Russell – Maverick Philosopher

Russell’s Paradox Explained

A reader asked for an explanation of Russell's Paradox. My pleasure.

1. From a contradiction, anything follows. Ex contradictione quod libet. Another way of putting it would be to say that every argument having contradictory premises is valid. 'Valid' is a technical term. An argument A is valid =_df no argument of A's form has true premises and a false conclusion. Now if A has two premises and they contradict each other, then the Law of Non-Contradiction (LNC) assures us that one of the premises must be false. It follows that no argument of A's form can have true premises and a false conclusion.

As long as 'valid' is understood as a technical term having all and only the meaning it is defined as having, then there should not be any trouble understanding how every argument with contradictory premises is valid.

Now consider this derivation:

a. Al is fat and Al is not fat.

b. Al is fat. (From (a) by Simplification)

c. Al is fat or Bush is blind (From (b) by Addition)

d. Al is not fat. (From (a) by Commutation and Simplification)

e. Bush is blind. (From (c) and (d) by Disjunctive Syllogism)

This illustrates how any proposition follows from a contradiction.

2. Now if Russell's Paradox is a contradiction, then set theory harbors a contradiction. And if anything follows from a contradiction, this is a serious problem for the logicist program of reducing all of mathematics to set theory.

3. Unrestricted Comprehension is the intuitively attractive idea that for any condition, or open sentence, or propositional function, there is a corresponding set. Thus, corresponding to the condition 'x is a cat' there is the set {x: x is a cat}, in plain English, the set of all cats. Intuitively, it seems that no matter how strange or complex the condition, there ought to be a set of things that satisfy the condition. Thus, corresponding to 'x is either an apple or a sparkplug' there is the set of all x such that x is either an apple or a sparkplug. Unrestricted Comprehension appears to be self-evident.

4. Now consider 'x is not in my pocket.' That condition picks out the set S of all things not in my pocket. Thus my wife and the Eiffel Tower are members of S. But so is S! The set of all things not in my pocket is not in my pocket. Thus S is a member of S. S is a self-membered set. But other sets are non-self-membered. The set of philosophers, for example, is not a member of itself. No set is a philosopher.

5. Now consider R, the set of all non-self-membered sets. Is R self-membered or not? Clearly, R is self-membered if and only if R is not self-membered — which is a contradiction.

This contradiction is known in the trade as Russell's Paradox. The name, I'd say, is a misnomer. It ought to be called Russell's Antinomy since a paradox need not issue in a contradiction.

6. It is easy to see that the antinomy cannot arise without the Unrestricted Comprehension axiom which implies that, corresponding to the condition 'x is the set of all non-self-membered sets' there corresponds the set R. So one solution to the antinomy is via rejection of Unrestricted Comprehension.

Why not reject LNC instead?

Ray Monk on Frege, Russell, Patriotism and Prejudice

Excerpt:

The single thing I can imagine Russell finding most shocking would be Frege’s endorsement of patriotism as an unreasoning prejudice. The absence of political insight characteristic of his times, Frege says, is due to “a complete lack of patriotism.” He acknowledges that patriotism involves prejudice rather than impartial thought, but he thinks that is a good thing: “Only Feeling participates, not Reason, and it speaks freely, without having spoken to Reason beforehand for counsel. And yet, at times, it appears that such a participation of Feeling is needed to be able to make sound, rational judgments in political matters.” These are surely surprising views for “an absolutely rational man” to express. The man who wanted to set mathematics on surer logical foundations, was content for politics to be based on emotional spasms.

This is a rich and fascinating topic, both intrinsically and especially for me, given my recent deep dive into the world of Carl Schmitt and his antecedents. I will be returning to him. But there is so bloody much else that clamors for my attention. I'm a scatter-shot man to my detriment. Quentin Smith detected that tendency in me way back when. How I miss that crazy guy.

Live long, old friends die, and new friends will never be old.

But Robert A. Heinlein is right: "Specialization is for insects." The trick is to be a jack of all trades but a master of one while running the risk of being a master of none.

Sorry Gottlob, Sorry Bertrand

Attributes are at the things to which they are attributed. Existence, then, is in a broad sense an attribute of existing items despite adding nothing to the quiddity of the thing to which it is attributed apart from its capacity to have a quiddity.

Is Empiricism Self-Refuting?

Russell says it is; I examine his claim. Substack latest.

Addenda (11/19)

Tony Flood writes,

Brian Kilmeade mentioned Ayaan Hirsi Ali's conversion to Christianity quickly as he introduced her, one of his guests tonight, but I heard it on TV which was on in the background; I thought I had misheard Kilmeade. I've always admired her courage and considered her professed atheism in the context of her experience of Islamic terror.

But her Wiki entry says she "converted to Christianity" (by which I hope she means that she received Christ as her savior), citing this and this.

