“On Scientific Method in Philosophy,” pages 97-124
People typically are led to philosophical contemplation either by religious/moral concerns (Plato and Hegel, say), or by scientific interests (Hume and Locke, for example) – or by a healthy mixture of these motives (e.g., Aristotle, Kant). “Herbert Spencer, in whose honour we are assembled to-day, would naturally be classed among scientific philosophers…[p. 97].” Nonetheless, religion and ethics are also central to Spencer’s thought, and to his attachment to the notion of evolution.
Despite the creativity spawned through ethical and religious motives, their net impact on philosophy has been negative. Science, at least the kind that is divorced from those same sorts of religious motives, should be the driving force in the future of philosophy. Within the realm of science, however, it is the methods of inquiry, and not the cutting-edge results, that are positioned to be profitably borrowed by philosophers.
The pull of religion and ethics on philosophy is evident in the amount of cogitation on the “universe” and on “good and evil.” All this talk of the universe is a leftover from a pre-Copernican mindset, where the key position of mankind derived from the notion that the earth itself is central to the cosmos. A related vestige is the quick resort to claims of a oneness to the universe. Post-Copernicus, we should recognize “that the apparent oneness of the world is merely the oneness of what is seen by a single spectator or apprehended by a single mind [p. 99].”
[Russell (page 100) initiates the first of two numbered but untitled sections -- largely via a lengthy quoted passage from William James about how the ability to conceive of different universes and to collect them under a common name does not imply any connection between them, any “oneness”.] Nevertheless, there are two smaller unities, one involving that subset of existence experienced by an individual consciousness, and a second concerning the constancy of scientific laws in the small piece of the cosmos known to us. But neither of these unities holds any external legitimacy, permits any valid generalizations beyond their sphere. General laws in physics are unavoidable, as there is a finite amount of particles and thus their complete data forms a sort of (degenerate) general law; “what is surprising in physics is not the existence of general laws, but their extreme simplicity [p. 102].” The rules are so simple that even we can discover them. But again, there’s no reason to expect that those rules remain simple outside of sample; indeed, the rules we have identified must perforce be non-complex, otherwise we would not have discovered them.
More generally, the data that we have collected are not necessarily representative of all that exists -- data are selectively encountered. And those general scientific results we possess are rather infirm, particularly likely to be overturned as we learn more. We must ensure that any philosophical insights that we deduce from scientific results are those that largely will withstand the likely future modifications to those results. We should be wary, for example, of being too dependent on the supposed conservation of energy or mass. Both mass and energy are proving to be more complex than previously thought, and while within the traditional realm of physical sciences the old results are sturdy, out-of-sample generalizations requiring the conservation of some measure of energy or mass are unfounded.
Philosophies developed around evolution, whether older (Hegel, Spencer) or more modern (Pragmatism, Bergson), involve a normative bias, a notion that evolution is progress. [Bergson and progress came up earlier in “Mysticism and Logic”.] The evolutionary philosophies (though not Hegel’s) tend to use biological evolution as their guide. But our biological sample is quite limited, and even within it, the claim of progress (“from the protozoon to the philosopher [p. 106]”) is made by those who think of themselves as, to date, the apex of this supposed upwards movement. More generally, the ethical ideas employed by those whose philosophical inquiries are morally motivated are human-centered, and constitute “an attempt, however veiled, to legislate for the universe on the basis of the present desires of men [p. 107].” Hopes get in the way of facts.
Ethics are really about social affiliation, offering justifications for the actions of the group to which one belongs. The fact that ethical schools support some (seemingly) socially desirable behaviors, such as self-sacrifice, does not undermine their ultimate, action-laundering purpose. The lack of neutrality in ethics is what renders moral considerations unsuitable as a complete basis for philosophical reasoning – even though there is much of practical value in some ethically-based philosophical approaches, such as that of Spinoza. A scientific philosophy must proceed upon facts, not upon hopes for human progress.
[Page 110 begins the second of Russell’s two numbered but untitled sections.] After spurious ideas about the universe and the good are expunged, we see that philosophical propositions must not depend on any specific worlds, but apply to all possible worlds: such are the sort of general propositions found in logic. While such propositions apply to all things separately, they say nothing about any universe, any collection of these separate things. “The philosophy which I wish to advocate may be called logical atomism or absolute pluralism, because, while maintaining that there are many things, it denies that there is a whole composed of those things [p. 111].” Philosophical claims must be a priori, incapable of being proven or disproven through empirical data: arguments built around the path of history, for instance, are not of this nature. In brief, “philosophy is the science of the possible [p. 111, italics BR’s],” or the general.
By this reckoning, philosophy and logic are identical. Logic is general: note the use of variables in stating propositions; further, logic identifies the forms of propositions that can apply to these general facts, it yields “an inventory of possibilities [p. 112].” Perhaps surprisingly, specific areas of inquiry, such as those concerning space and time, are hindered by a lack of understanding of logical forms; that is, particular sciences can still be helped by developments in logic.
Science has made definite progress over the centuries, but the same cannot be said for philosophy. Every philosopher starts out afresh, with new fundamentals, and then the shortcomings in those fundamentals render the entire chain of reasoning to be erroneous: there are no partial truths in this style of philosophy, nothing that can serve as a starting point for later advances. “A scientific philosophy such as I wish to recommend will be piecemeal and tentative like other sciences; above all, it will be able to invent hypotheses which, even if they are not wholly true, will yet remain fruitful after the necessary corrections have been made [p. 113].” Like science, philosophy can then make better and better approximations to the truth. Philosophers should not dream up grand systems; rather, they should look to break current conundrums into smaller questions that individually are susceptible, with the correct logical forms, to solution.
Consider the question of space as promulgated by Kant’s Transcendental Aesthetic [good explanatory lecture pdf here]. Kant’s problem is comprised of three separate questions in different areas of inquiry: logic, physics, and the theory of knowledge. The theory of knowledge issue is the thorny one, the one we are furthest from solving.
The logical problem involves recognizing that what is key about the geometry of space is not so much the underlying axioms that serve as the foundation of a specific geometry, but rather how points in the space can be (partially) ordered by a “betweenness” criterion, where it can be ascertained if point B lies between points A and C. There are many geometries that share the same betweenness criterion, and geometrical reasoning takes place in a strictly logical fashion at this more general level of relations, as opposed to acting on some underlying, and less general, set of axioms.
The physical problem is how we connect real-world objects to mathematical entities such as points and planes – after all, mathematical physics has proven itself to teach us quite a bit about actual objects, even though those objects do not meet the definitions employed in the mathematics. A. N. Whitehead has shown the way, to understand a point, for instance, as the class of all physical objects that contain the point (p. 117). This approach does not require that we assume that objects are made of points, but helps explain how theories based on points nevertheless have real-world relevance.
Kant’s concern about how we can have a priori knowledge of geometry is softened (or eliminated) when we distinguish the logic of geometry from its physical manifestations. We can have a priori knowledge of the logic, but our physical knowledge is synthetic, and only approximates the logical constructs. Kant’s worry about how we can have synthetic, a priori knowledge of geometry is answered by recognizing that we lack such knowledge. We don’t know what happens when we look at actual parallel lines in space, so we shouldn’t act as if we have a priori knowledge of them: those who claim such knowledge have taken a very constrained view of the nature of space.
A similar style of analysis can help clarify the reality of what we perceive and if that reality is independent of the observer. The objects we perceive might be like the supposed noise in a forest, non-existent when not perceived – and there is no way we could tell if this is the case. Independence is as ineffable as reality: we can always identify multiple channels of causation of events, so that in the end, there is only correlation, not causation. “The view which I should wish to advocate is that objects of perception do not persist unchanged at times when they are not perceived, although probably objects more or less resembling them do exist at such times…[p. 123].” [Russell points to his 1914 book, Our Knowledge of the External World, for elaboration.]
So a scientific approach to philosophy requires that we farm out a subset of questions to allied sciences; that we accept that answers to some other questions are beyond human capabilities; and, that with the analytic method of being careful with definitions and decomposing large questions into bite-sized chunks, philosophers can make the slow and steady progress that marks science more generally.
Saturday, September 22, 2018
Wednesday, August 29, 2018
Mysticism and Logic, Chapter V
“Mathematics and the Metaphysicians,” pages 74-96
[In the Preface (pages v-vi), Russell tells us that this chapter originally appeared in 1901, and that necessary updates are indicated in footnotes.]
Despite what you may have heard, pure mathematics is a recent discovery, made by Boole in 1854. Though unbeknownst even to Boole, mathematics and formal logic are equivalent. Pure mathematics is about general statements, along the lines of “If (some proposition) A is true, then (some proposition) B is true,” but precisely what A is and whether in fact it is true or not are issues for applied, not pure, mathematics. “Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true [p. 75].”
The method familiar from geometry – start with some primitive definitions and axioms, and then commence deducing – is not descriptive of pure mathematics, except as that method applies to unalloyed logic. The branches of mathematics (geometry, arithmetic, and so on) develop from the building blocks of logic. It used to be an item of contention in philosophy as to whether mathematics could be built solely upon logic; the mathematicians have ended the contention by actually doing the building.
Aristotle and his syllogism founded formal logic, which for centuries advanced no further. Since 1850, we advance more every decade than the cumulative progress “from Aristotle to Leibniz [p.76];” Charles Sanders Peirce’s Logic of Relatives has been instrumental in expanding the scope of logic.
Symbolic logic allows us to get at the foundations of mathematics, through the paradoxical method of making the initial part of the path more difficult. The symbolism eliminates any obviousness from even the simplest propositions (such as 2+2=4), so we must rely on mechanical operations. We can thereby uncover the minimal set of definitions and axioms to generate algebra, for instance. At first, it might seem frivolous to rigorously prove that 2+2=4, but by connecting obvious statements through the non-obvious applications of rigorous methods, we are learning. One thing that is learned is that obvious truths sometimes are false. For numbers in general, for instance, it is not the case that the addition of one item leads to a greater number of items (thanks to transfinite numbers).
