[The Mysticism and Logic Halftime report, on Chapters I through VI, is here; what follows in this post, the Full Time review, focuses on Chapters VII through X.]
I was snookered. When I embarked on Reading Bertrand Russell thirteen years ago (precisely today), I noted that my embryonic interest in Russell’s oeuvre did not extend to his serious philosophical and mathematical work: it is the public intellectual (and activist), not the professional philosopher/mathematician, that draws me to Russell. The first half of Mysticism and Logic lodged within my comfort zone, sometimes snugly and sometimes with a little effort. But starting in Chapter VII, sense-data and sensibilia and particulars and denotations came to the fore, and I found myself adrift. Having survived this (uh, three-year) storm, I now will go the full cognitive dissonance, and claim (as I believe) that the journey was worth the cost, and that I have emerged from the deluge somewhat cleaner – though ex ante, I might have preferred a hot (or even a cold) shower. (And ex post, I do not find myself running with undo haste towards Our Knowledge of the External World.)
Chapter VII ("The Ultimate Constituents of Matter") began intriguingly enough: object persistence is questionable, our senses are untrustworthy (of course), and a table is similar not to a trombone but to the role that a trombone plays in a symphony, where what is fundamental is the relationships among all the instruments. In the end, Russell provides a sort of dual view of physical objects, one perspective that is appropriate for physics, and a connected one that is appropriate for psychology, but where we need not fear that the psychological view can contaminate the physical view. Further, the psychological perspective challenges our commonsense notion of object permanence, and indicates that sense-data do not require a mind to have a physical presence.
Chapter VIII (“The Relation of Sense-Data to Physics”) doubles down on the abstruse philosophical investigation. The set-up is superb, obvious in retrospect but new to me: We directly experience sense-data, and from these data, and them alone, we attempt to make inferences about the external world. But as we only will ever directly experience the sense-data, we face a problem in knowing when our inferences are correct. What would be ideal would be to do away with inferences, to replace them with constructions – like mathematicians, starting from an imagined concept of irrational numbers, were able to replace (or fortify) their imaginings with a constructed version.
The road that Russell takes beyond the set-up of Chapter VIII is not an easy one, at least for me. It comes to some comfortable conclusions, however – when the appearance of an object changes because I squint, the object itself does not change. (Though if perspectives arbitrarily close to the object did change through squinting, then the object would change: objects are a sort of limit of a multitude of appearances that converge upon them. Squinting changes one appearance, but not the limit of the set of appearances.) Objects are physical, not simply matters of (potentially misleading) sense-data.
Hallucinations or dreams (or squinting?) that sever the usual connection between sense-data and objects present a problem, but one that Russell’s approach easily overcomes. As objects are collections of correlated appearances, the problem with hallucinations is not that the sense-data generating them are any less real, but that they lack the usual correlations with other appearances that characterize really-existing matter. Indeed, we need to compare the hallucinator’s reports with those of others before we realize that the hallucination is just that.
Having solved(?) the question of the nature of matter in chapters VII and VIII, Russell tackles causality in Chapter IX ("On the Notion of Cause"). And actually, the solutions are similar, resting on correlations – between appearances emanating from sense-data (or proto sense-data) in chapters VII and VIII, and between antecedents and effects in Chapter IX. These correlations are less than fully reliable, we can have intervening events undoing the usual connection between a “cause” and an “effect” (and, as noted, we can have hallucinations disconnecting one appearance from the usual object). Fortunately, the advance of science does not require any invariant cause-and-effect relationships. Philosophy, too, can thrive with less-than-assured, but time-tested, inductive causal relationships. Science itself essentially invokes a sort of inductive claim, that nature is largely uniform, so that relationships we see at one place or time are likely to exist at other places or times.
The question of the existence of free will is not answered by Russell’s discussion of causation. But Russell’s analysis does suggest that our feeling of the possession of free will is consistent with a deterministic system.
Chapter X ("Knowledge By Acquaintance and Knowledge By Description") applies to the realm of logic our lack of direct experience with everything other than sense data, again addressing the question of what we know. And once again, it is partly through somewhat exceptional cases (like those hallucinations or images produced by squinting) that Russell can test his ideas. Thus we meet “the present King of France [p. 225],” whose lack of existence does not hinder our ability to judge propositions that concern him. [Russell dwelt on the present King of France in multiple venues.] My suspicion is, much as I have struggled to make heads or tails out of Chapter X, that it has become pretty standard fare for mathematically sophisticated logicians.
Chapter X, like much of the second half of Mysticism and Logic, brought to my mind the stanza (number XXVII, it turns out) from the Fitzgerald translation of Omar Khayyam’s Rubaiyat, namely,
Myself when young did eagerly frequent
Doctor and Saint, and heard great Argument
About it and about: but evermore
Came out by the same Door as in I went.