She blogged about Russell last week (as you did today):

In 2002, I discovered a 1927 lecture by Bertrand Russell entitled “Why I am Not a Christian.” It did not cross my mind, as I read it, that one day, nearly a century after he delivered it to the South London branch of the National Secular Society, I would be compelled to write an essay with precisely the opposite title.

In high school in 1970 along the road to my Communism, I had read Russell's essay and decided I would study philosophy. I remember catching his obit in the papers, marveling at the longevity of this stellar Victorian intellectual who had been my contemporary for over a decade-and-a-half and therefore could have met.

Anyway, Ali's now firmly in my Hall of Hero(in)es. Feel free to share this, which may come as news to others as it did to me.

Thanks, Tony. I share your high opinion of Ali. The Unherd article which I excerpted earlier is important. I too read Russell's Why I am not a Christian in high school. Russell was a logical and philosophical technician of high rank, but unlike his pal Wittgenstein, he wrote popular works as well. Wittgenstein, as you know, took a dim view of Russell's popular writings. Russell was secular to the core; Wittgenstein, I could easily show, had the heart of the homo religiosus despite his bladed intellect.

Edward writes,

Interesting, and overlaps with a central theme of the book, as follows. Assume

1 Knowledge is propositional. That is, whatever counts as knowledge has to be expressible in language as a proposition.

2 Propositions have two terms and can be affirmative or negative, universal or particular. Thus to any two terms there correspond exactly four propositions.

3 There are a finite number of term types, as set out in Locke’s classification of ‘ideas’ in Book II of the Essay.

4 The meaning of any term is derived from experience. Locke assumes that every word either signifies a simple ‘sensible idea’, or signifies a complex idea that can be analysed into simple parts.

These assumptions define what Bennett calls meaning-empiricism, and Hanna calls semantic psychologism. It follows from them that every object of human understanding is defined by a proposition whose meaning depends on experience.

In this way we can set a limit to human understanding.

Note that the empiricist project differs from the scholastic-Aristotelian one. The scholastics generally did not believe in meaning-empiricism, because they thought that the proper signification of a term is an object, not an idea. So I think to settle your question we must look at whether words signify ‘ideas’, i.e. affections of the soul, or not.

Ad (1). Is all knowledge propositional? You are making a very strong claim here: necessarily, nothing counts as knowledge that is not expressible in declarative sentences. But knowing what something is like counts as knowledge. I know what it is like to be punched in the stomach, but not what it is like to undergo a menstrual period. I know some people by description only, others by acquaintance only, and still others by description and by acquaintance. Isn't knowledge by acquaintance a counterexample to your thesis? And then there is 'carnal knowledge.' Does it not count as knowledge? There is also 'know how.' My cats know how to open doors, but they would be hard-pressed to verbalize that knowledge.

Ad (2). "Thus to any two terms there correspond exactly four propositions." Since copulae are typically tensed, there have to be more. There have to be at least twelve. 'Every animal in the house was/is/will be a cat.' 4 categorical forms X 3 simple tenses = 12 different propositions. And then there are the tenseless uses of copulae, e,g, 'The cat is an animal.' 'The triangle is a three-sided plane figure that encloses a space.' Yogi Berra joke: "You mean now?" 'God is' is either eternally true/false or omnitemporally true/false, and tenseless either way.

Ad (3). OK.

Ad (4). "The meaning of any term is derived from experience." My question is: how could we know that this proposition is true if it is indeed true? To know that it is true, we have to know what it means. But it cannot mean anything if it is true. Do the terms of this proposition signify a sensible idea? No. 'The meaning of any terms' does not signify a sensible idea. The same goes for 'a meaning derived from experience.' Meaning-empiricism is meaningless on its own theory of meaning.

Of Russell’s Teapot and Abbey’s Angry Lunicorn

Does the angry unicorn on the dark side of the Moon manage his anger by sipping herbal tea from Russell's teapot?

Substack latest.

Untangling Plato’s Beard

I was asked by a commenter what motivates the thin theory of existence. One motivation is

. . . the old Platonic riddle of nonbeing. Nonbeing must in some sense be, otherwise what is it that there is not? This tangled doctrine might be nicknamed Plato's beard; historically it has proved tough, frequently dulling the edge of Occam's razor. (Willard Van Orman Quine, "On What There Is" in From a Logical Point of View, Harper Torchbook ed., 1963, pp. 1-2)

As I see it, here is how the paradox arises.

1) 'Pegasus does not exist' is true. Therefore:

2) The sentence in question has meaning. (Only meaningful sentences have a truth value.)

3) If a sentence has meaning, then so do its (sentential and sub-sentential) parts. (Compositionality of meaning.) Therefore:

4) 'Pegasus' has meaning. Therefore:

5) Something is such that 'Pegasus' refers to it. ('Pegasus' is a proper name, and the meaning of a proper name is its referent, that to which it refers.) Therefore:

6) 'Pegasus' refers to something that exists. (Everything exists; there are no nonexistent objects; one cannot refer to what does not exist for it is not there to be referred to.) Therefore:

7) Pegasus must exist for it to be true that Pegasus does not exist. Paradox!