Giuseppe Peano is at the forefront of mathematical logic. [Russell inserts a footnote indicating that in the original version of this chapter, he was unfamiliar with the work of Gottlob Frege, but that Frege should be included as a contemporary leader in logic.] Peano dispenses with words (including “therefore,” and “let us assume”) in developing most (and soon all) of mathematics to symbols. Excepting geometry, most mathematics needs only three primitives: zero, number, and “next after.” And even these three primitives can be replaced by two ideas, relation and class.
Leibniz glimpsed the method that Peano has developed, but Leibniz’s progress was constrained by his unwillingness to accept that Aristotle made logical errors. Though lampooned, Leibniz’s vision of philosophical disagreements resolved by calculations has, to a significant extent, been realized, at least in mathematical philosophy. What used to be mysteries (such as the nature of infinity) are now certainties.
For centuries it was believed that Aristotle had effectively answered the paradoxes of Zeno of Elea, but with the work of Karl Weierstrass, we learn that Zeno largely was right. Zeno’s sole mistake was to believe (if he did believe it) that the non-existence of a state of change implies an unchanging reality. Weierstrass’s use of mathematics avoids any mistaken inferences, with the result that Zeno’s paradoxes appear as straightforward statements, though perhaps at the cost of removing the delight that can accompany Zeno’s enigmas.
Zeno’s paradoxes fundamentally implicate “the problems of the infinitesimal, the infinite, and continuity [p. 81].” For centuries no serious progress was made on these problems, until Weierstrass, Dedekind, and Cantor solved them: “[t]his achievement is probably the greatest of which our age has to boast [p. 81].” Weierstrass, in particular, showed that the infinitesimal which had bedeviled thinkers for millennia could safely be dispensed with. We can always divide a length more finely without ever reaching a single point. We cannot say where a body in motion will be in the next instant, because there is no such thing as the next instant (p. 84).
Recent advances on infinity have taken rather the opposite path than new thinking on infinitesimals: in the case of infinity, a concept that once was thought to hold inherent logical contradictions has been rendered perfectly understandable by Dedekind and Cantor. Their first step was to offer a precise definition of infinity; Cantor then demonstrated that the standard contradictions disappear if a faulty line of reasoning employed in the proofs of the contradictions is rejected. That commonsensical but incorrect notion was that a proper subset of a collection has fewer items than the original collection. The notion is correct for a finite collection, but provides the definitional distinction for infinity: “A collection of terms is infinite when it contains as parts other collections which have just as many terms as it has [p. 86].” Since every positive integer has a unique double (which is even), the positive integers and the even integers have the same number of terms – and hence there is an infinite amount of positive integers.
In dealing with the infinite, we can’t determine the size of a set just by counting the terms – that process would never end. But of two infinite collections, we can ask (and determine) if one has more terms than the other. The method is like the even-number example: we look for a one-to-one mapping between the collections. If such a mapping exists, then the two infinite sets are of the same size. Some infinite collections are larger than others, however. Is there a greatest infinite number? Cantor says no, but his proof is mistaken. [Russell adds (page 89) a footnote in 1917 indicating that Cantor’s proof actually is correct, and that it was Russell who was mistaken.]
The paradoxcial Zenovian notion that fleet Achilles cannot catch a slow tortoise that possesses a head start goes away when we see that proper subsets do not have to be smaller than their parent collection. Why are people led to think that there is a serious argument that Achilles cannot catch the tortoise? Because people recognize that at each instant after the start of the race, Achilles must be in precisely one spot and the tortoise must be in precisely one spot. But with the head start, the tortoise necessarily has been in more spots along the race course than has Achilles. As each passing instant adds one new spot for Achilles and one more spot for the tortoise, Achilles can never have been in a greater number of spots than the tortoise: he cannot catch the tortoise. Once we recognize that Achilles’s portion of the course does not possess fewer spots than the tortoise’s longer portion of the course, however, the argument crumbles.
Russell offers “the paradox of Tristam Shandy [p.90],” building on Tristam’s recognition that as it takes him longer to write about a period of his life than the period itself, his autobiography will become increasingly further from completion even as he makes progress on it. But as we can match each day of Tristam’s life with the year that it takes to write about it — that one-to-one mapping again — then over infinite time, the autobiography is complete. For a similar reason, with enough time, the slow tortoise will go as far as fleet Achilles. With Cantor as a guide, the paradoxes that once seemed inherent to infinity no longer look so paradoxical -- just as scientific advances have rendered it uninteresting that people can live on the other side of the earth despite their ”necessity” to live upside down.
The puzzles of continuity likewise have given way to Cantor’s exactitude: continuity is one type of order. It is order, and not quantity, that now seems fundamental in mathematics; much can be accomplished without introducing numbers. Limits, formerly expressed as quantities, are now based upon order. “Thus, for instance, the smallest of the infinite integers is the limit of the finite integers, though all finite integers are at an infinite distance from it [p. 92].”
Geometry, too, appears in a different light as its non-Euclidean variants have multiplied. Geometry is not about the space in which we live: it is about the valid conclusions that can be drawn from some set of starting principles, where those principles need not accord with what we see in the real world. The leading books in geometry now do not even rely upon figures to demonstrate their arguments. Indeed, figures mislead, as they suggest conclusions that seem obvious from the figures, but do not follow with necessity from the first principles.
Modern geometry does not start with an assumption of some large space; rather, a point is assumed, and then a second distinct point, with lines and other points building upon these beginnings, so nothing is assumed to exist unless it is necessary for the next step of reasoning. The mathematicians responsible for much of this improvement are Peano and Fano. Euclid’s work itself now seems error-filled, in the sense that, strictly speaking, many of his theorems do not follow from his axioms alone. The difficulty of Euclid’s book, along with its errors, renders it unfit for any consideration beyond the historical; it should not be thrust upon English schoolboys. “A book should have either intelligibility or correctness; to combine the two is impossible, but to lack both is to be unworthy of such a place as Euclid has occupied in education [p. 95].” [Russell’s own youthful introduction to Euclid was both intelligible and revelatory. Recall that this chapter of Mysticism and Logic originally appeared in 1901; in 1902, Russell published a short essay with a more detailed critique of Euclid. Even earlier, Russell had dealt with the empirical validity of Euclid’s postulates, an issue he regards in Mysticism and Logic as “a comparatively trivial matter [p. 94].”]
Modern formalism and symbolic logic have brought rigor to mathematics, a rigor that was absent since the Ancient Greeks. Mathematical advances in the interim were so alluring that the foundations of the subject were unexamined. Weierstrass and his ilk were to mathematicians what Hume was to Kant, the prod that awoke a slumbering intellect. Formalism can seem pedantic, but its record in uncovering errors provides its justification.
Kant’s metaphysics cannot survive the fact that mathematics (including geometry) are but elements of symbolic logic: his theory of knowledge was meant to complete Euclid. Now that we know that Euclid is wrong, not simply incomplete, the Kantian theory is not viable. What is needed is for mathematical logic to come to full flower, and then for philosophy to repurpose the same rigorous tools. If this process is successful, the future might see a golden age in philosophy that parallels the recent era of advance in mathematics, and matches the glory that was philosophy in Ancient Greece.
[In the Preface (pages v-vi), Russell tells us that this chapter originally appeared in 1901, and that necessary updates are indicated in footnotes.]
Despite what you may have heard, pure mathematics is a recent discovery, made by Boole in 1854. Though unbeknownst even to Boole, mathematics and formal logic are equivalent. Pure mathematics is about general statements, along the lines of “If (some proposition) A is true, then (some proposition) B is true,” but precisely what A is and whether in fact it is true or not are issues for applied, not pure, mathematics. “Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true [p. 75].”
The method familiar from geometry – start with some primitive definitions and axioms, and then commence deducing – is not descriptive of pure mathematics, except as that method applies to unalloyed logic. The branches of mathematics (geometry, arithmetic, and so on) develop from the building blocks of logic. It used to be an item of contention in philosophy as to whether mathematics could be built solely upon logic; the mathematicians have ended the contention by actually doing the building.
Aristotle and his syllogism founded formal logic, which for centuries advanced no further. Since 1850, we advance more every decade than the cumulative progress “from Aristotle to Leibniz [p.76];” Charles Sanders Peirce’s Logic of Relatives has been instrumental in expanding the scope of logic.
Symbolic logic allows us to get at the foundations of mathematics, through the paradoxical method of making the initial part of the path more difficult. The symbolism eliminates any obviousness from even the simplest propositions (such as 2+2=4), so we must rely on mechanical operations. We can thereby uncover the minimal set of definitions and axioms to generate algebra, for instance. At first, it might seem frivolous to rigorously prove that 2+2=4, but by connecting obvious statements through the non-obvious applications of rigorous methods, we are learning. One thing that is learned is that obvious truths sometimes are false. For numbers in general, for instance, it is not the case that the addition of one item leads to a greater number of items (thanks to transfinite numbers).
Giuseppe Peano is at the forefront of mathematical logic. [Russell inserts a footnote indicating that in the original version of this chapter, he was unfamiliar with the work of Gottlob Frege, but that Frege should be included as a contemporary leader in logic.] Peano dispenses with words (including “therefore,” and “let us assume”) in developing most (and soon all) of mathematics to symbols. Excepting geometry, most mathematics needs only three primitives: zero, number, and “next after.” And even these three primitives can be replaced by two ideas, relation and class.
Leibniz glimpsed the method that Peano has developed, but Leibniz’s progress was constrained by his unwillingness to accept that Aristotle made logical errors. Though lampooned, Leibniz’s vision of philosophical disagreements resolved by calculations has, to a significant extent, been realized, at least in mathematical philosophy. What used to be mysteries (such as the nature of infinity) are now certainties.