I am OK with the door, it is a fine door – and maybe, though the door remains unchanged, I nonetheless have slightly been altered? [I recently learned that Russell once titled a book review that he wrote “The Same Door,” drawing on the identical stanza of the Rubaiyat; somehow, this has cheered me. Russell’s review appeared in 1919, one year after Mysticism and Logic.]
As I (or I 2.0) retreat out of the same door, I will, as always, take along some Russellian nuggets. One is Russell’s motivation (p. 129) to see his first movie: he wanted to test Bergson’s claim that mathematicians look at the world as a sort of film, where what appears to be a permanent object is really a series of closely connected instantaneous images. Also, not yet the third Earl Russell, Bertie slipped in a nice jibe at royalty, in talking about the unnecessary persistence of the law of causation, which survives “like the monarchy, only because it is erroneously believed to do no harm [p. 180].” And Bertie’s point (p. 102) that of course the known laws of nature are quite simple, because otherwise we wouldn’t know them, is surely right, though perhaps in danger of becoming less so: do big data and machine learning promise the uncovering of significantly more complex laws?
In many parts of Mysticism and Logic, I was reminded of Flatland, and the difficulties facing “someone” in a two dimensional space trying to understand three dimensions. Russell is aiming at something similar, to understand the universe while inside it, and only being able to access it through sense-data. (For what sounds to me like a compatible, more modern take, see this article in Quanta.) But I was also reminded of Flatland when thinking about my own situation, a non-philosopher trying to fully understand Mysticism and Logic! I fear I did better on the mysticism part. Happy 148th Birthday, Bertie.
Monday, May 18, 2020
Wednesday, March 25, 2020
Mysticism and Logic, Chapter X
“Knowledge By Acquaintance and Knowledge By Description,” pages 209-232
What if we know some general fact – the candidate with the most votes will win – without knowing who that candidate is? In such cases, what do we really know from the general description of the winner alone?
Being “acquainted” with something is to “have a direct cognitive relation [p. 209]” with it: in a sense, you have met that thing. “Acquaintance” requires both a subject (you) and an object (the thing) – but the object doesn’t have to be near at hand for you to maintain an acquaintance with it.
People are acquainted with their sense-data, like smells or sounds. (Sense-data have played a major role in the later stages of Mysticism and Logic, beginning in Chapter VII.) A sense-datum can itself be rather complex, with multiple parts connected spatially.
In this regard, consider consciousness. We can be aware of some object we see or some desire we have, while simultaneously being aware that it is us who is seeing the object or having the desire. But can we be aware of ourselves in isolation, without a connection to other elements of awareness? To return to our previous terminology, we are acquainted with the dual construct “Self-acquainted with A” (like “self aware of some object”) but also know “I am acquainted with A”. But what of this “I”? Is it known only by description – like being ‘the subject-term in awarenesses of which I am aware [p. 212]’ – or as a direct acquaintance? (So much for the consciousness detour.)
Awareness of sense-data is an example of awareness of particulars; we can also be aware of concepts more general, universals. For instance, we can be aware of many particular shades of yellow, but also aware of the concept of yellow, a universal. Statements such as “yellow is different from blue” are meaningful – we can be aware of the difference between yellow and blue, the relation of these two universals. And because we can aptly deduce from a few cases (A before B and B before C implies A before C), we must be able to know the universal relation “before” beyond just knowing some cases.
OK, we are aware of particulars (this and that, and properties (yellow) of this or that, and relations between them, this before that) and of universals. All non-particular objects are universals. The particular/universal dichotomy is akin to concrete/abstract.
While we are acquainted with sense-data, we are not acquainted with physical objects or with the minds of others. These we know by description, not by acquaintance. These descriptions can be definite (“the” object) or ambiguous (“an” object).
[Russell then (page 214) constrains himself to speaking of definite descriptions.] What if we know that there is an object that fits a definite description, but we are not acquainted with any such object? What is the nature of our knowledge? We know there was a man in the iron mask, though we don’t know his identity. We do not know who will get the most votes even though we know that the winner will be the person who receives the most votes: we have “'merely descriptive knowledge [page 215].'”
