to philosophy. If the enterprise is to succeed, then somehow the collective spirit of the discipline must put its hidden hand to the task of overall correlative integration and systematization.

The Expressive Sufficiency of Language in the Tractatus

The unifying framework of Ludwig Wittgenstein's intellectual life was provided by a project of vast and monumental ambition. Its ground plan was laid out in his earliest work, the Tractus Logico-Philosophicus, with its grandiose vision of a perfect language, a symbolic manifold able to provide the means for accurate and complete characterization of reality.

The crux of the Tractatus lies in its commitment to the problematic idea that language—not exactly as we have it but as we can get it with some logical repairs—is capable of a complete and adequate descriptive presentation of the world's facts. But there is good reason to think that this idea of the ontological adequacy of available language is not only problematic but also illusory—that linguistic completeness and accuracy are an unrealizable mirage, not because they are so difficult to achieve, but because the very idea of their realization is ultimately as incoherent as it the idea of a complete and detailedly accurate mapping of terrain. All in all, the Tractarian position betrays a yearning for an impracticable absolute.

The Tractatus gets off to a peculiar and problematic start by riding roughshod over the crucial distinction between fact and fiction, stating true and actual facts and unrealized possibilities. As it represents the situation: “Logic deals with every possibility and all possibilities are its facts” (2.0131). For logic all possibilities exist, and the distinction between actually and merely possible states of affairs is abolished. In logical rigor, nothing whatsoever is accidental or contingent: “In der Logic ist nichts zufallig” (2.012), and the world (1.2) is throughout a web of necessitation. The Tractatus thus becomes a logical revision to Spinoza's Ethics and on its principles, language and its inherent logic become means for the exposition of whatever can meaningfully be said.

Building Blocks of the Tractarian Position

On this basis, the position of Ludwig Wittgenstein's Tractatus Logico- Philosophicus regarding the relation of language to reality is predicated on his pivotal contentions regarding five crucial concepts. They stand as follows:

• I. World. The world (reality as he also calls it) is the totality of facts about what is actual and possible. (1-1.21)

• II. Facts. Facts are possible states of affairs. They comprise the world. (1.21- 2; 2.04)

• III. Thought.

The outbreak of war in the late 1930s created turmoil throughout the realm of European scholarship. Even in the distant USA, there were massive reverberations, and after America's entry into the conflict, the demands of war had a massive impact as a whole generation of young people was diverted from normal life into military activities. Academic philosophy could not but be affected. The generation born in the 1910–1920 decade was especially hard hit, with its ranks depleted by the demands of war. The present discussion will examine one instructive instance of this phenomenon, the diversion of one particular and a particularly significant individual from philosophical scholarship into a very different pathway of endeavor.

The person at the focus of my deliberations here is something of a paradox. He is the most important twentieth-century philosopher no living philosopher ever heard of. A scholarly official near the top of the Pentagon hierarchy (Alan C. Enthoven) said he “was the most important strategic analyst and thinker of his own time.” A high official in the State Department (Richard Rosencrance) wrote that “Probably no civilian strategist has had more influence in the nuclear age that [he].” I think it is fair to call him “the Clausewitz of nuclear age.” His name is Albert C. Wohlstetter. And he was a trained philosopher of science.

Albert James Wohlstetter was born in 1913 to an affluent Jewish family living in the then-fashionable Washington Heights section of Manhattan. (His father, an attorney, was the chief counsel to the Metropolitan Opera and a major investor in early filmography production.) Wohlstetter attended CCNY (with a scholarship in modern dance!) graduating with a B.A. in 1934. (There was always a touch of gracefulness to his movements.) Like many of his New York City contemporaries, he was enthralled by Trotskyite communism in his early years.

After college, he turned to philosophy—specifically to philosophy of science and logic. From 1935 to 1940 he was a graduate student at Columbia, studying logic and philosophy under Ernst Nagel and Morris Cohen, and statistics under Abraham Wald. He took his M.A. in 1938 with a thesis in symbolic logic with Nagel, and had his first publication in 1940 with a review of J. H. Woodger's book on The Technique of Theory Construction in the Journal of Symbolic Logic.