For centuries it was believed that Aristotle had effectively answered the paradoxes of Zeno of Elea, but with the work of Karl Weierstrass, we learn that Zeno largely was right. Zeno’s sole mistake was to believe (if he did believe it) that the non-existence of a state of change implies an unchanging reality. Weierstrass’s use of mathematics avoids any mistaken inferences, with the result that Zeno’s paradoxes appear as straightforward statements, though perhaps at the cost of removing the delight that can accompany Zeno’s enigmas.
Zeno’s paradoxes fundamentally implicate “the problems of the infinitesimal, the infinite, and continuity [p. 81].” For centuries no serious progress was made on these problems, until Weierstrass, Dedekind, and Cantor solved them: “[t]his achievement is probably the greatest of which our age has to boast [p. 81].” Weierstrass, in particular, showed that the infinitesimal which had bedeviled thinkers for millennia could safely be dispensed with. We can always divide a length more finely without ever reaching a single point. We cannot say where a body in motion will be in the next instant, because there is no such thing as the next instant (p. 84).
Recent advances on infinity have taken rather the opposite path than new thinking on infinitesimals: in the case of infinity, a concept that once was thought to hold inherent logical contradictions has been rendered perfectly understandable by Dedekind and Cantor. Their first step was to offer a precise definition of infinity; Cantor then demonstrated that the standard contradictions disappear if a faulty line of reasoning employed in the proofs of the contradictions is rejected. That commonsensical but incorrect notion was that a proper subset of a collection has fewer items than the original collection. The notion is correct for a finite collection, but provides the definitional distinction for infinity: “A collection of terms is infinite when it contains as parts other collections which have just as many terms as it has [p. 86].” Since every positive integer has a unique double (which is even), the positive integers and the even integers have the same number of terms – and hence there is an infinite amount of positive integers.
In dealing with the infinite, we can’t determine the size of a set just by counting the terms – that process would never end. But of two infinite collections, we can ask (and determine) if one has more terms than the other. The method is like the even-number example: we look for a one-to-one mapping between the collections. If such a mapping exists, then the two infinite sets are of the same size. Some infinite collections are larger than others, however. Is there a greatest infinite number? Cantor says no, but his proof is mistaken. [Russell adds (page 89) a footnote in 1917 indicating that Cantor’s proof actually is correct, and that it was Russell who was mistaken.]
The paradoxcial Zenovian notion that fleet Achilles cannot catch a slow tortoise that possesses a head start goes away when we see that proper subsets do not have to be smaller than their parent collection. Why are people led to think that there is a serious argument that Achilles cannot catch the tortoise? Because people recognize that at each instant after the start of the race, Achilles must be in precisely one spot and the tortoise must be in precisely one spot. But with the head start, the tortoise necessarily has been in more spots along the race course than has Achilles. As each passing instant adds one new spot for Achilles and one more spot for the tortoise, Achilles can never have been in a greater number of spots than the tortoise: he cannot catch the tortoise. Once we recognize that Achilles’s portion of the course does not possess fewer spots than the tortoise’s longer portion of the course, however, the argument crumbles.
Russell offers “the paradox of Tristam Shandy [p.90],” building on Tristam’s recognition that as it takes him longer to write about a period of his life than the period itself, his autobiography will become increasingly further from completion even as he makes progress on it. But as we can match each day of Tristam’s life with the year that it takes to write about it — that one-to-one mapping again — then over infinite time, the autobiography is complete. For a similar reason, with enough time, the slow tortoise will go as far as fleet Achilles. With Cantor as a guide, the paradoxes that once seemed inherent to infinity no longer look so paradoxical -- just as scientific advances have rendered it uninteresting that people can live on the other side of the earth despite their ”necessity” to live upside down.
The puzzles of continuity likewise have given way to Cantor’s exactitude: continuity is one type of order. It is order, and not quantity, that now seems fundamental in mathematics; much can be accomplished without introducing numbers. Limits, formerly expressed as quantities, are now based upon order. “Thus, for instance, the smallest of the infinite integers is the limit of the finite integers, though all finite integers are at an infinite distance from it [p. 92].”
Geometry, too, appears in a different light as its non-Euclidean variants have multiplied. Geometry is not about the space in which we live: it is about the valid conclusions that can be drawn from some set of starting principles, where those principles need not accord with what we see in the real world. The leading books in geometry now do not even rely upon figures to demonstrate their arguments. Indeed, figures mislead, as they suggest conclusions that seem obvious from the figures, but do not follow with necessity from the first principles.
Modern geometry does not start with an assumption of some large space; rather, a point is assumed, and then a second distinct point, with lines and other points building upon these beginnings, so nothing is assumed to exist unless it is necessary for the next step of reasoning. The mathematicians responsible for much of this improvement are Peano and Fano. Euclid’s work itself now seems error-filled, in the sense that, strictly speaking, many of his theorems do not follow from his axioms alone. The difficulty of Euclid’s book, along with its errors, renders it unfit for any consideration beyond the historical; it should not be thrust upon English schoolboys. “A book should have either intelligibility or correctness; to combine the two is impossible, but to lack both is to be unworthy of such a place as Euclid has occupied in education [p. 95].” [Russell’s own youthful introduction to Euclid was both intelligible and revelatory. Recall that this chapter of Mysticism and Logic originally appeared in 1901; in 1902, Russell published a short essay with a more detailed critique of Euclid. Even earlier, Russell had dealt with the empirical validity of Euclid’s postulates, an issue he regards in Mysticism and Logic as “a comparatively trivial matter [p. 94].”]
Modern formalism and symbolic logic have brought rigor to mathematics, a rigor that was absent since the Ancient Greeks. Mathematical advances in the interim were so alluring that the foundations of the subject were unexamined. Weierstrass and his ilk were to mathematicians what Hume was to Kant, the prod that awoke a slumbering intellect. Formalism can seem pedantic, but its record in uncovering errors provides its justification.
Kant’s metaphysics cannot survive the fact that mathematics (including geometry) are but elements of symbolic logic: his theory of knowledge was meant to complete Euclid. Now that we know that Euclid is wrong, not simply incomplete, the Kantian theory is not viable. What is needed is for mathematical logic to come to full flower, and then for philosophy to repurpose the same rigorous tools. If this process is successful, the future might see a golden age in philosophy that parallels the recent era of advance in mathematics, and matches the glory that was philosophy in Ancient Greece.
Saturday, July 21, 2018
Mysticism and Logic, Chapter IV
"The Study of Mathematics," pages 58-73
Deep contemplations lead to beautiful edifices, but that beauty is remote to the beginner and its achievement and appreciation require hard-to-obtain knowledge. “Dry pedants possess themselves of the privilege of instilling this knowledge: they forget that it is to serve but as a key to open the doors of the temple [pages 58-59].” Their students see only the steep upwards path, and not the gorgeous structure at the end.
In terms of concealing the ultimate purpose, mathematics education might be in even worse shape than classics. The significance of mathematics is often couched in how it leads to better machines, improved transport, and military might. Of course, the limited mathematics training that most people receive does not conduce to these ends. Why do they study mathematics? The typical response is that the study of math enhances the ability to reason – though this response is made primarily by people who themselves teach all sorts of fallacious nonsense. Improved reasoning itself is viewed as contributing to prudent personal decision-making: hardly a goal worthy of teaching mathematics to all educated people. But Plato understood that mathematics is requisite for the apotheosis of mankind.
Mathematics pairs truth with unvarnished beauty; it offers respite from the painful compromises of our quotidian existence. The beauty of mathematics is the result of rigorous logic, not a product of any conscious aesthetic design.
How can this beauty, this higher quality of mathematics, be communicated by teachers? In geometry, it is best to focus, at first, not on theorems and proofs, but on diverse illustrations (of triangles and their associated lines, meeting in a single point, for instance). “In this way belief is generated; it is seen that reasoning may lead to startling conclusions, which nevertheless the facts will verify; and thus the instinctive distrust of whatever is abstract or rational is gradually overcome [p. 62].” The concrete is the way to the general.
For new learners, algebra is hard to comprehend, with its reliance on letters (variables) instead of numbers. But algebra presents truths that go beyond the particular, general truths, and it is these that allow “the mastery of the intellect over the whole world of things [p. 63].” Teachers tend to fail to impart an understanding of the principles brought to bear in algebra, however, even if students learn recipes to apply rules that produce correct answers.
After algebra, it is dealing with infinity (as in the infinitesimal calculus) that presents the next hurdle. “The solution of the difficulties which formerly surrounded the mathematical infinite is probably the greatest achievement of which our own age has to boast [p. 64].” Cantor and Dedekind showed that when dealing with infinity, you could remove some elements from a set, and still have the same number of elements in the set. This notion cleared up all of the misconceptions concerning infinities, and has opened up grand new vistas of thought. In the past, much of the foundation of mathematics was clearly fallacious, a practical compromise that mixed logic with superstition; now, the need to compromise has been expunged. Pure mathematics, mathematics as an end in itself, can be built from first principles that themselves can survive intense scrutiny.
Textbooks typically fail to convey the unity and purposeful progression of mathematics. But the beauty and drama of mathematics lie in its interconnections, in the relation of many propositions to a few fundamental ideas. Learners must not be distracted from these core notions through a plethora of inessential or unconnected examples.
The ultimate unifying discipline within mathematics is symbolic logic, which is a product largely of the nineteenth century and still developing today. “The true method of discovery in symbolic logic, and probably also the best method for introducing the study to a learner acquainted with other parts of mathematics, is the analysis of actual examples of deductive reasoning, with a view to the discovery of the principles employed [p. 67].” The realization that only a few simple concepts underlie mathematics, and that those concepts are regularly (but perhaps unconsciously) employed in thinking, can be transformative. What had been glimpsed is now seen clearly, and the panorama is beautiful.
Symbolic logic has replaced the former foundations of mathematics, which were philosophical, and thus uncertain. The sounder base has rendered the superstructure more intellectually pleasing, and this pleasure should be made available to students.
Logic and mathematics exist outside of humans and their thoughts – but we can still appreciate the beauty of mathematical objects, whether they be our creations or our discoveries.