None of the first four propositions is plausibly denied. To avoid the conclusion, we must deny either (5) or (6) and the assumptions that generate them. Now Quine is no Meinongian/Wymanian. Quine advocates a Russellian solution which amounts to rejecting (5) by rejecting the assumption that the meaning of a proper name is exhausted by its reference. For Russell, ordinary proper names are definite descriptions in disguise. This allows them to have meaning or sense without reference. Thus 'Pegasus' is elliptical for 'the winged horse of Greek mythology.' This allows the following contextual paraphrase of 'Pegasus does not exist':

It is not the case that there exists an x such x is the winged horse of Greek mythology

which is free of paradox. What the paraphrase says is that the definite description which gives the sense of 'Pegasus' is not satisfied. Equivalently, it says that the concept winged horse of Greek mythology is not instantiated. Thus the original sentence, which appeared to be about something that does not exist but which, if it existed, would be an animal, is really about about a description or concept which does exist and which is assuredly not an animal.

It is a brilliant solution, prima vista. It works for negative general existentials as well. 'Unicorns do not exist,' despite its surface grammar, cannot be about unicorns — after all, there aren't any — it is about the concept unicorn and predicates of it the property of not being instantiated. Extending the analysis to affirmative general existentials, we can say that 'Horses exist,' for example, is not about horses — after all, which horses would it be about? — it is about the concept horse and predicates of it the property of being instantiated.

What about singular affirmative existentials such as 'Harry exists'? Quine maintains that, in a pinch, one can turn a name into a verb and say, with truth, 'Nothing pegasizes' thereby avoiding both Plato's Beard and Meinong's Jungle so as to enjoy, clean-shaven, the desert landscape bathed in lambent light. So what's to stop us from saying 'Something Harry-sizes'? (Quite a bit, actually, but I won't go into that in this post, having beaten it to death in numerous other entries. Briefly, there are no haecceity-concepts: there is no such concept Harry-ness that (i) can exist uninstantiated; (ii) if instantiated is instantiated by Harry and Harry alone in the actual world; (iii) is not instantiated by anything distinct from Harry in any possible world.)

Let us now pause to appreciate what the Russellian (or rather 'Fressellian') approach accomplishes in the eyes of its advocates. It untangles Plato's Beard. It avoids Meinong's jungle. It preserves the existence-nonexistence contrast by situating it at the second level, that of descriptions, concepts, propositional functions, properties, as the contrast between satisfaction-nonsatisfaction (for descriptions), instantiation-noninstantiation (for concepts and properties), and having a value-not having a value for propositional functions, or as Russell puts it, being sometimes true or the opposite.

What's more, it diagnoses the failure of certain versions of the ontological argument. Descartes' Meditation Five version has it that God exists because God has all perfections and existence is a perfection. But if Frege and Russell are right, existence is not even a property of God let alone a perfection of him inasmuch as '. . .exist(s)' has no legitimate use as a first-level predicate and can be be properly deployed only as a second-level predicate. (God is an individual.)

Last, but not least, the Fressellian analysis consigns entire libraries of school metaphysics to he flames, the books in which drone on endlessly about Being and Existence and the distinctio realis, and the analogia entis, and ipsum esse subsistens, ad nauseam. Swept aside are all the hoary and endlessly protracted debates about the relation of essence and existence in individuals: is it a real distinction, and what could that mean? Is it a formal distinction, and what could that mean? Etc. On the Frege-Russell approach there simply is no existence of individuals.

And now you know why the thin theory is called 'thin.' It could also be called 'shallow' in that it eliminates existence as a deep and mysterious topic. The thin theory disposes of existence as a metaphysical topic, reducing it to a merely logical topic. As Quine famously says in an essay other than the one cited above, "Existence is what existential quantification expresses." Thus 'Cats exist' says no more and no less than 'For some x, x is a cat.' You will note that the analysans makes no mention of existence. It features only the word 'cat' and some logical machinery. Existence drops out as a metaphysical topic.

Of course, I don't accept the thin theory; but as you can see, I appreciate what motivates it in the minds of its adherents.

How to Grow Old and the Question of an Immortality Worth Wanting

Sage advice from Bertrand Russell (1872-1970) who grew old indeed. The best part of his short essay follows:

I think that a successful old age is easiest for those who have strong impersonal interests involving appropriate activities. It is in this sphere that long experience is really fruitful, and it is in this sphere that the wisdom born of experience can be exercised without being oppressive. It is no use telling grownup children not to make mistakes, both because they will not believe you, and because mistakes are an essential part of education. But if you are one of those who are incapable of impersonal interests, you may find that your life will be empty unless you concern yourself with your children and grandchildren. In that case you must realise that while you can still render them material services, such as making them an allowance or knitting them jumpers, you must not expect that they will enjoy your company.