Pragmatism's Functionalistic Perspective

The crux of philosophical pragmatism is its insistence. The proper evaluation standard for all human projects—be they cognitive, practical, or normative, and be they personal or social—lies in the effective and efficient realization of appropriate needs and wants. According to pragmatism the merit of things should be judged in terms of their consequences, that merit is to be assessed by functional adequacy in realizing appropriate objectives. The issue of valid goals—of human needs and their properly coordinated desiderata— is thus a pivotal issue for pragmatism. And specifically as regards cognition, pragmatism proposes to see warranted beliefs as those which provide for successful implementation; meritorious actions are those that realize suitable ends; appropriate valuations are those which guide beneficial efforts. Pragmatism as a philosophical doctrine traces back to the Academic skeptics in classical antiquity. Denying the possibility of achieving authentic knowledge (epistêmê) regarding the real truth, they taught that we must make do with plausible information (to pithanon) adequate to the needs of practice. Throughout, functional efficacy in the realization of beneficial objectives is the ultimately correct standard of assessment.

Such pragmatism has many forms and versions. Some settle for the indifference of personal relativism: “Whatever works for you.” Others set objective standards of purposive suitability. Only this later, realistic version will be at issue here. The doctrine that concerns us nails its flag to the mast of functional effectiveness and purposive efficacy in the realizing of appropriate objectives. The correlative mode of pragmatism lies in the consideration that all rational human dealings and practices—cognitive and practical alike—are purposive in nature, and their legitimacy and validity lie in their efficacy and effectiveness in satisfying (meeting) appropriate human requirements (needs and appropriate wants).

We humans live subject to a manifold of processes: physical, chemical, biological, social, economic, and so on. Each such processual realm imposes various purposes upon us, subjecting us to needs, requirements, and desiderata of various sorts. The meeting of these purposes involves us in a wide variety of projects each with its own manifold of purpose-accommodating processes. We are thus committed to such projects as the pursuit of nourishment, or physical security, of comfort, of education, of sociability, of rest and recreation, and the like, designed to meet our requirements for food, shelter, clothing, knowledge, companionship, realization, etc., all equipped with their own complex of needs and desiderata.

For the most part, the deliberations of this book are the fruit of the era of the COVID-19 pandemic 2019–2022. With other activities curtailed, a philosopher's attention was increasingly impelled inwards to reflection on his own subject, its practice, and its practitioners.

I am grateful to Estelle Burris for her conscientious efforts to prepare this material for the publisher's needs.

Philosophers, even the best of them, sometimes take too much for granted and try to build ambitious structures on weak foundations. Purporting to secure their conclusions by rigorous reasonings, they actually take for granted far more than the available information warrants.

An instructive example of this is afforded by the following passage from David Hume's Dialogue Concerning National Religion:

Close scrutiny shows that Hume's contention is very problematic.

To elucidate Hume's line of reasoning, let us press a few items of symbolic machinery into service for the sake of precision in formulation and analysis. Let “p,” “q,” etc., serve as propositional variables, let “∼” represent negation, “&” conjunction, “→” logical entailment, and let “ξ” represent the impossible (or self-contradictory). Furthermore, let “E (p)” serve as an abbreviation for “ ‘p’ asserts existence,” “C (p)” for “ ‘p’ is conceivable,” and “D (p)” for “ ‘p’ is demonstrable.” Hume's argument can now be formulated as follows:

• Premiss 1: Nothing is demonstrable, unless the contrary implies a contradiction (i.e., is impossible).

  (P1) D (p) → (∼p → ξ)

• Premiss 2: Nothing, that is distinctly [coherently] conceivable, implies a contradiction (i.e., is impossible).

  (P2) C (p) → (∼p → ξ)

• Premiss 3: Whatever we conceive as existent, we can also conceive as nonexistent.

  (P3) C (E (p)) → C (∼E (p))

Given these premisses, can one demonstrate Hume's thesis that there is no (coherently conceivable) being whose existence is demonstrable, namely:

We now reason as follows.

By (P1) we have

By substituting E (p) for p, we obtain

To obtain Hume's conclusion (H ) it now suffices to show that:

But we already have

So what still we need is:

Equality before the (Moral) Law

Few issues have caused greater difficulty to expositors and students of Immanuel Kant's ethical teachings than that centerpiece of his moral philosophy, the Categorical Imperative. Together with the conception of moral universality on which it pivots, it raises a host of issues that both demand closer scrutiny and amply deserve it.