For students, the goal shouldn’t be just to inform them of conclusions, of the end points of a chain of reasoning, but also to take them along the most splendid path to those ends. “An argument which serves only to prove a conclusion is like a story subordinated to some moral which it is meant to teach: for aesthetic perfection no part of the whole should be merely a means [p. 70].” Elegance and generality in a mathematical argument, a proof, derive from using only the most fundamental, minimal assumptions necessary to reach the conclusion.
The common notion that truths are relative, that one person’s truth need not be another’s, and that there is no impartial standard to decide the matter, meets its demise in the arena of mathematics.
Mathematics needn’t rely on its practical effects for its justification. But in a world full of injustice, sometimes it seems hard to countenance a life spent in thought, aloof from the evils of the world, while enjoying a beauty that is not available to most people. Of course we need some people to “keep alive the sacred fire [p. 72],” but this rationale might seem inadequate in the face of current troubles. Here, the practical applications of mathematics can help, by reminding us that cloistered study in the near term can lead to tremendous improvements in human happiness down the road. Could we harness steam power or electricity without the development of mathematics? Of course, we cannot know what sorts of mathematics will lead to the best innovations in the future, so we should avoid investing solely in those branches of mathematics that have proven useful in the past.
The love of truth holds the power to raise our moral existence, “and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith [p. 73].” Cloistered study is its own reward, but it also ennobles our minds; the teaching of mathematics should keep in mind this indirect benefit.
Deep contemplations lead to beautiful edifices, but that beauty is remote to the beginner and its achievement and appreciation require hard-to-obtain knowledge. “Dry pedants possess themselves of the privilege of instilling this knowledge: they forget that it is to serve but as a key to open the doors of the temple [pages 58-59].” Their students see only the steep upwards path, and not the gorgeous structure at the end.
In terms of concealing the ultimate purpose, mathematics education might be in even worse shape than classics. The significance of mathematics is often couched in how it leads to better machines, improved transport, and military might. Of course, the limited mathematics training that most people receive does not conduce to these ends. Why do they study mathematics? The typical response is that the study of math enhances the ability to reason – though this response is made primarily by people who themselves teach all sorts of fallacious nonsense. Improved reasoning itself is viewed as contributing to prudent personal decision-making: hardly a goal worthy of teaching mathematics to all educated people. But Plato understood that mathematics is requisite for the apotheosis of mankind.
Mathematics pairs truth with unvarnished beauty; it offers respite from the painful compromises of our quotidian existence. The beauty of mathematics is the result of rigorous logic, not a product of any conscious aesthetic design.
How can this beauty, this higher quality of mathematics, be communicated by teachers? In geometry, it is best to focus, at first, not on theorems and proofs, but on diverse illustrations (of triangles and their associated lines, meeting in a single point, for instance). “In this way belief is generated; it is seen that reasoning may lead to startling conclusions, which nevertheless the facts will verify; and thus the instinctive distrust of whatever is abstract or rational is gradually overcome [p. 62].” The concrete is the way to the general.
For new learners, algebra is hard to comprehend, with its reliance on letters (variables) instead of numbers. But algebra presents truths that go beyond the particular, general truths, and it is these that allow “the mastery of the intellect over the whole world of things [p. 63].” Teachers tend to fail to impart an understanding of the principles brought to bear in algebra, however, even if students learn recipes to apply rules that produce correct answers.
After algebra, it is dealing with infinity (as in the infinitesimal calculus) that presents the next hurdle. “The solution of the difficulties which formerly surrounded the mathematical infinite is probably the greatest achievement of which our own age has to boast [p. 64].” Cantor and Dedekind showed that when dealing with infinity, you could remove some elements from a set, and still have the same number of elements in the set. This notion cleared up all of the misconceptions concerning infinities, and has opened up grand new vistas of thought. In the past, much of the foundation of mathematics was clearly fallacious, a practical compromise that mixed logic with superstition; now, the need to compromise has been expunged. Pure mathematics, mathematics as an end in itself, can be built from first principles that themselves can survive intense scrutiny.
Textbooks typically fail to convey the unity and purposeful progression of mathematics. But the beauty and drama of mathematics lie in its interconnections, in the relation of many propositions to a few fundamental ideas. Learners must not be distracted from these core notions through a plethora of inessential or unconnected examples.
The ultimate unifying discipline within mathematics is symbolic logic, which is a product largely of the nineteenth century and still developing today. “The true method of discovery in symbolic logic, and probably also the best method for introducing the study to a learner acquainted with other parts of mathematics, is the analysis of actual examples of deductive reasoning, with a view to the discovery of the principles employed [p. 67].” The realization that only a few simple concepts underlie mathematics, and that those concepts are regularly (but perhaps unconsciously) employed in thinking, can be transformative. What had been glimpsed is now seen clearly, and the panorama is beautiful.
Symbolic logic has replaced the former foundations of mathematics, which were philosophical, and thus uncertain. The sounder base has rendered the superstructure more intellectually pleasing, and this pleasure should be made available to students.
Logic and mathematics exist outside of humans and their thoughts – but we can still appreciate the beauty of mathematical objects, whether they be our creations or our discoveries.
For students, the goal shouldn’t be just to inform them of conclusions, of the end points of a chain of reasoning, but also to take them along the most splendid path to those ends. “An argument which serves only to prove a conclusion is like a story subordinated to some moral which it is meant to teach: for aesthetic perfection no part of the whole should be merely a means [p. 70].” Elegance and generality in a mathematical argument, a proof, derive from using only the most fundamental, minimal assumptions necessary to reach the conclusion.
The common notion that truths are relative, that one person’s truth need not be another’s, and that there is no impartial standard to decide the matter, meets its demise in the arena of mathematics.
Mathematics needn’t rely on its practical effects for its justification. But in a world full of injustice, sometimes it seems hard to countenance a life spent in thought, aloof from the evils of the world, while enjoying a beauty that is not available to most people. Of course we need some people to “keep alive the sacred fire [p. 72],” but this rationale might seem inadequate in the face of current troubles. Here, the practical applications of mathematics can help, by reminding us that cloistered study in the near term can lead to tremendous improvements in human happiness down the road. Could we harness steam power or electricity without the development of mathematics? Of course, we cannot know what sorts of mathematics will lead to the best innovations in the future, so we should avoid investing solely in those branches of mathematics that have proven useful in the past.
The love of truth holds the power to raise our moral existence, “and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith [p. 73].” Cloistered study is its own reward, but it also ennobles our minds; the teaching of mathematics should keep in mind this indirect benefit.
Sunday, October 29, 2017
Mysticism and Logic, Chapter III
"A Free Man’s Worship," pages 46-57
Russell begins with a lengthy quotation from Faust, where Mephistopheles explains how the Creator, bored with the praises from angels whose situations he had made joyous, decides to allow worlds and living creatures to develop – living creatures who can be led to worship Him even though they receive only torment, not joy. Eventually men succeed in this task, and even name as Sin the pursuit of their natural instincts. So the Creator destroys these worlds, that He might enjoy a similar pageant once again from the beginning. Russell endorses the fable: “Such, in outline, but even more purposeless, more void of meaning, is the world which Science presents for our belief [p. 47].” We must accept what our best knowledge makes all but certain, that what has been built has been accidental, unplanned, that the grave is our full ending, and that a similar grave awaits the solar system.
“What though the field be lost?/All is not lost.” The interim is ours (and perhaps ours alone), “to examine, to criticise, to know, and in imagination to create [p. 48].”
Savages, knowledgeable of their vulnerability to nature, worship power, even being willing to shed much blood in a fruitless attempt to appease brutal gods. The size of the sacrifice is indicative of the slavish commitment to suppressing any doubts as to the worthiness of the worshiped idol. They cannot conceive of a better world, so they worship what is powerful, not what is benevolent. Today’s might-makes-righters, including social Darwinists and militarists and followers of Carlyle and Nietzsche, are similarly in thrall to power.
The standard religious view is now different – it asserts that our world in fact comports with the benevolence of the all-powerful creator, but in a manner that is unfathomable to mortal minds. This claim is not easily reconciled with the fact that the world contains much evil. We must choose whether to accept that God is evil, or whether to accept that God is unreal, our own invention.
To worship strength is to sacrifice our ideals to mollify the powerful. If strength must be idolized, why not choose to idolize the strength shown by those who are willing to recognize that “is” does not imply “ought,” and the fact that there is much wrong with our world? Our actions must respect the unavoidable constraints of an imperfect world, but our vision – the vision that motivates our actions – should remain fixed on what is good.
The alternative of taking umbrage at the evil of the world is not a real alternative at all: it allows evil to preoccupy us. “Indignation is a submission of our thoughts, but not of our desires; the Stoic freedom in which wisdom consists is found in the submission of our desires, but not of our thoughts [p. 51].” Art and philosophy emerge from the visions of beauty that are licensed by unconstrained thoughts, thoughts uncontaminated by the need to serve our desires.
Austere religions are right, more often than not, in their contention that what is desired is bad. Even those things that we desire that really are beneficial should not become fetishized, if they cannot be attained. And though it is not understood by young people, those who are older know that many wonderful things will be unattainable. “What fates impose, that men must needs abide;/It boots not to resist both wind and tide.”
Along with our renunciation of desire, we need to make it possible to deify our ideals, through our embrace of reason and culture. “In all the multiform facts of the world – in the visual shapes of trees and mountains and clouds, in the events of the life of man, even in the very omnipotence of Death – the insight of creative idealism can find the reflection of a beauty which its own thoughts first made [p. 53].” Tragedy is the queen of the arts in that it takes evils such as death and despair and fashions beauty out of them. Even in the recognition of loneliness, loss, and powerlessness, we can forge a bond with the world, and overcome the sway of these potent adversaries.
The past’s beauty lies in its fixity and purity. “The Past does not change or strive; like Duncan, after life’s fitful fever it sleeps well; what was eager and grasping, what was petty and transitory, has faded away, the things that were beautiful and eternal shine out of it like stars in the night [p. 55].” The past’s beauty can provide a sort of religious rapture.