Without a doubt, "strong impersonal interests involving appropriate activities" is the key.

Some old people are oppressed by the fear of death. In the young there there is a justification for this feeling. Young men who have reason to fear that they will be killed in battle may justifiably feel bitter in the thought that they have been cheated of the best things that life has to offer. But in an old man who has known human joys and sorrows, and has achieved whatever work it was in him to do, the fear of death is somewhat abject and ignoble. The best way to overcome it -so at least it seems to me- is to make your interests gradually wider and more impersonal, until bit by bit the walls of the ego recede, and your life becomes increasingly merged in the universal life. An individual human existence should be like a river: small at first, narrowly contained within its banks, and rushing passionately past rocks and over waterfalls. Gradually the river grows wider, the banks recede, the waters flow more quietly, and in the end, without any visible break, they become merged in the sea, and painlessly lose their individual being. The man who, in old age, can see his life in this way, will not suffer from the fear of death, since the things he cares for will continue. And if, with the decay of vitality, weariness increases, the thought of rest will not be unwelcome. I should wish to die while still at work, knowing that others will carry on what I can no longer do and content in the thought that what was possible has been done.

[from “Portraits From Memory And Other Essays”]

The second paragraph raises deep and difficult questions. The philosopher in me has often entertained, with considerable hospitality, the thought that an immortality worth wanting must involve a transcending of the petty and personal ego, the self that separates us from other selves and the world. An immortality worth wanting must involve a sloughing off of the petty self and a merging into an impersonal, universal, transcendental awareness of impersonal Platonica including eternal truths, changeless essences, absolute values, and noble ideals. Those philosophers of a predominantly theoretical bent will be attracted to this conception reminiscent as it is of Aristotle's bios theoretikos as exemplified in its highest instance, noesis noeseos.

"But then you would no longer exist! You would be swallowed up in death, the greatest calamity of them all." To this objection I had a ready reply: "It all depends on who I am in the innermost core of my selfhood; if I am in truth the eternal Atman, and not this indigent and limited psychophysical complex; if I am the transcendental witness self, then I will not cease to exist. In the measure that I identify with that deathless, impersonal awareness of eide and Wahrheiten an sich, I am proof against extinction by the body's death. I will merge at last with the sea of transcendental awareness which is my true self and give up my false petty individuality for a greater individuality, that of the Absolute.

That is one strand, the monistic strand, in my thinking about selfhood and immortality. It dominated my thinking in my twenties and thirties.

But another is the personalist strand which takes very seriously the reality of persons in the plural and the possibility of deep I-Thou (as opposed to I-It) relations between persons and between a finite person and the ultimate person, the First Person, if you will, God.

On both conceptions there is a distinction between the true self and the false self. Controversy erupts over the nature of the true self. Is it trans-individual, or is it individuated? Is there one true self or many? Are we to aspire to an obliteration of the individual self or to its transformation? On neither conception is survival the schlepping on of the crass and carnal earthly self. Is the death of the individual a great calamity or is it a benign release into true selfhood? The controversy is ancient. Ramanuja to Shankara: I don't want to become sugar; I want to taste sugar!

As for Lord Russell, he would not have spoken of the eternal Atman, but he was a convinced atheist and mortalist. He was sure his individual consciousness would cease at death. But this did not bother him because the objects of his ultimate concern were impersonal. "The things I care for will continue, and others will carry on what I can no longer do."

Their Cocks Make Them Sure

There are those who are cocksure that there is no God, no soul, no post-mortem judgment, no ultimate meaning to human existence, and that we are all just material bits of a material world. Now it may be so for all we know. This is not an area in which proofs or disproofs are possible.

But for those who are cocksure about it, I suspect that it is their cocks that make them sure.

Crudity aside, their natural concupiscence blinds them to the spiritual reality of God and the soul, dulls their consciences, and ties them to a passing world that their lust convinces them is ultimately real.

This is why I do not trust the atheisms of Russell and Sartre. They were sensualists and worldlings who failed to satisfy the prerequisites of spiritual insight. Pride and lust dimmed their eyes.

Half-Way Fregeanism About Existence: Questions for Van Inwagen

In section 53 of The Foundations of Arithmetic, Gottlob Frege famously maintains that

. . . existence is analogous to number. Affirmation of existence is in fact nothing but denial of the number nought. Because existence is a property of concepts the ontological argument for the existence of God breaks down. (65)

Frege is here advancing a double-barreled thesis that splits into two sub-theses.

ST1. Existence is analogous to number.

ST2. Existence is a property (Eigenschaft) of concepts and not of objects.