Kant's criterion for determining the moral appropriateness of human actions pivots the feasibility of having the motivating principle of the act serve as a universally operative principle. “Honoring a promise” is thus the morally requisite thing to do because promise honoring can and should serve as a general standard for behavior. “Lying when convenient” is the wrong thing to do since doing so as a general practice would prove a communal catastrophe. And this is universally so: A mode of behavior whose generality would be disastrous is ipso facto wrong.

And so, for Kant an act's moral appropriateness requires that the universalization of its modus operandi (its implicit rule of proceeding) could unproblematically form part of the operating code of a viable social order. “The idea is that one should act in a way that everyone would in a wellfunctioning community.”) Its generalizability in this way is a necessary condition for an act's qualifying as morally appropriate.

In maintaining this idea of the viability of procedural generalization as a sine quo nonstandard of moral appropriateness Kant rejects as morally inappropriate those acts whose generalization as a maxim of standard procedure would be catastrophic. But what sort of catastrophe does he envision here?

This is a question Kant (understandably) addresses via examples rather than general principles because of the variability of unacceptable consequences. For those impediments to generalizability can take different forms as the accompanying tabulation indicates.

While the failure maxim generalizability in the case of immoral action will always impose an unacceptable (and avoidable) price on the community as a whole, Kant envisions a diversity of grounds of non-universalizability here in that this could prove to be:

• 1. impossible through logical incoherence and self-contradiction (“Act randomly”)

• 2. impracticable through procedural incoherence and potential self-defeat. (“Do whatever your inclinations at the moment favor.”

Aims

This chapter’ deliberates on explaining and clarifing the principles of Leibnizian metaphysics by means of the resources afforded by the formalisms of modern symbolic logic and the instrumentalities of modern value theory.

A common practice in philosophical exegesis is to explain how historical figures treated our issues in their terms of reference. Here, however, we follow the reverse course of treating their issues in our terms of reference, in deploying the expository resources of modern, logic, semantics, and valuation theory upon Leibniz's philosophical proceedings.

This line of argument is to be typical of the present treatment of philosophical history throughout the book.

Possibilities, State of Affairs, Circumstances

First, some conceptual preliminaries must be addressed.

Possibilities are states of affairs that could conceivably obtain: they represent hypothetically entertainable circumstances and envision conjecturally available situations. Possibilities can be divided into necessary, actual, and merely possible. A possibility is necessarily realized if its obtaining can be established via reductio ad absurdum, that is, if the supposition of their not obtaining entails a (logico-conceptual) contradiction. A possibility is actual if what it claims is indeed the case. Finally, coherent contentions that are neither necessary nor actual are mere possibilities.

We shall employ the propositional variables p, q, r, etc. to range over possibilities at large. To claim p as actually true, we write Tp (or often simply p when this creates no harmful ambiguity).

Since p represents a possibility, we have it that both (∀p)◊p and (∀p)(p → ◊p), where ◊ explicitly betokens the modality of possibility. To affirm that p is necessary, we write □p. It is a matter of logic that □p ↔ ∼◊∼p → p. We accordingly have (∀p)(□p → Tp) and (∀p)(Tp → ◊p).

A proposition is contingent if it is neither necessary nor impossible. With ○ to represent contingency, we have ○p ↔ (∼□p & ∼□∼p) or equivalently ○p ↔ (◊p & ◊∼p).

Possible Worlds

A possible world (abbreviated PW ) will here be represented by the variables w, w1, w2, etc. Such a world embodies a manifold of possibilities which, taken overall, is both consistent (in that never p ∈ w and ∼p ∈ w) and saturated in the sense that for every possibility either it or its negation (but never both) obtains within it.

The Futurology Bubble

The 1965–1975 decade witnessed an explosion of activity in the predictive domain. One prominent example was the Commission for the Year 2000, a study-group chaired by Daniel Bell for the American Academy of Arts and Sciences in 1965. Resources for the Future in Washington D.C. and the National Planning Association were also active in future-oriented inquiries. Then too, there was the influential Club of Rome's investigation of the social and environmental import of industrial and technological development, which issued in the widely publicized “Limits of Growth” study. Not to be outdone in the U.S., the Congressional Research Service established a Futures Research Group to provide support for policy deliberations.