Someone who knew Bismarck (but was not Bismarck) is acquainted with sense data about Bismarck’s body and mind, but the body and mind themselves are known only by description, as reflecting the sense data. One might have various descriptions of Bismarck, but they all refer to the same person. For those who do not know Bismarck, our descriptions of him are presumably some bits of historical knowledge, such as “’the first Chancellor of the German Empire [p. 217].’” These predominantly abstract words, if we are to be sure we are dealing with an accurate description of Bismarck that allows us to form some judgment, must eventually be connected with “a particular with which we are acquainted [p. 217]”. If we claim that this first German Chancellor was gifted in diplomacy, we can only be confident in our claim if we reference some sort of testimony or related particular we are acquainted with. (Bismarck’s diplomatic acuity we can know to be true, even though we are not directly acquainted with him, and thus don’t know the proposition concerning his skill. That is, we communicate with propositions that we can know to be true without being acquainted with the proposition.) Place names like London or the solar system similarly implicate acquainted particulars. But logic applies to things beyond the actual existing, and requires no connection to specific particulars.
“The fundamental epistemological principle in the analysis of propositions containing descriptions is this: Every proposition which we can understand must be composed wholly of constituents with which we are acquainted [p. 219].” [Russell goes on to support this principle, citing his own Philosophical Essays and endorsing (though without threatening the principle) a criticism lodged by Wittgenstein. How can we make a judgment without knowledge of what it is we are judging? Russell also dismisses the notion that we don’t know objects of judgments such as Julius Caesar, but only know some abstract mental idea of Caesar. This (misguided) notion, he believes, leads to the view that we never know something, only ideas about something – but why not go further, and say that we only know ideas of those ideas, ad infinitum?]
“Meaning” and “denotation” frequently are distinguished; for instance, in the phrase “featherless bipeds,” the denotation is humans, though the meaning is more complex. A statement such as “’men are the same as featherless bipeds [p. 224]’” (implicitly) presents an assertion that the denotations are the same. But Russell claims that actual propositions do not concern denotations, excepting the case of proper names. We can know the truth of a proposition without being acquainted with the denotation. [Russell is well known for his work on denotation, and some of his previous efforts he follows here.]
Consider (p. 226) the phrase “Scott is Sir Walter” – these are two names for the same person. But if Sir Walter Scott often was called “the author of Waverley,” that would not make him the author – the author of Waverley is whoever wrote Waverley. The authorship is a fact that goes beyond mere names. [Russell, getting into what for me are deep philosophical weeds, cites (p. 228n) a fuller discussion in Volume I of Principia Mathematica.]
These developments allow the denotation of a phrase like “the author of Waverley” to be defined. “If we know that the proposition ‘a is the so-and-so’ is true, we call a the denotation of the phrase ‘the so-and-so’ [p. 229].” When we assert a proposition about “the so-and-so,” its truth or falsity generally can be assessed by checking its truth with respect to a. This useful feature of denotations hinders a proper logical understanding, as it leads us to mistake the denotation for the description, and to believe (again, incorrectly) that propositions concern denotations: to understand propositions, “we need acquaintance with the constituents of the description, but do not need acquaintance with its denotation [p. 230].”
To recapitulate: Knowledge by acquaintance can be distinguished from knowledge by description. It is sense-data, universals, and possibly ourselves with which acquaintance exists – we are not acquainted with other people and objects. We can have descriptive knowledge of an object, say, if we know that it is the sole object having a property (or properties) with which we are acquainted (page 231). Propositions that we can understand must only directly relate to things we are acquainted with. A judgment (connected to a mind) must also concern only objects of acquaintance to that mind. Thus when we see descriptive phrases in propositions, “the objects denoted by such phrases are not constituents of judgments in which such phrases occur (unless these objects are explicitly mentioned) [p. 231-232].” When we assert the proposition that the author of Waverley is the same as the author of Marmion, Sir Walter Scott plays no role in our judgment of that proposition.
[End Matter: My copy of Mysticism and Logic proper ends on p. 232, but there are some more printed pages: two pages of Index; a page with the elaborate St. George-slaying-dragon emblem of the publisher (George Allen & Unwin); and five pages advertising fifteen other books by Russell for sale, with prices – the “Fifth Impression” of Marriage and Morals, for instance, apparently can be had for 8s. 6d.
What if we know some general fact – the candidate with the most votes will win – without knowing who that candidate is? In such cases, what do we really know from the general description of the winner alone?
Being “acquainted” with something is to “have a direct cognitive relation [p. 209]” with it: in a sense, you have met that thing. “Acquaintance” requires both a subject (you) and an object (the thing) – but the object doesn’t have to be near at hand for you to maintain an acquaintance with it.
People are acquainted with their sense-data, like smells or sounds. (Sense-data have played a major role in the later stages of Mysticism and Logic, beginning in Chapter VII.) A sense-datum can itself be rather complex, with multiple parts connected spatially.