Appreciating the force of nature in its tragic form is a source of power and freedom. “To abandon the struggle for private happiness, to expel all eagerness of temporary desire, to burn with passion for eternal things – this is emancipation, and this is the free man’s worship [p. 55].”
We are united in the tomb, our common end. As we march along our path, our comrades (along with us, eventually) fall off the cliff, lost forever. We do not have long to ease their steps, to light their path. We shouldn’t concern ourselves with their desert, but with their need. They, too, are fated to be players in a tragedy. When they pass into eternity, let us hope that we did not stoke their sorrows, but rather relieved their pains and enhanced their joys.
Old Man River keeps on rolling; we can be proud in our temporary defiance, as we briefly construct and maintain a world based on our ideals.
Russell begins with a lengthy quotation from Faust, where Mephistopheles explains how the Creator, bored with the praises from angels whose situations he had made joyous, decides to allow worlds and living creatures to develop – living creatures who can be led to worship Him even though they receive only torment, not joy. Eventually men succeed in this task, and even name as Sin the pursuit of their natural instincts. So the Creator destroys these worlds, that He might enjoy a similar pageant once again from the beginning. Russell endorses the fable: “Such, in outline, but even more purposeless, more void of meaning, is the world which Science presents for our belief [p. 47].” We must accept what our best knowledge makes all but certain, that what has been built has been accidental, unplanned, that the grave is our full ending, and that a similar grave awaits the solar system.
“What though the field be lost?/All is not lost.” The interim is ours (and perhaps ours alone), “to examine, to criticise, to know, and in imagination to create [p. 48].”
Savages, knowledgeable of their vulnerability to nature, worship power, even being willing to shed much blood in a fruitless attempt to appease brutal gods. The size of the sacrifice is indicative of the slavish commitment to suppressing any doubts as to the worthiness of the worshiped idol. They cannot conceive of a better world, so they worship what is powerful, not what is benevolent. Today’s might-makes-righters, including social Darwinists and militarists and followers of Carlyle and Nietzsche, are similarly in thrall to power.
The standard religious view is now different – it asserts that our world in fact comports with the benevolence of the all-powerful creator, but in a manner that is unfathomable to mortal minds. This claim is not easily reconciled with the fact that the world contains much evil. We must choose whether to accept that God is evil, or whether to accept that God is unreal, our own invention.
To worship strength is to sacrifice our ideals to mollify the powerful. If strength must be idolized, why not choose to idolize the strength shown by those who are willing to recognize that “is” does not imply “ought,” and the fact that there is much wrong with our world? Our actions must respect the unavoidable constraints of an imperfect world, but our vision – the vision that motivates our actions – should remain fixed on what is good.
The alternative of taking umbrage at the evil of the world is not a real alternative at all: it allows evil to preoccupy us. “Indignation is a submission of our thoughts, but not of our desires; the Stoic freedom in which wisdom consists is found in the submission of our desires, but not of our thoughts [p. 51].” Art and philosophy emerge from the visions of beauty that are licensed by unconstrained thoughts, thoughts uncontaminated by the need to serve our desires.
Austere religions are right, more often than not, in their contention that what is desired is bad. Even those things that we desire that really are beneficial should not become fetishized, if they cannot be attained. And though it is not understood by young people, those who are older know that many wonderful things will be unattainable. “What fates impose, that men must needs abide;/It boots not to resist both wind and tide.”
Along with our renunciation of desire, we need to make it possible to deify our ideals, through our embrace of reason and culture. “In all the multiform facts of the world – in the visual shapes of trees and mountains and clouds, in the events of the life of man, even in the very omnipotence of Death – the insight of creative idealism can find the reflection of a beauty which its own thoughts first made [p. 53].” Tragedy is the queen of the arts in that it takes evils such as death and despair and fashions beauty out of them. Even in the recognition of loneliness, loss, and powerlessness, we can forge a bond with the world, and overcome the sway of these potent adversaries.
The past’s beauty lies in its fixity and purity. “The Past does not change or strive; like Duncan, after life’s fitful fever it sleeps well; what was eager and grasping, what was petty and transitory, has faded away, the things that were beautiful and eternal shine out of it like stars in the night [p. 55].” The past’s beauty can provide a sort of religious rapture.
Appreciating the force of nature in its tragic form is a source of power and freedom. “To abandon the struggle for private happiness, to expel all eagerness of temporary desire, to burn with passion for eternal things – this is emancipation, and this is the free man’s worship [p. 55].”
We are united in the tomb, our common end. As we march along our path, our comrades (along with us, eventually) fall off the cliff, lost forever. We do not have long to ease their steps, to light their path. We shouldn’t concern ourselves with their desert, but with their need. They, too, are fated to be players in a tragedy. When they pass into eternity, let us hope that we did not stoke their sorrows, but rather relieved their pains and enhanced their joys.
Old Man River keeps on rolling; we can be proud in our temporary defiance, as we briefly construct and maintain a world based on our ideals.
Thursday, September 21, 2017
Mysticism and Logic, Chapter II
"The Place of Science in a Liberal Education," pages 33-45
This essay is divided into two untitled parts, with part I covering pages 33-39, and part II covering pages 39-45.
Most people see science through the persistent parade of new technological marvels. Man’s growing control over nature is a good reason to promote scientific research, but there are other strong, though less appreciated reasons, including the inculcation of a scientific cast of thought. Inventions like wireless telegraphs stem from impressive and fundamental theoretical advances, with the eventual application in useful products valuable but possessing less of a broad sweep.
Even scientists are likely to associate culture not with their own activities but with the productions of those trained in literary or classical pursuits. That is, scientists themselves justify their supposedly inferior activity through the practical gadgetry that results, and not from the careful, disinterested build-up of knowledge that sharpens mental acuity.
An education in the classics has great value, though “I have not myself enjoyed its benefits…[p. 35].” [Russell makes this point elsewhere – RBR] The focus on the past, especially on a rather refined version of the past, however, can lead to insufficient appreciation of the present and future. Such a concern goes beyond the study of classics, to any excessively static and academic education.
What is the aim of education? First, let’s describe what I [Russell] mean by education. I do not mean the broad definition that includes all life learning; nor do I mean the narrow definition of formal instruction concerning specific information, like the three R’s in elementary school. Education here will be taken to mean “the formation, by means of instruction, of certain mental habits and a certain outlook on life and the world [p. 37, italics Russell’s].”
We all are driven by a finite number of primary impulses. Each of these primary drives is supported by a plethora of secondary desires that arise in support of the primary impulse. If we lose a primary impulse, the supportive ones will themselves wither and die: our previous interest in them will be deprived of all zest, all color. Meaning in our lives is always connected to a primary desire – the secondary ones, unlinked with a primary drive, cannot lend meaning to our existence.
Education, therefore, does not create a heretofore non-existent primary drive nor generate new meaning for living, but it can enlarge the scope of our existing primary interests. Unfortunately, much education in practice has attempted to thwart natural impulses, thereby producing “stunted and contorted hypocrites [p. 38].”
A proper education does not serve to impede instincts, but rather hones them, managing their conflicts and limiting negative consequences. It broadens one’s contacts with the world and its people, both across time and across space. “It is this simultaneous softening in the insistence of desire and enlargement of its scope that is the chief moral end of education [p. 39].” The intellectual end is to see the human and the non-human world, and the relations between them, as they are, and not as we might like them to be. Educational success can be measured by the outcome of this de-biasing project.
With the second untitled part of this essay beginning on page 39, Russell returns to discussing science. Relative to art and literature, science possesses the advantage of providing hope, both for the future and for what a dedicated student can accomplish. This hope helps to counter a cost that can accompany science’s other comparative advantage, namely, the independence of scientifically-revealed truths from human desires.
Study of art and literature is backward looking, to Ancient Greece or the Renaissance. The pinnacles reached in the past “actually increase the difficulty of fresh triumphs by rendering originality harder of attainment [p. 40].” Science builds on past successes, but not so art; indeed, civilization produces a sophistication that inhibits the sort of wide-eyed wonder that spurs artistic creativity. Artists cavil at the present, and their impulse for originality is reflected in a bizarre iconoclasm.
Since Galileo, we have had the scientific method at hand, and hence have a recipe for generating progress that is not available to artists. We do not need a person of genius to produce every advance in science, though artistic breakthroughs require such prodigies. Those who contribute most to science are those who develop a new method, though many of the valuable discoveries will subsequently be made by others who apply the method.
Beyond the individual methods is the more general scientific method, which “includes deduction as much as induction, logic and mathematics as much as botany and geology [p. 42].” This method develops from an outlook which understands that the world is what it is, irrespective of how we might wish it to be. Though such an outlook might seem to be the obvious one to adopt, in practice it has proven hard to inculcate. Aristotle thought that the stars move in circles because he viewed the circle as the most perfect of curves – and thereby let his preferences decide questions of fact. Malthus, who wrote post-Galileo, did better: his mistaken population theory derived from a dispassionate view of people as creatures exhibiting consistent behaviors that would bring certain consequences. Darwin, inspired by Malthus, has helped to cement the scientific approach to the study of man.
Philosophy remains rather unscientific, even if philosophers like to deploy scientific terms. The scientific approach requires the abjuration of feelings or anything else that impedes the search for truth, for a view of reality untarnished by preconceptions or hopes. Our attachment to rationality and desire for progress should not, on its own, lead us to believe that the universe coheres with our logic and improves (or deteriorates) over time. Our hopes and fears limit the potential for philosophy.
The desire to build something lasting can be satisfied more intensely in science than in poetry. Our curiosity can realize the payoff of new knowledge when deployed in a scientific manner – it broadens and depersonalizes our interests, promoting our wellbeing. A scientist who makes a new discovery receives the additional satisfaction of public admiration and the knowledge that society has been benefitted. “A life devoted to science is therefore a happy life, and its happiness is derived from the very best sources that are open to dwellers on this troubled and passionate planet [p. 45].”