In the early 1970s, the Natural Science Foundation launched its project to devise science indicators on the analogy of the economic indications of the Commerce Bureau. And this was filled in 1979/80 by the USF's extensive two-volume study of The Five Year Outlook: Problems, Opportunities, and Constraints in Science and Technology (Washington DC: United States Government Printing Office, 1980). All of these studies served the same fundamental objective: to provide guidance about the future as background for public policy formulation.

This diffusion of futurism was bound up with the ever-increasing prominence in all industrialized nations of what might be called the Advice Establishment: academics, working scientists, technical experts, and pundits of all sorts serving on advisory boards, policy study groups, and public commissions developing information, ideas, and speculations to provide guidance about the future as background for public policy formulation. Enthusiasm also sprung up not only for making concrete predictions, but also for projecting scenarios— pictures of “alternative futures” (and of course possible and plausible—not wholly improbable—futures). Developed out of war-gaming techniques, this methodology of possibility projection was initially conceived at The RAND Corporation in California in the 1950s, and was subsequently applied extensively to issues in economics, politics, and international relations.

This rise of a movement—indeed virtually an industry—of “futurism” or “futurology” in the Cold-War period was in fact one of the characterizing features the period, with many writers urging the elaboration and recognition of such a new science, whose prime task is that of forecasting the nature and impact of technical innovations.

The best and most instructive way to learn about philosophy is by examining the history of the field. It is here that we come to see how its particulars are identified and addressed by some of humankind's sharpest intellects. Philosophy began hundreds of years BCE and by now has grown to scope and scale beyond acceptability by any single mind. Sampling of some of the philosophical episodes and issues can provide some insights into the nature of the field. And it is with this goal in view—clarifying the detail of some key philosophical issues—that these studies are being put into print. These are published with a hope that it is better to look at some of the steps—and mis-steps—that some of the eminent philosophers of the modern era have taken in order to deal with basic issues. It is thus the aim of these forays into philosophical history to illustrate how contemporary perspectives, methods, and instruments of analysis can clarify some of the key philosophical teachings both by highlighting the difficulties they encounter and by providing instructive means for addressing them.

Over and above their common concern—for key issues in modern (post-Cartesian) philosophy what links all of these logically diverse chapters together—is what might be called “the methodology of the road not taken.” In each instance of philosophical problem-solving with which we will have to be concerned, there are alternatives for the course adopted by the protagonist that he (not always wisely) did not take—but always for reasons that greatly clarify our understanding of his position.

Historians of philosophy are generally reporters: they endeavor to present the ideas of their protagonists and to give us a picture of what and how they think. The three Cs—criticism, cavil, and correction—they leave to those protagonists themselves. The present attempt, by contrast, takes a somewhat different line. Both historians and reporters try to elucidate some of the core conceptions of their subjects but suggest how certain problems and difficulties that arise in this context can be overcome. In effect, the aim is to realize something of a critical dialogue with some major philosophers in an endeavor to address—and ideally overcome—difficulties in their positions.

Philosophers themselves, as well as scholars and inquirers of all sorts, have long compared philosophy invidiously with the natural sciences, especially contrasting it with physics. Those who were not unkind enough to attribute this to the intellectual inferiority of philosophers were inclined to the view that the problems of philosophy were inherently intractable and insoluble. But Immanuel Kant was convinced that he had a different answer here. He wrote as follows:

Here Kant has put his finger on a sensible and sensitive spot. One salient difference between natural science and philosophy is that science controls its problem agenda and can dismiss awkward questions. If a question is not tractable in terms that science finds convenient, then science can simply reject it as meaningless. It has—or rather takes—control over its question agenda. But philosophy has not been in a position to do this.

Consider an example: “What is the cause of cancer?” “What is the mass of phlogiston?” Science can dismiss the issue with the reply: “There just is no such thing: concern is not a single-cause phenomenon, phlogiston does not exist.” Science can send an entire issue agenda into exile—witness alchemy, astrology, shamanism, and the occult. Even medicine can reject entire ranges phenomenon—as with acupuncture and hypnosis, saying “The day may well come when we can deal with this—but not yet.” But philosophy—unlike science—is not really in a position to eject questions: it has to do the best it can with the questions it confronts. Science can dissolve and reject questions based on erroneous presuppositions. Philosophy has not enjoyed this privilege: It must take the issues at face value and cope with them but has simply struggled on as best it can.