In this regard, consider consciousness. We can be aware of some object we see or some desire we have, while simultaneously being aware that it is us who is seeing the object or having the desire. But can we be aware of ourselves in isolation, without a connection to other elements of awareness? To return to our previous terminology, we are acquainted with the dual construct “Self-acquainted with A” (like “self aware of some object”) but also know “I am acquainted with A”. But what of this “I”? Is it known only by description – like being ‘the subject-term in awarenesses of which I am aware [p. 212]’ – or as a direct acquaintance? (So much for the consciousness detour.)
Awareness of sense-data is an example of awareness of particulars; we can also be aware of concepts more general, universals. For instance, we can be aware of many particular shades of yellow, but also aware of the concept of yellow, a universal. Statements such as “yellow is different from blue” are meaningful – we can be aware of the difference between yellow and blue, the relation of these two universals. And because we can aptly deduce from a few cases (A before B and B before C implies A before C), we must be able to know the universal relation “before” beyond just knowing some cases.
OK, we are aware of particulars (this and that, and properties (yellow) of this or that, and relations between them, this before that) and of universals. All non-particular objects are universals. The particular/universal dichotomy is akin to concrete/abstract.
While we are acquainted with sense-data, we are not acquainted with physical objects or with the minds of others. These we know by description, not by acquaintance. These descriptions can be definite (“the” object) or ambiguous (“an” object).
[Russell then (page 214) constrains himself to speaking of definite descriptions.] What if we know that there is an object that fits a definite description, but we are not acquainted with any such object? What is the nature of our knowledge? We know there was a man in the iron mask, though we don’t know his identity. We do not know who will get the most votes even though we know that the winner will be the person who receives the most votes: we have “'merely descriptive knowledge [page 215].'”
Someone who knew Bismarck (but was not Bismarck) is acquainted with sense data about Bismarck’s body and mind, but the body and mind themselves are known only by description, as reflecting the sense data. One might have various descriptions of Bismarck, but they all refer to the same person. For those who do not know Bismarck, our descriptions of him are presumably some bits of historical knowledge, such as “’the first Chancellor of the German Empire [p. 217].’” These predominantly abstract words, if we are to be sure we are dealing with an accurate description of Bismarck that allows us to form some judgment, must eventually be connected with “a particular with which we are acquainted [p. 217]”. If we claim that this first German Chancellor was gifted in diplomacy, we can only be confident in our claim if we reference some sort of testimony or related particular we are acquainted with. (Bismarck’s diplomatic acuity we can know to be true, even though we are not directly acquainted with him, and thus don’t know the proposition concerning his skill. That is, we communicate with propositions that we can know to be true without being acquainted with the proposition.) Place names like London or the solar system similarly implicate acquainted particulars. But logic applies to things beyond the actual existing, and requires no connection to specific particulars.
“The fundamental epistemological principle in the analysis of propositions containing descriptions is this: Every proposition which we can understand must be composed wholly of constituents with which we are acquainted [p. 219].” [Russell goes on to support this principle, citing his own Philosophical Essays and endorsing (though without threatening the principle) a criticism lodged by Wittgenstein. How can we make a judgment without knowledge of what it is we are judging? Russell also dismisses the notion that we don’t know objects of judgments such as Julius Caesar, but only know some abstract mental idea of Caesar. This (misguided) notion, he believes, leads to the view that we never know something, only ideas about something – but why not go further, and say that we only know ideas of those ideas, ad infinitum?]
“Meaning” and “denotation” frequently are distinguished; for instance, in the phrase “featherless bipeds,” the denotation is humans, though the meaning is more complex. A statement such as “’men are the same as featherless bipeds [p. 224]’” (implicitly) presents an assertion that the denotations are the same. But Russell claims that actual propositions do not concern denotations, excepting the case of proper names. We can know the truth of a proposition without being acquainted with the denotation. [Russell is well known for his work on denotation, and some of his previous efforts he follows here.]
Consider (p. 226) the phrase “Scott is Sir Walter” – these are two names for the same person. But if Sir Walter Scott often was called “the author of Waverley,” that would not make him the author – the author of Waverley is whoever wrote Waverley. The authorship is a fact that goes beyond mere names. [Russell, getting into what for me are deep philosophical weeds, cites (p. 228n) a fuller discussion in Volume I of Principia Mathematica.]
These developments allow the denotation of a phrase like “the author of Waverley” to be defined. “If we know that the proposition ‘a is the so-and-so’ is true, we call a the denotation of the phrase ‘the so-and-so’ [p. 229].” When we assert a proposition about “the so-and-so,” its truth or falsity generally can be assessed by checking its truth with respect to a. This useful feature of denotations hinders a proper logical understanding, as it leads us to mistake the denotation for the description, and to believe (again, incorrectly) that propositions concern denotations: to understand propositions, “we need acquaintance with the constituents of the description, but do not need acquaintance with its denotation [p. 230].”