This essay is divided into two untitled parts, with part I covering pages 33-39, and part II covering pages 39-45.
Most people see science through the persistent parade of new technological marvels. Man’s growing control over nature is a good reason to promote scientific research, but there are other strong, though less appreciated reasons, including the inculcation of a scientific cast of thought. Inventions like wireless telegraphs stem from impressive and fundamental theoretical advances, with the eventual application in useful products valuable but possessing less of a broad sweep.
Even scientists are likely to associate culture not with their own activities but with the productions of those trained in literary or classical pursuits. That is, scientists themselves justify their supposedly inferior activity through the practical gadgetry that results, and not from the careful, disinterested build-up of knowledge that sharpens mental acuity.
An education in the classics has great value, though “I have not myself enjoyed its benefits…[p. 35].” [Russell makes this point elsewhere – RBR] The focus on the past, especially on a rather refined version of the past, however, can lead to insufficient appreciation of the present and future. Such a concern goes beyond the study of classics, to any excessively static and academic education.
What is the aim of education? First, let’s describe what I [Russell] mean by education. I do not mean the broad definition that includes all life learning; nor do I mean the narrow definition of formal instruction concerning specific information, like the three R’s in elementary school. Education here will be taken to mean “the formation, by means of instruction, of certain mental habits and a certain outlook on life and the world [p. 37, italics Russell’s].”
We all are driven by a finite number of primary impulses. Each of these primary drives is supported by a plethora of secondary desires that arise in support of the primary impulse. If we lose a primary impulse, the supportive ones will themselves wither and die: our previous interest in them will be deprived of all zest, all color. Meaning in our lives is always connected to a primary desire – the secondary ones, unlinked with a primary drive, cannot lend meaning to our existence.
Education, therefore, does not create a heretofore non-existent primary drive nor generate new meaning for living, but it can enlarge the scope of our existing primary interests. Unfortunately, much education in practice has attempted to thwart natural impulses, thereby producing “stunted and contorted hypocrites [p. 38].”
A proper education does not serve to impede instincts, but rather hones them, managing their conflicts and limiting negative consequences. It broadens one’s contacts with the world and its people, both across time and across space. “It is this simultaneous softening in the insistence of desire and enlargement of its scope that is the chief moral end of education [p. 39].” The intellectual end is to see the human and the non-human world, and the relations between them, as they are, and not as we might like them to be. Educational success can be measured by the outcome of this de-biasing project.
With the second untitled part of this essay beginning on page 39, Russell returns to discussing science. Relative to art and literature, science possesses the advantage of providing hope, both for the future and for what a dedicated student can accomplish. This hope helps to counter a cost that can accompany science’s other comparative advantage, namely, the independence of scientifically-revealed truths from human desires.
Study of art and literature is backward looking, to Ancient Greece or the Renaissance. The pinnacles reached in the past “actually increase the difficulty of fresh triumphs by rendering originality harder of attainment [p. 40].” Science builds on past successes, but not so art; indeed, civilization produces a sophistication that inhibits the sort of wide-eyed wonder that spurs artistic creativity. Artists cavil at the present, and their impulse for originality is reflected in a bizarre iconoclasm.
Since Galileo, we have had the scientific method at hand, and hence have a recipe for generating progress that is not available to artists. We do not need a person of genius to produce every advance in science, though artistic breakthroughs require such prodigies. Those who contribute most to science are those who develop a new method, though many of the valuable discoveries will subsequently be made by others who apply the method.
Beyond the individual methods is the more general scientific method, which “includes deduction as much as induction, logic and mathematics as much as botany and geology [p. 42].” This method develops from an outlook which understands that the world is what it is, irrespective of how we might wish it to be. Though such an outlook might seem to be the obvious one to adopt, in practice it has proven hard to inculcate. Aristotle thought that the stars move in circles because he viewed the circle as the most perfect of curves – and thereby let his preferences decide questions of fact. Malthus, who wrote post-Galileo, did better: his mistaken population theory derived from a dispassionate view of people as creatures exhibiting consistent behaviors that would bring certain consequences. Darwin, inspired by Malthus, has helped to cement the scientific approach to the study of man.
Philosophy remains rather unscientific, even if philosophers like to deploy scientific terms. The scientific approach requires the abjuration of feelings or anything else that impedes the search for truth, for a view of reality untarnished by preconceptions or hopes. Our attachment to rationality and desire for progress should not, on its own, lead us to believe that the universe coheres with our logic and improves (or deteriorates) over time. Our hopes and fears limit the potential for philosophy.
The desire to build something lasting can be satisfied more intensely in science than in poetry. Our curiosity can realize the payoff of new knowledge when deployed in a scientific manner – it broadens and depersonalizes our interests, promoting our wellbeing. A scientist who makes a new discovery receives the additional satisfaction of public admiration and the knowledge that society has been benefitted. “A life devoted to science is therefore a happy life, and its happiness is derived from the very best sources that are open to dwellers on this troubled and passionate planet [p. 45].”
Monday, July 31, 2017
Mysticism and Logic, Chapter I, second part
The second numbered section (pages 18-21) of “Mysticism and Logic” is titled “Unity and Plurality.” (The first section, which began on page 12, was “Reason and Intuition.”) Section II is followed by section III, “Time,” pages 21-26, and Section IV, “Good and Evil,” pages 26-32.
Beginning with Parmenides, a mystical turn in philosophy has been to emphasize the inherent oneness, the unity of all things. The differences that we sense are apparent, not real. There are moods that seem to predispose us to believing in the deception of appearances and the existence of a separate reality, and this belief is based not on logic, but on revelation. After the mood passes, we look for logical reasons to buttress our belief in the higher unity. The logic that is produced is faulty, purpose-built to generate the called-for paradoxes, and makes philosophers unable to speak with authority on either science or quotidian existence. Nonetheless, philosophers who never experienced the seminal (but misleading) moment of insight nevertheless adopted the resulting mis-logic, and remain unperturbed by the gulf between their logic and science. They choose to read Nature with contradiction as their motive, with the aim of verifying that all is illusion.
The mystically-inspired contention of the unreality of time is the subject of Section III (“Time”). And there surely is some sense in the notion that the differences between past, present, and future are superficial. “The importance of time is rather practical than theoretical, rather in relation to our desires than in relation to truth [p. 21].” The recognition of the larger “unimportance of time is the gate to wisdom [p. 22].”
We differentiate the past from the future because we have some control over the future, but not the past. All pasts were, previously, futures, and all futures will become pasts, so the difference between past and future arises in their relations to us. From an impartial or disinterested viewpoint – the viewpoint of wisdom – past and future are indistinguishable. [Recall the phrase of Henry Sidgwick, reconstructed by Katarzyna de Lazari-Radek and Peter Singer as “The Point of View of the Universe.” – RBR] This notion is contrary to systems of philosophy, sometimes drawing upon evolution, that are based on notions of progress, of some built-in improvement over time: Nietzsche, Bergson, and pragmatism provide examples.
Evolution and astronomy have rendered humans as less special, less distinct from other animals. Species are not fixed, nor are planets and suns. But philosophers were able to reassert human exceptionalism through claims of evolutionary advance, the progression from amoebas to man. Not every thinker can accept a fixed ideal, however – they need the goal to change along the path, so that there is no end point, and the rules or truths which characterize any finite time stream do not apply along the rest of the eternal river. Nonetheless, there remains an implicit assumption that the stream that heads towards the future also constitutes progress.
Evolutionary philosophies, by incorporating progress as a necessary component of change, depart from the disinterested approach that science requires. Knowledge of the future cannot be achieved on the cheap through philosophical speculation; when it is the type of knowledge that falls within the boundaries of other sciences, it must meet the standards of those sciences.
To possess its own ambit, philosophy must aim at knowledge that cannot be achieved by other sciences. Evolutionary philosophies with their underpinnings in progress make a despot of their considerations of time, as they abjure impartiality at the outset. Avoiding this misstep does not mean that the reality of time must be denied; nevertheless, the motive that leads to such denials, the recognition that past, present, and future have symmetric connections to reality, is worth preserving – though it is a recognition contrary to the approach of the evolutionary philosophies.
Section IV (pages 26-32), “Good and Evil,” opens by noting that the mystical approach to philosophy tends to identify two types of “good” – Russell references Heraclitus and Spinoza as examples. Our everyday conception of good and evil, in this view, is our own imposition upon the misleading appearances of this world, not a feature of reality. The actual, higher reality, cannot help but to be good. “It is difficult to give a logically tenable account of this position without recognising that good and evil are subjective, that what is good is merely that towards which we have one kind of feeling, and what is evil is merely that towards which we have another kind of feeling [p. 27].”
In our active life, we must make distinctions between better and worse actions. But as a matter of disinterested speculation, we can see the unity of good and evil. The mystics must go farther still, however, and view the world in its entirety as a blessed thing – Russell quotes Wordsworth without attribution.
In terms of happiness, the ability to see the good in everything is valuable. The mystical stance helps us to see the potential for a nobler life; what it cannot do, however, is to provide us any general truths about the universe as a whole.
Earlier we saw how evolutionary philosophies end up in a slavish relationship with time, through the assumption of progress. Likewise, they cut themselves off from the “reality is wholly good” notion, given their conception of inferior states giving way to better ones.
Many of the greatest philosophers and religious figures put substantial focus on good and evil. Nevertheless, philosophy should be shorn of ethical considerations – it is the scientific and the ethical approach to take!
We might like to believe that the world possesses desirable ethical characteristics, but philosophy’s role is not to cater to that hope. Love and hate are quite analogous from the point of view of philosophy, as attitudes that we possess towards things, though their differences are fundamental for psychology. Philosophers might find inspiration in their work through ethical considerations, but they must leave those considerations behind when they engage in their scientific speculations. Note how modern biologists or chemists are not expected to prove the high ethical quality of their discoveries. Astronomy developed out of astrology, which was motivated to look for the influence of heavenly bodies on human affairs. Once “the apathy of the stars” was established, many people lost their interest in astronomy. Even the advance of the science of psychology requires an ethically neutral stance.
