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Is Philosophy Left With Unsolved Problems?

Updated on October 15, 2014

Philosophic Problems

Ever since the dawn of philosophic thought - across many different philosophic traditions - the thinkers known as "philosophers" seemed unusually drawn to certain difficult problems or riddles. In the 20th century, a celebrated mathematician and philosopher, Bertrand Russell, titled a rather popular book on philosophy The Problems of Philosophy. There is even a view that philosophy, as an academic discipline, should rather be dedicated to the study of problems. At the same time, one of the most common popular notions about philosophy, which is generally seen as a negative, is that philosophical studies appear to be engaged, unprofitably, in the discussion of certain problems that may well be unsolvable. Russell himself opined that the problems of philosophy are unsolvable - at least, most of them are - although, strictly speaking, he couldn't know this for certain. To make matters even worse, the contrast with Mathematics and the Sciences, which appear to be problem-solvers, is keen. Since scientific inquiry itself began within the cocoon of philosophic investigations, we could even get the impression that science comes to maturity in direct proportion as it becomes a problem-solver, leaving its unemancipated childhood companion, philosophy, behind in a perennial, and fruitless, struggle to solve problems. The problems themselves are typically obscure; it is not evident to the uninitiated why time and energy should be expended in trying to solve them especially if they have not been disposed of after centuries of debate; and those who are initiated in philosophy, and clearly enjoy the activity, more often than not confess that there are insuperable difficulties in solving these problems.

Characteristic philosophic problems revolve around ordinary notions like truth, reality, space and time, existence, moral and other values, the possibility or preconditions for obtaining knowledge about experience, criteria for evaluating claims, free will, the status of mental events, and so on. Even though it is surprising that a notion like truth would generate problems that seem unsolvable, it has been known since antiquity that this is precisely what happens. The infamous Liar Paradox, whose first author, Epimenides, allegedly killed himself out of frustration that he couldn't solve, still eludes a universally accepted solution. It should not be disputed that competent users of language know how to use words like "true" and "false" correctly. This, however, does not necessarily make the philosophic discovery of a problem automatically suspicious. At any rate, the claim that such problems are not genuine itself belongs integrally within the broader circle of philosophic debates. Sometimes, it is because "philosophy" is defined, circularly, as the activity that is stuck only with the unsolved problems that it appears that philosophy is at fault.

The matter is not trivial. An ambitious program in mathematics floundered in the early 20th century because paradoxes - somewhat like the Liar Paradox - were discovered in the foundations of Set Theory. Though few people realize the immense importance of mathematics for civilization, it should still be self-evident that problems that challenge the ability of reasoning to solve can wreak real damage.

Are Mathematics or Science Left with Unsolved Problems?

Modern science has a pragmatic unerpinning to it: if the model works in terms of what is expected of it, it is to be kept. A science like physics runs into crises often - unbeknownst to the lay person. The replacement of Newtonian mechanics by Special Relativity was the outcome of a crisis that emerged as a result of pairing Newton's system with the theory of electromagnetic phenomena. For the latter, but not for the former, the speed of light ought to be correctly calculated as a constant through a characteristic medium. It was proven empirically that there is, oddly, no characteristic medium for light. This privileged Einstein's move of stipulating that the velocity of light as such is a universal constant. Earlier solutions had depended on the conceit that light's presumed medium, called ether, was "conspiring" through its own movements to cancel out additive speeds and produce the result that all observer measure the same speed for light regardless as to how they move relative to the light source. Unlike what the case is in the debate of philosophic problems, this fantastic oddity is not itself the reason that vitiated adoption of the alternative (to which even Lorenz himself subscribed.) So, one reason a science like physics does not run into perennial debates about problems is because the rules of the game are different there: the model built to fit assumptions comes along with its ontology (the kinds of things it requires, as the case was with respect to substantival space and time for Newton and spacetime for Einstein's theory; had an ether been detected, its implausible participation to cancelling out moves by the light source would hardly pose a challenge to accepting the alternative theory.) Philosophical debates, on the other hand, have tended to engage metaphysical postulates across the board instead of seeking to make sense of them within, and constrained by, specific theoretical constructs. As soon as philosophic debates themselves are relativized to given theories, they solve problems but they may reemerge as controversial once an external point of view is adopted seeking to query a theory's right to its assumptions.