To recapitulate: Knowledge by acquaintance can be distinguished from knowledge by description. It is sense-data, universals, and possibly ourselves with which acquaintance exists – we are not acquainted with other people and objects. We can have descriptive knowledge of an object, say, if we know that it is the sole object having a property (or properties) with which we are acquainted (page 231). Propositions that we can understand must only directly relate to things we are acquainted with. A judgment (connected to a mind) must also concern only objects of acquaintance to that mind. Thus when we see descriptive phrases in propositions, “the objects denoted by such phrases are not constituents of judgments in which such phrases occur (unless these objects are explicitly mentioned) [p. 231-232].” When we assert the proposition that the author of Waverley is the same as the author of Marmion, Sir Walter Scott plays no role in our judgment of that proposition.
[End Matter: My copy of Mysticism and Logic proper ends on p. 232, but there are some more printed pages: two pages of Index; a page with the elaborate St. George-slaying-dragon emblem of the publisher (George Allen & Unwin); and five pages advertising fifteen other books by Russell for sale, with prices – the “Fifth Impression” of Marriage and Morals, for instance, apparently can be had for 8s. 6d.
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Sunday, February 2, 2020
Mysticism and Logic, Chapter IX
"On the Notion of Cause," pages 180-208
[Posted on the fiftieth anniversary of Bertrand Russell's death, February 2, 2020.] This chapter addresses some confusions around the notion of “cause” as used by philosophers – confusions that are substantial enough that it would be best if the term were avoided. The misunderstanding of causality leads to other mistaken notions. And though philosophers are confused about the “law of causation,” what does science actually employ in its stead?
Many sciences never talk of causation, even though philosophers assert its fundamental nature to science. But perhaps the lack of talk about causes in physics, for instance, isn’t dereliction of duty, but recognition of the absence of causes. The law of causation is outdated, and survives “like the monarchy, only because it is erroneously believed to do no harm [p. 180].”
Russell examines dictionary definitions of “causality” and related words, leading to the distinction between a propositional function (“x is a number”) and a proposition (3 is a number). Propositions are either true or false, but propositional functions can sometimes be true (for some values of x, say), and sometimes false. This line of reasoning suggests that something is necessary if it is the “predicate” of a propositional function, which means that the statement is true for all possible values of its argument.
Eventually, Russell avers that causality (event e2 is caused by event e1, say) is when, for any event e1 that occurs, within some interval of time τ, event e2 occurs. (Variations of this definition have been provided by John Stuart Mill and by Henri Bergson.) Some alternative definitions suffer from circularity or from not limiting the time between cause and effect.
To examine the definition and explore its applicability or inapplicability to science, Russell puts aside (for now) the problem of multiple causes, to focus instead on the meaning of “event,” and on the length of time separating cause from effect.
If we define an event too narrowly, then we will never again see its exact match in the future, and so the notion of causation would lose all purchase. “An ‘event,’ then, is a universal defined sufficiently widely to admit of many particular occurrences in time being instances of it [p. 187].”
The effect cannot take place at the same instant of time, nor immediately afterwards, thanks to the lack of infinitesimal time intervals – so, there must be some finite passage of time twixt cause and effect. As soon as we allow for such a time lapse, however, it becomes possible that in that interval, an intervening event (a meteorite strikes?) changes conditions sufficiently that the proposed “effect” will not occur. But this in turn means that the proposed cause is not itself sufficient to ensure the effect. Were we to start adding the state of the environment into our cause, we end up draining our cause-and-effect claim of any applicability, through the previously noted problem with excessive narrowness.
Despite our difficulties with explicitly expressing the logic of cause and effect, in our quotidian lives, there are many reliable “regularities of sequence [p. 187].” Some of them may be completely dependable, and even less dependable correlations can spur scientific advances. But science pursues or requires no “law” of cause and effect, it does not assume that there is an invariant causal relationship out there waiting to be discovered. As sciences advance, our old causal claims become more nuanced, with finer partitions of antecedents and consequences. When the antecedents are finely enough delineated that we are certain of the consequences, they are also fine enough that they will not occur again, that there is no predictive value to the causal relationship.
Philosophy has been riddled with misconceptions around causation. One is that causes and effects have to be similar, so that mental processes, for instance, could not arise from inert matter alone. Another [Russell enumerates five – RBR] is connected to free will, the notion that causes cannot make someone do something that they do not desire to do. But these desires themselves might be “caused,” even if there is free will in the sense of only doing what is desired.