Most philosophers have not sought to be ethically neutral. People make intellectual speculations that are in accord with what they want to believe. But seeking the good, like seeking happiness, might be self-defeating: seeking the facts is more likely to promote good than is hoping to uncover evidence of the ubiquity or inevitability of the good. This is the sense in which a disinterested approach to philosophy is more ethically sound than imposing one’s preconceptions of good and evil on reality. Note how common it is in religion to promote the recognition of the weakness of human action. Adopting a disinterested approach to speculation reflects a similar submission in the realm of thought, but philosophy’s advances have resulted from such submission.
“The good which it concerns us to remember is the good which it lies in our power to create – the good in our own lives and in our attitude towards the world [p. 31].” We compromise this achievable good when we devote ourselves to forcing the world to fit a procrustean vision of the good, one that does not comport with facts.
Scientific philosophy is the pinnacle of human thought, bringing us the closest to understanding reality. For primitive people, everything is met with liking or hostility. Philosophers go the furthest when they jettison such judgments; evolutionary philosophy, by embracing an interested approach, is hampered from the outset. Let us instead eschew the flattery of our hopes, and accept the world as it is.
Beginning with Parmenides, a mystical turn in philosophy has been to emphasize the inherent oneness, the unity of all things. The differences that we sense are apparent, not real. There are moods that seem to predispose us to believing in the deception of appearances and the existence of a separate reality, and this belief is based not on logic, but on revelation. After the mood passes, we look for logical reasons to buttress our belief in the higher unity. The logic that is produced is faulty, purpose-built to generate the called-for paradoxes, and makes philosophers unable to speak with authority on either science or quotidian existence. Nonetheless, philosophers who never experienced the seminal (but misleading) moment of insight nevertheless adopted the resulting mis-logic, and remain unperturbed by the gulf between their logic and science. They choose to read Nature with contradiction as their motive, with the aim of verifying that all is illusion.
The mystically-inspired contention of the unreality of time is the subject of Section III (“Time”). And there surely is some sense in the notion that the differences between past, present, and future are superficial. “The importance of time is rather practical than theoretical, rather in relation to our desires than in relation to truth [p. 21].” The recognition of the larger “unimportance of time is the gate to wisdom [p. 22].”
We differentiate the past from the future because we have some control over the future, but not the past. All pasts were, previously, futures, and all futures will become pasts, so the difference between past and future arises in their relations to us. From an impartial or disinterested viewpoint – the viewpoint of wisdom – past and future are indistinguishable. [Recall the phrase of Henry Sidgwick, reconstructed by Katarzyna de Lazari-Radek and Peter Singer as “The Point of View of the Universe.” – RBR] This notion is contrary to systems of philosophy, sometimes drawing upon evolution, that are based on notions of progress, of some built-in improvement over time: Nietzsche, Bergson, and pragmatism provide examples.
Evolution and astronomy have rendered humans as less special, less distinct from other animals. Species are not fixed, nor are planets and suns. But philosophers were able to reassert human exceptionalism through claims of evolutionary advance, the progression from amoebas to man. Not every thinker can accept a fixed ideal, however – they need the goal to change along the path, so that there is no end point, and the rules or truths which characterize any finite time stream do not apply along the rest of the eternal river. Nonetheless, there remains an implicit assumption that the stream that heads towards the future also constitutes progress.
Evolutionary philosophies, by incorporating progress as a necessary component of change, depart from the disinterested approach that science requires. Knowledge of the future cannot be achieved on the cheap through philosophical speculation; when it is the type of knowledge that falls within the boundaries of other sciences, it must meet the standards of those sciences.
To possess its own ambit, philosophy must aim at knowledge that cannot be achieved by other sciences. Evolutionary philosophies with their underpinnings in progress make a despot of their considerations of time, as they abjure impartiality at the outset. Avoiding this misstep does not mean that the reality of time must be denied; nevertheless, the motive that leads to such denials, the recognition that past, present, and future have symmetric connections to reality, is worth preserving – though it is a recognition contrary to the approach of the evolutionary philosophies.
Section IV (pages 26-32), “Good and Evil,” opens by noting that the mystical approach to philosophy tends to identify two types of “good” – Russell references Heraclitus and Spinoza as examples. Our everyday conception of good and evil, in this view, is our own imposition upon the misleading appearances of this world, not a feature of reality. The actual, higher reality, cannot help but to be good. “It is difficult to give a logically tenable account of this position without recognising that good and evil are subjective, that what is good is merely that towards which we have one kind of feeling, and what is evil is merely that towards which we have another kind of feeling [p. 27].”
In our active life, we must make distinctions between better and worse actions. But as a matter of disinterested speculation, we can see the unity of good and evil. The mystics must go farther still, however, and view the world in its entirety as a blessed thing – Russell quotes Wordsworth without attribution.
In terms of happiness, the ability to see the good in everything is valuable. The mystical stance helps us to see the potential for a nobler life; what it cannot do, however, is to provide us any general truths about the universe as a whole.
Earlier we saw how evolutionary philosophies end up in a slavish relationship with time, through the assumption of progress. Likewise, they cut themselves off from the “reality is wholly good” notion, given their conception of inferior states giving way to better ones.
Many of the greatest philosophers and religious figures put substantial focus on good and evil. Nevertheless, philosophy should be shorn of ethical considerations – it is the scientific and the ethical approach to take!
We might like to believe that the world possesses desirable ethical characteristics, but philosophy’s role is not to cater to that hope. Love and hate are quite analogous from the point of view of philosophy, as attitudes that we possess towards things, though their differences are fundamental for psychology. Philosophers might find inspiration in their work through ethical considerations, but they must leave those considerations behind when they engage in their scientific speculations. Note how modern biologists or chemists are not expected to prove the high ethical quality of their discoveries. Astronomy developed out of astrology, which was motivated to look for the influence of heavenly bodies on human affairs. Once “the apathy of the stars” was established, many people lost their interest in astronomy. Even the advance of the science of psychology requires an ethically neutral stance.
Most philosophers have not sought to be ethically neutral. People make intellectual speculations that are in accord with what they want to believe. But seeking the good, like seeking happiness, might be self-defeating: seeking the facts is more likely to promote good than is hoping to uncover evidence of the ubiquity or inevitability of the good. This is the sense in which a disinterested approach to philosophy is more ethically sound than imposing one’s preconceptions of good and evil on reality. Note how common it is in religion to promote the recognition of the weakness of human action. Adopting a disinterested approach to speculation reflects a similar submission in the realm of thought, but philosophy’s advances have resulted from such submission.
“The good which it concerns us to remember is the good which it lies in our power to create – the good in our own lives and in our attitude towards the world [p. 31].” We compromise this achievable good when we devote ourselves to forcing the world to fit a procrustean vision of the good, one that does not comport with facts.
Scientific philosophy is the pinnacle of human thought, bringing us the closest to understanding reality. For primitive people, everything is met with liking or hostility. Philosophers go the furthest when they jettison such judgments; evolutionary philosophy, by embracing an interested approach, is hampered from the outset. Let us instead eschew the flattery of our hopes, and accept the world as it is.
Tuesday, June 20, 2017
Mysticism and Logic, Chapter I, first part
"Mysticism and Logic," first part, pages 1-18
The first chapter in the book Mysticism and Logic and Other Essays is itself entitled "Mysticism and Logic;" I have elected to break its summentary into two posts on Reading Bertrand Russell, and this is the first of those posts.
An impulse towards mysticism and another impulse towards science together propel the development of philosophy. Hume was dominated by the scientific urge, Blake by the mystical one. The best of philosophers draw from both inspirations, and in the process metaphysics can appear superior to science or religion alone.
Consider Heraclitus, he of the “all is change” notion. The fragments of his thinking that come down to us are suggestive of a predominantly scientific, empirical, approach, though science has moved beyond Heraclitus’s specific claims. But even the “can’t step into the same river twice” trope has a more mystical version in Heraclitus: “’We step and do not step into the same rivers; we are and are not [p. 2].’” Mysticism reveals itself as “a certain intensity and depth of feeling in regard to what is believed about the universe [p. 3].” In Heraclitus, mystical statements often take on a rather moving quality [appropriately enough], sometimes via the assertion that opposites are, in fact, identical: “’To God all things are fair and good and right, but men hold some things wrong and some right [p.3].’”
Such refashioning of scientific facts through the application of an intense, emotional flame yields the utmost brilliance of which human thinkers are capable. We see it again in Plato, although at the end of the day, the mystical side takes precedence in Plato’s thought – as is evident in the parable of the cave in Plato’s Republic [which Russell quotes at length, pages 4-6]. The parable leads to Plato’s conflation of what is real with what is good, and this coerced identity harms the scientific search for reality as well as the philosophical investigation of ethics.
The scientific temperament receives better treatment elsewhere in Plato, such as when Parmenides advises young Socrates not to despise lowly things like dirt, when philosophizing about beauty and goodness. “It is with this impartial temper that the mystic’s apparent insight into a higher reality and a hidden good has to be combined if philosophy is to realise its greatest possibilities [p. 7].” But much philosophy ignores such a grounding (!) in reality, to its detriment.
Much modern mystical philosophy of the logical variety, such as that of Hegel, also draws upon roots in the thought of Parmenides. In particular, Parmenides claims that what can be spoken or thought of must exist, because one cannot think of a void, a non-entity. In this sense change is impossible, as the past must still exist.
The mystical approach privileges flashes of insight over patient, analytic thought; it leaps from the sensed unreality of the quotidian world – a phenomenon that is quite common – to a trust that phantasms of the brain are more real, constitute a deeper reality. Mystics, like poets, give to airy nothing a local habitation and a name.