In the background is the sharp distinction between property (Eigenschaft) and mark (Merkmal). Three-sided is a mark of the concept triangle, but not a property of this concept; being instantiated is a property of this concept but not a mark of it. The Cartesian-Kantian ontological argument "from mere concepts" (aus lauter Begriffen), according to Frege, runs aground because existence cannot be a mark of any concept, but only a property of some concepts. And so one cannot validly argue from the concept of God to the existence of God.

Existence as a property of concepts is the property of being instantiated. We can therefore call the Fregean account of existence an instantiation account. A concept is instantiated just in case it has one or more instances. So on a Fregean reading, 'Cats exist' says that the concept cat is instantiated. This seems to imply, and was taken by Frege and Russell to imply that 'Cats exist' is not about cats, but about a non-cat, a concept or propositional function, and what it says about this concept or propositional function is not that it (singularly) exists, but that it is instantiated! (Frege: "has something falling under it"; Russell: "is sometimes true.") A whiff of paradox? Or more than just a whiff?

The paradox, in brief, is that 'Cats exist' which one might naively take to be about cats, is in reality about a non-cat, a concept or propositional function.

Accordingly, as Russell in effect states, 'Cats exist' is in the same logical boat with 'Cats are numerous.' Now Mungojerrie is a cat; but no one will infer that Mungojerrie is numerous. That would be the fallacy of division. On the Fressellian view, one who infers that Mungojerrie exists commits the same fallacy. 'Exist(s)' is not an admissible first-level predicate.

My concern in this entry is the logical relation between the above two sub-theses. Does the first entail the second or are they logically independent? There is a clear sense in which (ST1) is true.

Necessarily, if horses exist, then the number of horses is not zero, and vice versa. So 'Horses exist' is logically equivalent to 'The number of horses is not zero.' This is wholly unproblematic for those of us who agree that there are no Meinongian nonexistent objects. But note that, in general, equivalences, even logical equivalences, do not sanction reductions or identifications. So it remains an open question whether one can take the further step of reducing existence to instantiation, or of identifying existence with instantiation, or even of eliminating existence in favor of instantiation. Equivalence, reduction, elimination: those are all different. But I make this point only to move on.

(ST1), then, is unproblematically true if understood as expressing the following logical equivalence: 'Necessarily Fs exist iff the number of Fs is not zero.' My question is whether (ST1) entails (ST2). Peter van Inwagen in effect denies the entailment by denying that the 'the number of . . . is not zero' is a predicate of concepts:

I would say that, on a given occasion of its use, it predicates of certain things that they number more than zero. Thus, if one says, 'The number of horses is not zero,' one predicates of horses that they number more than zero. 'The number of . . . is not zero' is thus what some philosophers have called a 'variably polyadic' predicate. But so are many predicates that can hardly be regarded as predicates of concepts. The predicates 'are ungulates' and 'have an interesting evolutionary history,' for example, are variably polyadic predicates. When one says, 'Horses are ungulates' or 'Horses have an interesting evolutionary history' one is obviously making a statement about horses and not about the concept horse. ("Being, Existence, and Ontological Commitment," pp. 483-484)

It is this passage that I am having a hard time understanding. It is of course clear what van Inwagen is trying to show, namely, that the Fregean sub-theses are logically independent and that one can affirm the first without being committed to the second. One can hold that existence is denial of the number zero without holding that existence is a property of concepts. One can go half-way with Frege without going all the way.

But I am having trouble with the claim that the predicate 'the number of . . . is not zero' is 'variably polyadic' and the examples van Inwagen employs. 'Robbed a bank together' is an example of a variably polyadic predicate. It is polyadic because it expresses a relation, that of robbing, and it is variably polyadic because it expresses a family of relations having different numbers of arguments. For example, Bonnie and Clyde robbed a bank together, but so did Ma Barker and her two boys, Patti Hearst and three members of the ill-starred Symbionese Liberation Army, and so on. (Example from Chris Swoyer and Francesco Orilia.)

Now when I say that the number of horses is not zero, what am I talking about? It is plausible to say that I am talking about horses, not about the concept horse. (Recall the whiff of paradox, supra.) What I don't understand are van Inwagen's examples of variably polyadic predicates. Consider 'are ungulates.' If an ungulate is just a mammal with hooves, then I fail to see how 'are ungulates' is polyadic, let alone variably polyadic. I do understand that some hooved animals have one hoof per foot, some two hooves per foot, and so on, which implies variability in the number of hooves that hooved animals have. What I don't understand is the polyadicity. It seems to me that 'Are hooved mammals' is monadic.