What is left when philosophy abandons any putative law of cause and effect? Accept for the nonce the logic of induction, that when we have a long series of cases where a “cause” is followed by an “effect,” then this relationship is quite likely to hold in similar future cases. These series that spark induction, however, speak to likelihoods, not necessary consequences, with respect to future observations. The inductive cause-and-effect might lead us to claim that striking a match causes the match to ignite, but we will find that striking a wet match will still not do so. Nor does the inductive approach suggest that every event has some cause. And it seems to be overly inclusive, supporting the claim that night causes day, but we will not back away from accepting that in the sense we are now discussing, night does cause day. The rules we get from the inductive approach can always fail in the next observation, without violating any scientific law.
As science progresses, we tend to move away from cause and effect claims. Gravity involves rules that masses follow, but we cannot isolate one aspect of gravitational forces as causes and others as effects. The correct formulation is mathematical, a stability in the differential equations that characterize the system. But this is hardly some a priori rule of science, as some philosophers expect from their “law of cause and effect.”
Note also that in physics, the complete state at an instant not only determines the future, but the past. There is no temporal priority that makes earlier things causes of later things, and not the other way around.
While science does not stipulate any law of causality, it does accept, in the background, a certain uniformity of nature. Functions that have characterized relationships in the past are expected (inductively) to hold in the future, and if they do not hold, there is some more general law, capturing both sets of data, that does hold. As with other inductive arguments, this uniformity assertion is only likely, not certain, to hold. And if it prove false with respect to some scientific “law,” the rest of science is not thereby invalidated.
The effects of gravitation within the solar system depend, though minutely, on matter that lies outside of the solar system. As we have little knowledge of that matter, we cannot fully verify gravitational theory. But we can be very confident of our claims about gravity within the solar system anyway, irrespective of what is going on in the rest of the universe. The solar system, with respect to gravitation and over a given time period, is a “‘relatively isolated system [p. 197],’” where it will behave in a uniform manner (approximately) during that time period, no matter what is happening elsewhere. A system is “’practically isolated [p. 198]’” if, though there might be some outside situations that would lead relative isolation to fail, we rightly suspect that those situations do not arise. When it comes to falling bodies, the earth is relatively isolated, but it is not isolated with respect to tides.
It is evidence, not a priori reasoning, that leads us to believe some systems are relatively or practically isolated. “The case where one event A is said to ‘cause’ another event B, which philosophers take as fundamental, is really only the most simplified instance of a practically isolated system [p. 198].” The fact that A is always followed by B is true thanks to the relative unimportance, in this case and for this time, of what is going on in the rest of the universe. The (unknown) laws of the universe could still hold but produce instances where A is not followed by B.
Causality is the reed upon which people make out-of-sample inferences. If these inferences are legitimate, the system is deterministic. A non-deterministic system is capricious (p. 199).
Brains are part of the universe. It seems that there is a one-to-one mapping between states of one person’s brain and states of the universe. Assume also that there is a one-to-one relationship between the state of a mind and the state of the corresponding brain. This leads to the notion that there is a one-to-one mapping between a mind and the state of the universe. Whatever (sub)set of states determines the universe, then, we can find the same number of states of one person’s mind that also “determines” the universe. Those who are concerned that mind is determined by matter (outside of the brain) should recognize that the determination goes both ways. Even if there are multiple states of mind for any state of the brain [Russell, page 203, cites Bergson for this claim], people are not thereby forced (by the world of matter) to take actions that they do not desire to take. A similar point applies to whether or not the universe is goal-directed (teleological); the answer to this query is independent of whether or not the world is mechanical, deterministic given the precise state of matter.
It is believed that our desires cannot alter the past but can alter the future. But this belief is a relic of our memory acting only in the backwards direction (and because generally we only have desires for things unknown to us): we could equally say that the future cannot be altered by our wishes (and were our wishes different the past would have been different).
Most supporters of determinism go beyond claims that whatever may be may be – they regard the world as being determined function-like, a function of earlier data. But with no constraints on the complexity of the function, such determinism is surely the case: at the extreme, the full data themselves can be mapped trivially into “functions” that describe their state at a given time. But what science seeks is the simplest formula consistent with the known facts, from within the infinite set of possible, and so far unfalsified, formulae.
Perhaps what science really seeks is formulae where time (in an absolute sense – as opposed to lapses of time) does not enter as an independent variable, and hence those formulae are uniform in the sense that they hold at any time.
What of free will? Surely the known facts suggest that some of our volitions are determined. But at this point, we cannot be sure that all of our volitions are determined (except in the trivial sense noted above). Nonetheless, our sense of freedom is irrelevant to the scientific question of free will. “The view that it has a bearing rests upon the belief that causes compel their effects, or that nature enforces obedience to its laws as governments do [p. 206].” Our sense of freedom in our volitions is consistent with an appropriate view of determinism.