“The mystic insight begins with the sense of a mystery unveiled, of a hidden wisdom now suddenly become certain beyond the possibility of a doubt [p. 9].” It is the certainty, and not the whole array of beliefs, that is central to the approach. But some beliefs are shared by all mystics, including the belief that insight trumps reason, and that appearances do not capture actual reality. Artists, poets, and lovers can glimpse that reality, but the mystic takes in the entire panorama. Mystics also share a belief in an underlying unity, and hence are led to claims of the type that “A” and “not A” are identical. A common corollary is that time is unreal, that past, present, and future are of a piece.
Finally, mystics are prone to believe that evil (and sometimes good) is an appearance, not part of the deeper reality. The unity that mystics sense (or profess to know) lends an acceptance to all appearances, an attitude of peace and contentment.
So the mystical mindset presents four questions: (1) are reason and intuition two separate paths to knowledge, and is one of these paths privileged?; (2) are differences and distinctions unreal, camouflaging a deeper unity?; (3) “[i]s time unreal? [p. 11];” and, (4) what is the nature of the reality of good and evil? The mystical answers to these questions are incorrect, but nevertheless the mystical approach does offer some value that is otherwise inaccessible. “If this is the truth, mysticism is to be commended as an attitude towards life, not as a creed about the world [p. 11].” Mysticism’s emotional framework leads not to truth, but does lend itself to inspiration and intensification in life. “Even the cautious and patient investigation of truth by science, which seems the very antithesis of the mystic’s swift certainty, may be fostered and nourished by that very spirit of reverence in which mysticism lives and moves [p. 12].”
[Russell now (page 12) introduces section I (“Reason and Intuition”), informing us in a footnote that this section and some later paragraphs were previously printed in Our Knowledge of the External World, 1914. Recall that this current RBR post provides a summentary of Chapter I only through the end of section I, with an ensuing post picking up the remainder of the chapter.]
The flash of insight that mystics experience is no guarantee of the truth of their revelation – even though many advances have their genesis in such a vision. Reason and instinct (or intuition) needn’t be opposed, as a cursory view of the Enlightenment versus the Romantic movement might suggest. Instinct or intuition provides hypotheses which reason then can test. “Reason is a harmonizing, controlling force rather than a creative one [p. 13].”
Instinct leads us astray when it causes us doggedly to hold onto beliefs that are inconsistent with what else we know. Instinct is pretty discerning when it makes us wary of others, for instance, without being able to articulate our concerns. Reason can help us discard those instinctual beliefs that cannot stand up to scrutiny. Contra Bergson (an intuitionist), both intuition and reason have evolved because of their usefulness to survival. Either reason or intuition can become harmful when the guides they give us diverge from truth. It seems that older and more educated humans rely less on intuition than their younger or less educated brethren, and less than dogs do, too. The primacy of intuition might be fine for savage forest dwellers, but doesn’t serve us well in civilized society.
Intuition isn’t even reliable in bringing self-awareness; in fact, it is notoriously unreliable. But intuitive beliefs are held with unwarranted certitude. Nor do novel situations require intuition – though they do require the senses to collect the new information. Generally it is intellect that is best situated to process that information in a useful way. Intuition develops to handle customary situations, and becomes more unreliable in unfamiliar environments.
Intuition is not helpful for highly civilized pursuits such as philosophy; rather, its comparative advantage lies in ancient concerns that we share with non-human animals. “In such matters as self-preservation and love, intuition will act sometimes (though not always) with a swiftness and precision which are astonishing to the critical intellect [p. 17].” In philosophy especially, we must beware of sudden, supposedly deep (but unanalyzed) insights. Taking a disinterested, encompassing view of matters philosophical is the scientific method, but also corresponds in approach – though often not in ultimate conclusions – to the remote mindset that many religions advocate. The animating spirit of mysticism counsels for a scientific approach to knowledge.
The first chapter in the book Mysticism and Logic and Other Essays is itself entitled "Mysticism and Logic;" I have elected to break its summentary into two posts on Reading Bertrand Russell, and this is the first of those posts.
An impulse towards mysticism and another impulse towards science together propel the development of philosophy. Hume was dominated by the scientific urge, Blake by the mystical one. The best of philosophers draw from both inspirations, and in the process metaphysics can appear superior to science or religion alone.
Consider Heraclitus, he of the “all is change” notion. The fragments of his thinking that come down to us are suggestive of a predominantly scientific, empirical, approach, though science has moved beyond Heraclitus’s specific claims. But even the “can’t step into the same river twice” trope has a more mystical version in Heraclitus: “’We step and do not step into the same rivers; we are and are not [p. 2].’” Mysticism reveals itself as “a certain intensity and depth of feeling in regard to what is believed about the universe [p. 3].” In Heraclitus, mystical statements often take on a rather moving quality [appropriately enough], sometimes via the assertion that opposites are, in fact, identical: “’To God all things are fair and good and right, but men hold some things wrong and some right [p.3].’”
Such refashioning of scientific facts through the application of an intense, emotional flame yields the utmost brilliance of which human thinkers are capable. We see it again in Plato, although at the end of the day, the mystical side takes precedence in Plato’s thought – as is evident in the parable of the cave in Plato’s Republic [which Russell quotes at length, pages 4-6]. The parable leads to Plato’s conflation of what is real with what is good, and this coerced identity harms the scientific search for reality as well as the philosophical investigation of ethics.
The scientific temperament receives better treatment elsewhere in Plato, such as when Parmenides advises young Socrates not to despise lowly things like dirt, when philosophizing about beauty and goodness. “It is with this impartial temper that the mystic’s apparent insight into a higher reality and a hidden good has to be combined if philosophy is to realise its greatest possibilities [p. 7].” But much philosophy ignores such a grounding (!) in reality, to its detriment.
Much modern mystical philosophy of the logical variety, such as that of Hegel, also draws upon roots in the thought of Parmenides. In particular, Parmenides claims that what can be spoken or thought of must exist, because one cannot think of a void, a non-entity. In this sense change is impossible, as the past must still exist.
The mystical approach privileges flashes of insight over patient, analytic thought; it leaps from the sensed unreality of the quotidian world – a phenomenon that is quite common – to a trust that phantasms of the brain are more real, constitute a deeper reality. Mystics, like poets, give to airy nothing a local habitation and a name.
“The mystic insight begins with the sense of a mystery unveiled, of a hidden wisdom now suddenly become certain beyond the possibility of a doubt [p. 9].” It is the certainty, and not the whole array of beliefs, that is central to the approach. But some beliefs are shared by all mystics, including the belief that insight trumps reason, and that appearances do not capture actual reality. Artists, poets, and lovers can glimpse that reality, but the mystic takes in the entire panorama. Mystics also share a belief in an underlying unity, and hence are led to claims of the type that “A” and “not A” are identical. A common corollary is that time is unreal, that past, present, and future are of a piece.
Finally, mystics are prone to believe that evil (and sometimes good) is an appearance, not part of the deeper reality. The unity that mystics sense (or profess to know) lends an acceptance to all appearances, an attitude of peace and contentment.
So the mystical mindset presents four questions: (1) are reason and intuition two separate paths to knowledge, and is one of these paths privileged?; (2) are differences and distinctions unreal, camouflaging a deeper unity?; (3) “[i]s time unreal? [p. 11];” and, (4) what is the nature of the reality of good and evil? The mystical answers to these questions are incorrect, but nevertheless the mystical approach does offer some value that is otherwise inaccessible. “If this is the truth, mysticism is to be commended as an attitude towards life, not as a creed about the world [p. 11].” Mysticism’s emotional framework leads not to truth, but does lend itself to inspiration and intensification in life. “Even the cautious and patient investigation of truth by science, which seems the very antithesis of the mystic’s swift certainty, may be fostered and nourished by that very spirit of reverence in which mysticism lives and moves [p. 12].”
[Russell now (page 12) introduces section I (“Reason and Intuition”), informing us in a footnote that this section and some later paragraphs were previously printed in Our Knowledge of the External World, 1914. Recall that this current RBR post provides a summentary of Chapter I only through the end of section I, with an ensuing post picking up the remainder of the chapter.]
The flash of insight that mystics experience is no guarantee of the truth of their revelation – even though many advances have their genesis in such a vision. Reason and instinct (or intuition) needn’t be opposed, as a cursory view of the Enlightenment versus the Romantic movement might suggest. Instinct or intuition provides hypotheses which reason then can test. “Reason is a harmonizing, controlling force rather than a creative one [p. 13].”
Instinct leads us astray when it causes us doggedly to hold onto beliefs that are inconsistent with what else we know. Instinct is pretty discerning when it makes us wary of others, for instance, without being able to articulate our concerns. Reason can help us discard those instinctual beliefs that cannot stand up to scrutiny. Contra Bergson (an intuitionist), both intuition and reason have evolved because of their usefulness to survival. Either reason or intuition can become harmful when the guides they give us diverge from truth. It seems that older and more educated humans rely less on intuition than their younger or less educated brethren, and less than dogs do, too. The primacy of intuition might be fine for savage forest dwellers, but doesn’t serve us well in civilized society.
Intuition isn’t even reliable in bringing self-awareness; in fact, it is notoriously unreliable. But intuitive beliefs are held with unwarranted certitude. Nor do novel situations require intuition – though they do require the senses to collect the new information. Generally it is intellect that is best situated to process that information in a useful way. Intuition develops to handle customary situations, and becomes more unreliable in unfamiliar environments.
Intuition is not helpful for highly civilized pursuits such as philosophy; rather, its comparative advantage lies in ancient concerns that we share with non-human animals. “In such matters as self-preservation and love, intuition will act sometimes (though not always) with a swiftness and precision which are astonishing to the critical intellect [p. 17].” In philosophy especially, we must beware of sudden, supposedly deep (but unanalyzed) insights. Taking a disinterested, encompassing view of matters philosophical is the scientific method, but also corresponds in approach – though often not in ultimate conclusions – to the remote mindset that many religions advocate. The animating spirit of mysticism counsels for a scientific approach to knowledge.
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