Indeed, both Leibniz and Spinoza, among philosophers, were expecting to complete a compendious philosophic system about all that is real, which would yield every empirical claim as a theorem to be proven on the basis of the system's definitions and postulates. Leibniz did not have time to devote to this and did not get far but Spinoza produced a superb, even if unconvincing, system in his work entitled Ethics. Notwithstanding its commitment to an empiricist method, science, at least in physics, works like this; the math takes over. There is, however, a key difference: the assumptions Einstein put down (only two of them - the Galilean principle of inertial movement and the postulate of the constant speed of light) were themselves widely accepted, investigated empirically and tested. In philosophic systems like Spinoza's, on the other hand, the principles themselves are conceived rationally. This is not necessary, though; Newton thought he was engaging in a philosophic activity as he was proceeding from principles that had empirical "bite." The reason Newton's system takes off and departs from a standard philosophic endeavor has a great deal to do with his development of the differential calculus. But philosophers too, depending on their outlooks, have also aspired to use mathematical techniques and this has become increasingly possible over time.

A science like Evolutionary Biology, triumphant today, gives rise to many problems that arise from the ambitiously broad scope of its application and explanatory prowess. Although experts in the field do not think of themselves as engaging in a philosophic activity when they apply the science to discuss, for instance, topics in moral thought, it can be contended that this is precisely what they do. Moreover, celebrated evolutionary theorists like O. Wilson are very much engaged in a grandiose project - a "consilience" program - that would account for the whole range of human phenomena on a foundation furnished by the discoveries of empirical biology plus the evolutionary model. When they do so, they often come across as rather amateurish in the role of philosophizers. For instance, the debate about the distinction between fact and value might not interest them - they are prone to dismissing it as yet another example of philosophic waste of time - but they often seem guilty of perpetrating the is/ought fallacy! If a discussion emerged over this subject, this would be one of those philosophic discussions that seem to lead nowhere. If, on the other hand, no discussion is to be had, we have in no way have settled whether a fallacy is committed by the theorizing scientist. All this can be taken in a couple of different ways: on the one hand, we could argue that philosophic debates, and the problems they rake up, are foundational and inevitable; even if they are to be understood as restricted to specific theories (not as cutting across all possible theoretical frameworks), they are still necessary as house-keeping investigations within theoretical models. On the other hand, one could make the case that pragmatic criteria ought to be used, as they are used in science to such good, profitable and fertile effect. Nevertheless, when applied to our basic tools of reasoning Pragmatism does not at all come across as an intuitively appealing way of thinking. For instance, the pragmatist definition of truth is "p is true if and only if there are defensibly good reasons within some specified context for accepting p as if it were true." To avoid circularity in the definition let us take the second occurrence of "true" to be the "naïve" or standard definition of true. The pragmatist definition comes across as unintuitive. Surely, there must be instances in which what is advantageous to adopt as "true" is not true.

In Mathematics there is a plethora of open challenges - conjectures that have been proven or disrpoven yet. There are philosophic debates in mathematics - something obscured from the view of the lay person. The most notorious dispute may have been instigated by the school of Math known as Intuitionists (not to be confused with other schools in other activities, which have the same name.) The Mathematical Intuitionist is essentially a Constructivist - demanding that proofs are constructible in principle (thus, rejecting indirect proof methods) and also refusing to accept as true any proposition simply because it does not entail logical absurdity (which is the standard mathematical view.) This is crucial when entities are posited, even though they are not to be fully constructed; standard mathematics permits positing any entity, defining it into existence as it were, insofar as this does not lead to absurdity. The Intuitionist also refuses to accept that a mathematical conjecture is either true or false. By true the Intuitionist understands: p is true if and only if there is in principle some process by which a constructive proof can be had, by which p may be deduced as conclusion. p is false if and only if there is in principle some process by which a constructive proof can be had, by which we can deduce as conclusion that "if p, then absurdity." So, the law of excluded middle (p or not-p) is rejected by the Intuitionist. It may well be that there is no proof of p (so p is not true), and there is no proof of not-p (so, p is not false either!) This gives us a taste of how philosophic debates about mathematics and about the items and operations of mathematics take place as well. Once again, there is an unspoken pragmatic turn: were we to accept Intuitionism, we would have to give up more than half of the math we have (for one, we would have to give up all those proofs that are obtained by use of the method known as reductio ad absurdum or proof by contradiction.) So, the practicing mathematician plows his or her trade ignoring such subtleties. From the point of view of an abstract interest in human knowledge, the problems of philosophy do not disappear. Of course, one could argue that it is an error to speak of such an overarching perspective or interest in human knowledge - but this too is a philosophic point of view which, as such, clashes with alternative philosophies.