If our will is determined, is it determined in the mechanical sense, where data concerning material elements are sufficient to generate our will? If our will is so determined, we still need not view this as the triumph of matter over mind: a system with a set of material determinants can also have a set of mental determinants. Nor does a deterministic system require some uncomfortable notion of necessity, where, for instance, we must act against our wishes.
Russell (pages 207-208) offers a one-paragraph summary of this chapter. What philosophers think of as a law of cause and effect is mistaken. Systems can have multiple sets of determinants. Free will may or may not exist, but in any event, it does not have to be in opposition to determinism.
[Posted on the fiftieth anniversary of Bertrand Russell's death, February 2, 2020.] This chapter addresses some confusions around the notion of “cause” as used by philosophers – confusions that are substantial enough that it would be best if the term were avoided. The misunderstanding of causality leads to other mistaken notions. And though philosophers are confused about the “law of causation,” what does science actually employ in its stead?
Many sciences never talk of causation, even though philosophers assert its fundamental nature to science. But perhaps the lack of talk about causes in physics, for instance, isn’t dereliction of duty, but recognition of the absence of causes. The law of causation is outdated, and survives “like the monarchy, only because it is erroneously believed to do no harm [p. 180].”
Russell examines dictionary definitions of “causality” and related words, leading to the distinction between a propositional function (“x is a number”) and a proposition (3 is a number). Propositions are either true or false, but propositional functions can sometimes be true (for some values of x, say), and sometimes false. This line of reasoning suggests that something is necessary if it is the “predicate” of a propositional function, which means that the statement is true for all possible values of its argument.
Eventually, Russell avers that causality (event e2 is caused by event e1, say) is when, for any event e1 that occurs, within some interval of time τ, event e2 occurs. (Variations of this definition have been provided by John Stuart Mill and by Henri Bergson.) Some alternative definitions suffer from circularity or from not limiting the time between cause and effect.
To examine the definition and explore its applicability or inapplicability to science, Russell puts aside (for now) the problem of multiple causes, to focus instead on the meaning of “event,” and on the length of time separating cause from effect.
If we define an event too narrowly, then we will never again see its exact match in the future, and so the notion of causation would lose all purchase. “An ‘event,’ then, is a universal defined sufficiently widely to admit of many particular occurrences in time being instances of it [p. 187].”
The effect cannot take place at the same instant of time, nor immediately afterwards, thanks to the lack of infinitesimal time intervals – so, there must be some finite passage of time twixt cause and effect. As soon as we allow for such a time lapse, however, it becomes possible that in that interval, an intervening event (a meteorite strikes?) changes conditions sufficiently that the proposed “effect” will not occur. But this in turn means that the proposed cause is not itself sufficient to ensure the effect. Were we to start adding the state of the environment into our cause, we end up draining our cause-and-effect claim of any applicability, through the previously noted problem with excessive narrowness.
Despite our difficulties with explicitly expressing the logic of cause and effect, in our quotidian lives, there are many reliable “regularities of sequence [p. 187].” Some of them may be completely dependable, and even less dependable correlations can spur scientific advances. But science pursues or requires no “law” of cause and effect, it does not assume that there is an invariant causal relationship out there waiting to be discovered. As sciences advance, our old causal claims become more nuanced, with finer partitions of antecedents and consequences. When the antecedents are finely enough delineated that we are certain of the consequences, they are also fine enough that they will not occur again, that there is no predictive value to the causal relationship.
Philosophy has been riddled with misconceptions around causation. One is that causes and effects have to be similar, so that mental processes, for instance, could not arise from inert matter alone. Another [Russell enumerates five – RBR] is connected to free will, the notion that causes cannot make someone do something that they do not desire to do. But these desires themselves might be “caused,” even if there is free will in the sense of only doing what is desired.
What is left when philosophy abandons any putative law of cause and effect? Accept for the nonce the logic of induction, that when we have a long series of cases where a “cause” is followed by an “effect,” then this relationship is quite likely to hold in similar future cases. These series that spark induction, however, speak to likelihoods, not necessary consequences, with respect to future observations. The inductive cause-and-effect might lead us to claim that striking a match causes the match to ignite, but we will find that striking a wet match will still not do so. Nor does the inductive approach suggest that every event has some cause. And it seems to be overly inclusive, supporting the claim that night causes day, but we will not back away from accepting that in the sense we are now discussing, night does cause day. The rules we get from the inductive approach can always fail in the next observation, without violating any scientific law.
