Ventures in Philosophical History

By Nicholas Rescher

Philosophy began hundreds of years BCE, and by now has grown to a scope and scale beyond acceptability by any single mind. But a sampling of episodes and issues can convey some idea of the nature of the field.  It is the goal of the book to clarify a wide spectrum of key philosophical issues.

• Language: English
• Publisher: Anthem Press
• Release date: Oct 4, 2022
• ISBN: 9781839986369

Nicholas Rescher

Nicholas Rescher is Distinguished University Professor of Philosophy at the University of Pittsburgh. He is the Co-Chairman of the Center for Philosophy of Science and has formerly served as Chairman of the Philosophy Department. He is the author of 175 books, including Objectivity: The Obligations of Impersonal Reason (University of Notre Dame Press, 1997).

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PREFACE

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.

Pittsburgh PA

January 2022

INTRODUCTION

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.

Philosophy at its best is an exercise in problem-solving. This is inherent in its defining mission of seeking answers to the big questions. The depth and complexity of the questions are not that different answers are always possible. And the resulting quality of appropriateness—What way of answering is the best at any rate for us?—always gives rise to problems and perplexities. And at this point yet further questions come: are they really the most pressing problems? By what methods and procedures should we address them? Is our treatment of problem A consistent with that of the correlative problem B. Even as the proverbial cat may look at being so the most fledging philosopher can assess the way in which a master manages the difficulties that his own efforts raised for him. If he is ever to progress the novice must venture out in the world.

Even great thinkers can go astray. Close scrutiny of their work can show how their positions can require clarifications, amendment, and even outright correction. To say this is not, of course, to lay an absurd claim to greater acuity. What is at issue is not a superior insight but rather the benefit of hindsight from the vantage point of subsequent developments.

Chapter 1

THE PRINCIPLES OF LEIBNIZIAN METAPHYSICS

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. We thus have

P W (w) iff (∀p)(~[ p ∈ w &~p ∈ w]&(∀p) [p ∈ w v~p ∈ w])

We shall employ the notation Rw(p) to affirm that what the possibility p maintains is realized in the possible world w. This amounts to p ∈ w, that is, "p obtains in world w."

It is postulated that possible worlds are subject to three principles:

Explanation

Let zEp stand for "z explains (why it is the case that) Tp"

The principle of sufficient reason (PSR) has it that every true fact has an adequate explanation for being so: (∀p)(T(p) → (∃z)zEp).

There are two modes of explanation: Necessity explanation for necessary truths and factual (or contingency) explanation for non-necessary truths.

The principle of necessity (PN)—also called the principle of contradiction—has it that the explanation of a necessary truth lies in the consideration that its denial would entail a contradiction.

□ p ↔ (~p → p)Ep

All necessary truths are thus demonstrable by reductio ad absurdum: their negation would lead to a logico-semantical absurdity (i.e., a contradiction).

We defer consideration of the principle of contingency.

Conceptual Analysis

Propositional analysis is, for Leibniz, the procedure of replacing defined conceptions by their definition. For example, consider

man ≡ rational animal

rational [being] ≡ intelligent agent

intelligent [being] ≡ informative-guided chooser

animal ≡ organism

This group of definitions would provide for the substantiations that validate analyticity—and thus truth—of the proposition: Man is a choice capable organism.

Here we have it that the definitional equations at issue yield

Man ~ {organism, agent, information-guided being, choice-capable}

And the predicate term’s conceptual decomposition yields

{choice-capable, organism}

Given the former group’s containment of the latter, the proposition’s (finite) analysis is assured.

Leibniz sees linguistic claims as taking the form of attributing a predicate to a subject: proposition can all be reduced to a group taking the normal form of "S is P."¹ And on this basis, truth becomes a matter of definition factuality containment along the just-illustrated lines.

Leibniz contemplates two modes of analysis:

• Conceptual analysis which disassembles concepts into subordinate constituent concepts and can ultimately result in primitive (basic, unanalyzable) concepts.

• Proportional analysis which disassembles proportional claims into subordinate constituent claims and ultimately results in primitive (basic, tautologously self-evident) prepositions.

And the two are related. For the truth of propositions whose standard form is "A is B" is manifested through an analysis of its constituted components A and B when every B-comprising subordinate concept is included among those that are A-comprising.

And of course what can be analytically disassembled can also be aggregatively conjoined:

• A complete manifold of predicative concepts is one in which for any and all descriptively predicative conception neither it nor its negation and any such complete concepts manifold constitutes is substance-defining in constituting the complete individual concept (CIC) of a (possible) individual substance.

And moreover

• A complete manifold of propositional claims is one in which, for any propositional claims, either it or its negation is encompassed. And any such complete propositional manifold is a possible world.

A possible substance is thus descriptively complete via its CIC: any specifiable property or its negativity obtains with respect to it. And any possible world is similarly assertorically complete: any possible claims or its negation obtains with respect to it.

There indeed are complications to Leibniz’s doctrine of truth as analyticity. For there are two sorts of truths: the necessary and the contingent. And Leibniz coordinates the two to finite, and respectively infinite, analysis.

The crux here is that in analyzing the conceptual constituent of the subject/product terms as a necessary proposition, we come to an eventual end in the lowest species as represented by atomic (further unanalyzable) conceptions. And so in considering "S is P," we arrive in the finite case at the decompositions S [S1, S2, S3, … Sn] and P [P1, P2, P3, … Pn]. And here analyticity comes to tautology in that every Pi will be identical with some Si. And the determination that this so is a finite process—that of checking that each member of the {P} inventory is identical with some member of the {S} inventory and is also present there. Throughout the realm of necessary truth, analysis becomes a finite, terminating process.