One could defer to science altogether - to the extent that one would subordinate philosophic activity to the pronouncements of science itself. This view has been adopted by at least some proponents of the Analytic School of philosophy in the 20th century. Yet, metaphysics itself has made an unexpected comeback even among analytically trained philosophers - one of the perhaps unwitting instigators of this has been Saul Kripke.

Logical Grammar and Philosophic Problems

The view propounded by the Analytic School of philosophy, under the influence of Ludwig Wittgenstein, is that the variety of problems, especially in the field of metaphysics, which appear perennially debated and open-ended, comprises only pseudo-problems. What is common as the pathological denominstor of such problems is abuse of language. If the surface grammar is violated - we may not necessarily get nonsense- it is easy to detect where the flaw lies. Yet, languages have an underlying logical grammar. The surface grammar, we all study all too well, can be misleading with respect to the logical grammar. It is with respect to the logical grammar that flaws go undetected. Because of this, it is lost on philosophic students that the problems that occupy their attention are based on nonsense generated by abuse of language. An example can illustrate this.

As a matter of surface grammar, the sentence "nothing's outside" seems exactly like the sentence "Bob is outside." Yet, in terms of logical grammar, the two propositions made by these sentences are quite different. The former has the structure, discovered by regimenting or paraphrasing to bring out the logical structure: "there is no x such that x refers to an item from our universe if discourse and x has the property if being outside." The latter sentence has the structure, "the entity referred to by the name "Bob" has the property of being outside." Notice that it woulfd be an error, resulting in paying the price of speaking nonsense, to predicate of "nothing" attributes; but we could surely do this of the person named "Bob." There is a long tradition of philosophic puzzles and problems, stretching as far back as Parmenides and the Eleatic school he founded and descending to such recent thinkers as Martin Heidegger, which make predicate attributions to what supposedly denoted by "nothing" even though "nothing" does not have a logical grammar like that of terms or names - indeed "nothing" is logically "no thing" or a matter of quantification over variable terms. Heidegger infamously wrote that "nothing nothings" and Parmenides proved paradoxically that only one undifferentiated eternal thing can, and must, exist by using in the proof the premise that what is denoted by "nothing" has the property of non-existence.

Even if the whole slew of metaphysical problems were disqualified, we would still be left with many types of problems that remain open. A further move, also favored by the Analytic School and by the Logical Positivist tradition, is to impose the requirement that any genuine problem have soecifications as to the conditions under which it would be verifiable that it is solved or not. Attacks on verifiability have vitiated the appeal of this position. At a deeper level, this view seems akin to the theory that truth and falsehood have to do with in-principle verifiability - an interesting position but one from which many positivists have recoiled. (Notice the similarities of this position and the theory we called Mathematical Intuitionism above.)

Karl Marx once stipulated, at least of History, that only solvable problems can come up. Whether this is true or not is in itself a philosophic problem. It is not that philosophy is left with problems others won't touch but the other way round. If philosophy addresses some problem, you can bet that some area of mental discipline "secretes" this problem as a matter of the preconditions for its own operation and expansion. Disciplines, including scientific disciplines, proceed undeterred and undistracted. It is philosophy that minds the ship all the way deep down to its foundations.

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