As science progresses, we tend to move away from cause and effect claims. Gravity involves rules that masses follow, but we cannot isolate one aspect of gravitational forces as causes and others as effects. The correct formulation is mathematical, a stability in the differential equations that characterize the system. But this is hardly some a priori rule of science, as some philosophers expect from their “law of cause and effect.”
Note also that in physics, the complete state at an instant not only determines the future, but the past. There is no temporal priority that makes earlier things causes of later things, and not the other way around.
While science does not stipulate any law of causality, it does accept, in the background, a certain uniformity of nature. Functions that have characterized relationships in the past are expected (inductively) to hold in the future, and if they do not hold, there is some more general law, capturing both sets of data, that does hold. As with other inductive arguments, this uniformity assertion is only likely, not certain, to hold. And if it prove false with respect to some scientific “law,” the rest of science is not thereby invalidated.
The effects of gravitation within the solar system depend, though minutely, on matter that lies outside of the solar system. As we have little knowledge of that matter, we cannot fully verify gravitational theory. But we can be very confident of our claims about gravity within the solar system anyway, irrespective of what is going on in the rest of the universe. The solar system, with respect to gravitation and over a given time period, is a “‘relatively isolated system [p. 197],’” where it will behave in a uniform manner (approximately) during that time period, no matter what is happening elsewhere. A system is “’practically isolated [p. 198]’” if, though there might be some outside situations that would lead relative isolation to fail, we rightly suspect that those situations do not arise. When it comes to falling bodies, the earth is relatively isolated, but it is not isolated with respect to tides.
It is evidence, not a priori reasoning, that leads us to believe some systems are relatively or practically isolated. “The case where one event A is said to ‘cause’ another event B, which philosophers take as fundamental, is really only the most simplified instance of a practically isolated system [p. 198].” The fact that A is always followed by B is true thanks to the relative unimportance, in this case and for this time, of what is going on in the rest of the universe. The (unknown) laws of the universe could still hold but produce instances where A is not followed by B.
Causality is the reed upon which people make out-of-sample inferences. If these inferences are legitimate, the system is deterministic. A non-deterministic system is capricious (p. 199).
Brains are part of the universe. It seems that there is a one-to-one mapping between states of one person’s brain and states of the universe. Assume also that there is a one-to-one relationship between the state of a mind and the state of the corresponding brain. This leads to the notion that there is a one-to-one mapping between a mind and the state of the universe. Whatever (sub)set of states determines the universe, then, we can find the same number of states of one person’s mind that also “determines” the universe. Those who are concerned that mind is determined by matter (outside of the brain) should recognize that the determination goes both ways. Even if there are multiple states of mind for any state of the brain [Russell, page 203, cites Bergson for this claim], people are not thereby forced (by the world of matter) to take actions that they do not desire to take. A similar point applies to whether or not the universe is goal-directed (teleological); the answer to this query is independent of whether or not the world is mechanical, deterministic given the precise state of matter.
It is believed that our desires cannot alter the past but can alter the future. But this belief is a relic of our memory acting only in the backwards direction (and because generally we only have desires for things unknown to us): we could equally say that the future cannot be altered by our wishes (and were our wishes different the past would have been different).
Most supporters of determinism go beyond claims that whatever may be may be – they regard the world as being determined function-like, a function of earlier data. But with no constraints on the complexity of the function, such determinism is surely the case: at the extreme, the full data themselves can be mapped trivially into “functions” that describe their state at a given time. But what science seeks is the simplest formula consistent with the known facts, from within the infinite set of possible, and so far unfalsified, formulae.
Perhaps what science really seeks is formulae where time (in an absolute sense – as opposed to lapses of time) does not enter as an independent variable, and hence those formulae are uniform in the sense that they hold at any time.
What of free will? Surely the known facts suggest that some of our volitions are determined. But at this point, we cannot be sure that all of our volitions are determined (except in the trivial sense noted above). Nonetheless, our sense of freedom is irrelevant to the scientific question of free will. “The view that it has a bearing rests upon the belief that causes compel their effects, or that nature enforces obedience to its laws as governments do [p. 206].” Our sense of freedom in our volitions is consistent with an appropriate view of determinism.
If our will is determined, is it determined in the mechanical sense, where data concerning material elements are sufficient to generate our will? If our will is so determined, we still need not view this as the triumph of matter over mind: a system with a set of material determinants can also have a set of mental determinants. Nor does a deterministic system require some uncomfortable notion of necessity, where, for instance, we must act against our wishes.
Russell (pages 207-208) offers a one-paragraph summary of this chapter. What philosophers think of as a law of cause and effect is mistaken. Systems can have multiple sets of determinants. Free will may or may not exist, but in any event, it does not have to be in opposition to determinism.
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