Contingency and Infinite Analyticity in Leibniz

Some scholars are baffled by Leibniz’s theory of contingency. One of them writes:

Nobody has made respectable sense of what Leibniz says about finite and infinite analysis of subject-concepts. Furthermore, even if he did succeed in that, nobody thinks the result would have anything to do with contingency as we understand it, or, therefore, that it could satisfy Leibniz’s need to defend contingency (in our sense) so that God has real choices to make. We should drop the matter. It is too late in the day to expect the mystery to be cleared up, and I guess that if Leibniz or scholarship did remove the veil, we would conclude that the search had not been worth our trouble. I mean: worth our trouble as philosophers. It is different for antiquarians. (Bennett 2001, 329)²

However, the issue is not really all that complex. For Leibniz, the question is at bottom logical.

Contingent truths for Leibniz relate to matters of fact and existence: They characterize situations that obtain in reality and detail how things stand in the real world of actually existing substances. It is the nature and comportment of existence substances that determine the truth status of contingent propositions. The grounding of contingent truth always goes back to the CICs of the world’s substances.

Thus, consider a simple but typical case.

—Caesar crossed the Rubicon.

Caesar, of course, is defined and individuated by his CIC: He is the person who answers to a certain antecedence genealogy, matures under various circumstances, preferred various actions, entered into various relationships, moved about various geographic regions, and so on ad infinitum. Discovering that the particular property or set of properties involved in crossing the Rubicon on a certain occasion forms part of this is to seek for a particular item within such an infinitude. It is like looking for the sequence 5322 in the infinite series 34756829 …, an end that is never seriously evident going on ad infinitum, and this lies beyond human realization. We can only ascertain contingent facts by experience, never by reason and allocation as God can do.

But it is not so with contingent proposition. And the process of checking whether a given item is present in the Si inventory need not end in a finite number of steps. And when the process of checking whether the requisite subject/predicate contentment relation obtains is nonterminating, this becomes something we finite beings (unlike God) cannot manage to perform.

Leibniz’s account of the infinite analyticity of contingent propositions is set out on sections 132–36 of his General Investigations Concerning the Analysis of Concepts and Truths (Tr. W. H. O’Briant, Athens, GA: University of Georgia Press, 1968).

Leibniz would like to analogize the informative analysis of the predicate’s compliment concept in the subject of a contingent truth in the manner of an asymptotes approach. However, he sees a problem here:

But a difficulty stands in the way. We can see that one line perpetually approaches another in the case of an asymptotes, and that two quantities will eventually come to equal one another, so that with asymptotes by showing that an indefinitely extended progression we can foresee what will eventually be. And it would seem that in this way men too will be able to ascertain certainly in the case of contingent truths. (General Investigations, sect, 136)

His response to this problem is to reject the analogy: We must reply that though there is indeed some similitude, there is not complete agreement (loc. cit.).

However, Leibniz’s best option would be to say that while in the analysis of contingent truth there is indeed an eventual convergence there is no possible way to foresee at any given juncture when it will set in. And he does indeed come fairly close to saying that: For such a contained analysis would never reveal [at any point] what is enough for certainty, but can be realized perfectly only by him [viz. God] whose intellect is infinite [and thus able to view the series as a whole] (loc. cit.).

For Leibniz, a possible substance is defined by its CIC, and every concept that is complete (in his sense) will define a substance: Si qua notio sit completa […] est notio substantia individualis, et contra.³

More on Infinite Analysis

Of course the determination that a certain property (or group of properties) is to be found among the complete (and thus infinitely elaborate) concept of a given individual is always a matter of infinite search. And no matter how long this search continues, the determination of whether a certain property belongs to a substance’s infinite collection is never decidedly realistic by a finite search, no matter how extensive.

Walter O’Briant suggests that perhaps Leibniz would regard them [i.e. contingently true propositions] as contingent only because of our [human] epistemological limitations.⁴ But this entirety overlooks the purport of Leibniz’s distinction between finite and infinite analyticity. Granted, both modes of analyticity pivot on concept containment. But with necessities it is solely definitions that are the basis, while with contingencies it is CICs. And so in the former case, finitely many items suffice for the demonstration of this containment while in the latter case, it pivots on a process of infinite extensiveness. The difference lies in the nature of the task; the question of our capacity to perform it is peripheral.

With necessary truth, as we have seen, finitely convoluted definitional substantiation will do the job of truth establishment. But contingency is something else again.

Louis Couturat states the issue with insuperably clarity:

L’infinité des conditions ou réquisits logique [d’une verité contingente] coincide avec l’infinitée des causes physiques, c’est à dire des phenomes antécédents. Ainsi la recherché de la cause d’un phenomène se ramène à l’analyse [infici] logique d’une verité contigente.⁵

The (infinitely complex) CIC of a contingent substance embraces that l’infinitée des causes physiques, c’est à dire, les phenomènes antecedents.

Thus, consider in a Leibnizian perspective the contrast between

(1) Oaks are trees

and

(2) Oaks are deciduous

The first (so we may suppose) is a necessary truth, obtaining by definition since tree-hood is included directly in the analysis of the very concept of being an oak.

But the second is something else again. To locate seasonal leaf shedding is not included in oak-hood. So here we cannot proceed with abstract generality: the matter is not one of general principles but of the workings of the world. Here we have to assert to particularities and deal with oaks distributively