The other example is 'Horses have an interesting evolutionary history.' This sentence is clearly not about the concept horse. But it is not about any individual horse either. Consider Harry the horse. Harry has a history. He was born in a certain place, grew up, was bought and sold, etc. and then died at a certain age. He went through all sorts of changes. But Harry didn't evolve, and so he had no evolutionary history. No individual evolves; populations evolve:

Evolutionary change is based on changes in the genetic makeup of populations over time. Populations, not individual organisms, evolve. Changes in an individual over the course of its lifetime may be developmental(e.g., a male bird growing more colorful plumage as it reaches sexual maturity) or may be caused by how the environment affects an organism (e.g., a bird losing feathers because it is infected with many parasites); however, these shifts are not caused by changes in its genes. While it would be handy if there were a way for environmental changes to cause adaptive changes in our genes — who wouldn't want a gene for malaria resistance to come along with a vacation to Mozambique? — evolution just doesn't work that way. New gene variants (i.e., alleles) are produced by random mutation, and over the course of many generations, natural selection may favor advantageous variants, causing them to become more common in the population.

'Horses have an interesting evolutionary history,' then, is neither about the concept horse nor about any individual horse. The predicate in this sentence appears to be non-distributive or collective. It is like the predicate in 'Horses have been domesticated for millenia.' That is certainly not about the concept horse. No concept can be ridden or made to carry a load. But it is also not about any individual horse. Not even the Methuselah of horses, whoever he might be, has been around for millenia.

As I understand it, predicate F is distributive just in case it is analytic that whenever some things are F, then each is F. Thus a distributive predicate is one the very meaning of which dictates that if it applies to some things, then it applies to each of them. 'Blue' is an example. If some things are blue, then each of them is blue.

If a predicate is not distributive, then it is non-distributive (collective). If some Occupy-X nimrods or Antifa thugs have the building surrounded, it does not follow that each such nimrod or thug has the building surrounded. If some students moved a grand piano into my living room, it does not follow that each student did. If bald eagles are becoming extinct, it does not follow that each bald eagle is becoming extinct. Individual animals die, but no individual animal ever becomes extinct. If the students come from many different countries, it does not follow that each comes from many different countries. If horses have an interesting evolutionary history, it does not follow that each horse has an interesting evolutionary history.

My problem is that I don't understand why van Inwagen gives the 'Horses have an interesting evolutionary history' example — which is a collective predication — when he is committed to saying that each horse exists. His view , I take it, is that 'exist(s)' is a first-level distributive predicate. 'Has an interesting evolutionary history,' however, is a first-level non-distributive predicate. Or is it PvI's view that 'exist(s)' is a first-level non-distributive predicate?

Either I don't understand van Inwagen's position due to some defect in me, or it is incoherent. I incline toward the latter. He is trying to show that (ST1) does not entail (ST2). He does this by giving examples of predicates that are first-level, i.e., apply to objects, but are variably polyadic as he claims 'the number of . . . is not zero' is variably polyadic. But the only clear example he gives is a predicate that is non-distributive, namely 'has an interesting evolutionary history.' 'Horses exist,' however, cannot be non-distributive. If some horses exist, then each of them exists. And if each of them exists, then 'exists' is monadic, not polyadic, let alone variably polyadic.

Russell, Sense Data, and Qualia

Reader K. G. writes,

I recently came across a passage in Russell's Mysticism and Logic which you may find interesting. In the essay "The Ultimate Constituents of Matter," Russell writes (p. 144), "… the existence of sense-data [qualia] is logically independent of the existence of mind, and is causally dependent upon the body of the percipient, rather than upon his mind.” [. . .] On the contrary, I propose that any tenable definition of qualia must construe them as mental items, i.e. items whose esse is their percipi. [. . .]

What are your thoughts on this argument?

I think you are confusing qualia with sense data. I grant you that qualia are mental items, and that they cannot exist apart from minds. But sense data are not qualia. First of all, Russell does not use 'quale' (singular) or 'qualia' (plural) in the two essays you mention. But he does tell us what he means by 'sense data': ". . . I believe that the actual data in sensation, the immediate objects or sight or touch or hearing, are extra-mental, purely physical, and among the ultimate constituents of matter." (10th ed., 128)

Suppose I am staring at a blue coffee cup. The particular blue that I visually sense, precisely as I sense it, is a sense datum: it is the direct or immediate object of my visual sensing. It is distinct from the sensing. The sensing is something I undergo or experience or live through; it is part of my mental life. As such it is mental in nature. The sense datum, however, is not mental. It is not an episode of experiencing or part of an episode of experiencing; it is the direct object of an experiencing. For Russell, the blue sense datum is not only not mental; it is physical: it is a proper part of the coffee cup. I read Russell in these essays as a bundle theorist: physical objects are bundles of sense data both synchronically and diachronically.

Note also that while a blue sense datum is blue, a sensing of a blue sense datum is not blue. (An adverbialist who speaks of sensing-blue-ly gives up the act-object schema that Russell presupposes.)

Sense data, then, are objects of sensings. For Russell, they are extra-mental and indeed physical. Qualia, however, are the phenomenal characters of experiencings. For example, the felt quality, the what-it-is-like, of a twinge of pain, precisely as it is felt. Or the smell of burnt garlic. Or the taste of licorice.