Science—and especially physics—limits its concerns to matters of generality and precision.

The Liar

Concern for logical problems of self-reference originated with the Liar Riddle (pseudomenos) of the Greek dialectician Eubulides of Megara (ca. 440–ca. 380 BC), who included it in his register of seven paradoxes. In his telling, it posed the puzzle: “Does the person who says ‘I am lying’ actually lie?” (Or again: “Does the witness who declares ‘I am perjuring myself’ thereby perjure himself?”) The problem that arises here can be posed via the following dilemma:

Accordingly, what we have in this ancient puzzle is an untenable contention that involves an inherent conflict of truth-claims.

The situation is paradoxical because individually plausible theses are collectively inconsistent here. And this situation can be set in train by a single proposition, as per the Liar’s:

L: This statement is false.

For it now emerges that we have both

• (1) L is true

• and

• (2) L is false.

Here, (2) is simply what L itself affirms. And (1) follows because (2) is exactly what (1) itself maintains. L is accordingly paradoxical in that it creates this conf lict of affirmation among the various claims it plausibly authorizes.

As logicians address it, the Liar Paradox pivots on the puzzling truth-status of statements that affirm their own falsity (be it directly or obliquely), and thereby will apparently be true when false, and false when true. This situation arises not only with the Liar but also with such contentions as:

(A) Statement (B) is false.

(B) Statement (A) is true.

Here, if (A) is true, then (B) is false, so (A) is not true. And if (A) is false, then (B) is not false, so (A) is true.

Such contentions have puzzled theorists since classical antiquity when Greek philosophers approached the problem via the ancient story of Epimendes the Cretan, who is supposed to have said that “All Cretans are liars”—with “liar” being understood in the sense of a “congenital liar,” someone incapable of telling the truth.

Quantum Oddities

Quantum physics seeks to explain the physical micro-processes that occur at very small levels of metric scale. And these processes involve phenomena that are highly unusual when regarded from the vantage point of the familiar macro-level of physical reality. Specifically, the anomalous phenomena at issue include such oddities as:

• –Probabilism and impredictability, as when we encounter such processes as the radical decay of heavy transuranic elements, occurrences predictable with statistical probabilities on the larger scale, but individually unpredictable.

• –Complementary uncertainty of physical state parameters with a see-saw relation where the more precise specification of one constrains the other into greater unspecifiability.

• –Position-ambiguity via an infeasibility of specifying the precise location of physical processes and providing for continuity in physical interactions.

• –State superposition with different quantum states combining or conjoining otherwise incompatible possibilities in an impenetrable fog of indetermination.

• –Wave-packet collapse with observation presenting a definiteness that physical theory does not provide for and indeed disallows.

All such eventualities are “something completely different” from what we encounter in the course of commonplace experience. In the physics of the macro-objects we encounter in everyday life we have transactions that are subject to lawful determination, physical parameters that assume definite values not subject to probabilistic variation, descriptively different states that are disjoined and incomparable, and state-conditions that evolve in smooth continuity and are not disjointed in abrupt inexplicability. At the physical macro-level where we humans standardly function things thus behave very differently.

Schrödinger's Cat and the Basic Problem Posed by the Quantum Theory

Reality at the quantum level enjoys a dramaturgy of its own. The everyday reality of our experience yields observationally definite resolutions, whereas quantum theory can at most provide for probabilistically indefinite alternatives: quantum waves functioning with smooth regularity among alternative possibilities in line with Schrödinger's Equation unless and until observation intervenes to disrupt matters a the theory-inexplicable collapse to a single alternatives. This so-called “wave-packet” collapses when issue arises in the curious thought-experiment of Schrödinger's Cat.

This thought experiment is predicated on the following suppositions. At time t the cat is placed in an opaque box containing an apparatus that potentially produces a quantum event triggering the release of a jet of cyanide gas sufficient to kill the cat. But no further changes occur in the box subsequently.