There are many tricky questions here. Suppose I am given a piece of black, semi-soft candy and asked what it is. I put it in my mouth to find out. I discover that it is a piece of licorice. I seem to have discovered something objective about a physical object, namely, that this bit of candy is licorice. This would suggest that the object of my gustatory sensing is extra-mental and indeed physical. Or should we say merely that I had a gustatory experience with a certain phenomenal character and that the characteristic taste of the thing I put in my mouth is wholly mental in nature?

Bertrand Russell: Empiricism is Self-Refuting. Is He Right?

An Inquiry into Meaning and Truth (1940), 1969 Pelican ed., pp. 156-157:

I will observe, however, that empiricism, as a theory of knowledge, is self-refuting. For, however it may be formulated, it must involve some general proposition about the dependence of knowledge upon experience; and any such proposition, if true, must have as a consequence that [it] itself cannot be known. While therefore, empiricism may be true, it cannot, if true, be known to be so. This, however, is a large problem.

It is indeed a large problem. But, strictly speaking, is empiricism self-refuting? A self-refuting proposition is one that entails its own falsehood. *All generalizations are false* is self-refuting in this sense. It is either true or not true (false). (Assume Bivalence) If true, then false. If false, then false. So, necessarily false. Other self-refuting propositions are antinomies: if true, then false; if false, then true.

Let empiricism be the proposition, *All knowledge derives from sense experience.* Clearly, this proposition does not refute itself. For it does not entail its own falsehood. It is not the case that if it is true, then it is false. Rather, if it is true, then it cannot be known to be true. For it is not known by experience, and therefore not knowable if true.

Empiricism, then, is not self-refuting, but self-vitiating, self-weakening. It is in this respect like the thesis of relative relativism (RR): it is relatively true that all truths are relative. (RR) does not refute itself, but it does weaken itself. Presumably, what the relativist really wants to say is something stentorian and unqualified: all truths are relative! But the demands of logical consistency force him to relativize his position.

The real problem is that if empiricism is true, then it cannot be believed with justification. For on empiricism the only justificatory grounds are those supplied by sense experience. It is also quite clear that empiricism is not a formal-logical truth or an analytic truth. A logical positivist would have to say it is cognitively meaningless. But we shouldn't go that far. It plainly enjoys cognitive meaning.

You might say that empiricism is just a linguistic proposal, a non-binding suggestion as to how we might use words. Equivalently, one might say it is just a stance one might adopt. If you tell me that, then I will thank you for 'sharing,' but then politely voice my preference for either a non-empirical stance or a stance that is not a mere stance, but the blunt asseveration that empiricism is false. After all, I know that kindness is to be preferred over cruelty, ceteris paribus, and I know this by a non-empirical value intuition.

Another wrinkle is this. If all knowledge derives from sense experience, then presumably this cannot just happen to be the case. I should think that if empiricism is true, then it is necessarily true. But what could be the ground of the necessity? I have already noted, in effect, that the necessity is neither formal-logical nor analytic. Is the necessity grounded in the nature, essence, eidos, of knowledge? That would be a rather unempirical thing to say. Empiricists have no truck with essences or Forms or eide.

Here then we appear to have a further embarrassment for empiricism. It cannot be the nature of knowledge to derive from and have its sole justificatory ground in sense experience. So it just happens to be the case. This cannot be ruled out as logically impossible. But it smacks of deep incoherence and is, shall we say, profoundly unsatisfactory.

Please note that similar reasoning can be deployed against scientism. If all knowledge is natural-scientific knowledge, then this proposition, if true, cannot be known to be true. Is it then merely believed without justification? Is it merely a matter of adopting the 'scientistic stance' or doing the 'scientistic shuffle'? If so, I will thank you for 'sharing' but then politely refuse your invitation to dance.

Hat Tip: I thank Patrick Cronin for reminding me of the Russell passage.

Can Anyone Recommend a Good History of Philosophy?

A graduate student in philosophy asks about histories of philosophy:

Suppose I wanted, over time, to work through a text or series of texts. Which ones are worthy of consideration? I've heard good things about Copleston's 11 volumes. There's also Russell's history of western philosophy and Anthony Kenny has done a history as well. Do you recommend any of those (or perhaps another)? I should say that any history text will not supplant primary sources; it would be an addition to them.

While Bertrand Russell is entertaining, I can't recommend his history. He wrote it for money, or rather he dictated it for money. (When he was asked why he wrote a blurb for a certain book, he said that he had a hundred good reasons: the author paid him $100.) For a taste, consider the following passage from Bertrand Russell, A History of Western Philosophy (New York: Simon & Shuster, 1945), p. 427. I found it here, but without a link and without a reference. So, exploiting the resources of my well-stocked library, I located the passage, and verified that it had been properly transcribed. Whether Russell is being entirely fair to the Arabs is a further question. In fact, I am pretty sure that he is not being fair to Avicenna (Ibn Sina) who played a key role in the development of the metaphysics of essence and existence.

Arabic philosophy is not important as original thought. Men like Avicenna and Averroes are essentially commentators. Speaking generally, the views of the more scientific philosophers come from Aristotle and the Neoplatonists in logic and metaphysics, from Galen in medicine, from Greek and Indian sources in mathematics and astronomy, and among mystics religious philosophy has also an admixture of old Persian beliefs. Writers in Arabic showed some originality in mathematics and in chemistry; in the latter case, as an incidental result of alchemical researches. Mohammedan civilization in its great days was admirable in the arts and in many technical ways, but it showed no capacity for independent speculation in theoretical matters. Its importance, which must not be underrated, is as a transmitter. Between ancient and modern European civilization, the dark ages intervened. The Mohammedans and the Byzantines, while lacking the intellectual energy required for innovation, preserved the apparatus of civilization, books, and learned leisure. Both stimulated the West when it emerged from barbarism; the Mohammedans chiefly in the thirteenth century, the Byzantines chiefly in the fifteenth. In each case the stimulus produced new thought better than that produced by the transmitters — in the one case scholasticism, in the other the Renaissance (which however had other causes also).

Copleston is good, and you might also consider Hegel. He will broaden you and counteract the probably excessively analytic atmosphere which you now breathe. But the Swabian genius is quirky and opinionated just like Lord Russell. When he comes to the medieval period in his Lectures on the History of Philosophy, he puts on his “seven-league boots” the better to pass over this thousand year period without sullying his fine trousers. (Vol. III, 1)

Summing up the “General Standpoint of the Scholastics,” he has this to say: “…this Scholasticism on the whole is a barbarous philosophy of the finite understanding, without real content, which awakens no true interest in us, and to which we cannot return.” “Barren,” and “rubbishy” are other terms with which he describes it. (Vol. III, 94-95) The politically correct may wish to consider whether the descendants of Hegel should pay reparations to the descendants of Thomas Aquinas, et al.

ComBox open for anyone with recommendations.

Not Enough Evidence?

"Not enough evidence, God, not enough evidence!" (Bertrand Russell)

It may well be that our predicament is such as to disallow conclusive or even sufficient evidence of the truth about it. If Plato's Cave Allegory is apt, if it lays bare the truth of the human predicament, then it must be that the evidence that the cave is a cave and that there is an outer world, whether it be the evidence of someone's testimony or the evidence of one's own rare and fleeting experiences, is scant and flimsy and easily doubted and denied. What I merely glimpse on rare occasions I can easily doubt. One can also doubt what any church teaches for the simple reason that there are many churches and they contradict each other on many points of doctrine and practice. And the same goes for what I believe on the testimony of others.

We don't know that the human condition is a cave-like predicament along Platonic lines, but if it is then we have an explanation of the paucity of sufficient evidence of its being what it is. (By sufficient evidence for a proposition p I mean evidence that renders p more likely than its negation.)

It is vitally important to us whether God or some form of Transcendence exists, and whether a higher life is possible for us beyond the miserably short and indigent predicament in which we presently find ourselves. But it may be that the truth in this matter cannot be known here below, but only believed on evidence that does not make it more likely than not. It may be that our predicament is such as to make impossible sufficient evidence of the truth about it.

Do I violate an ethics of belief if I believe on insufficient evidence? But don't I also have a duty to myself to pursue what is best for myself? And seek my ultimate happiness? Why should the legitimate concern to not be wrong trump the concern to find what is salvifically right? Is it not foolish to allow fear of error to block my path to needed truth?

Lately I've heard bandied about the idea that to have faith is to pretend to know what one does not know. Now that takes the cake for dumbassery. One can of course pretend to know things one does not know, and pretend to know more about a subject than one does know. The pretence might be part of a strategy of deception in the case of a swindler or it might be a kind of acting as in the case of an actor playing a mathematician.

But in faith one does not pretend to know; one honestly faces the fact that one does not know and ventures beyond what one knows so as to gain access to a needed truth that by its very nature cannot satisfy the strictures that we moderns and post-moderns tend to build into 'know.'

Peter Unger on Bertrand Russell on the Value of Philosophy

This from a reader:

In one portion of Grace Boey's interview of Peter Unger, Unger discusses what Russell had to say about the value of philosophy, and I was a bit taken aback because that particular quotation by Russell resonates with me a lot, and Unger's swift dismissal of it as garbage left me almost wounded.

What Unger appears to be saying is that claims about the value of philosophy are either quasi-mystical nonsense, or these are claims which can be empirically tested, and therefore should not be assumed a priori. We can only say philosophy has value if we take a bunch of philosophy students, measure parameters such as their dogmatism, creativity, rationality etc at the start and then at the end when they graduate, see if learning philosophy has improved these parameters, and whether this improvement is more than the graduates of other subjects like psychology and literature. Only then we can say that there is value in studying philosophy.

Your thoughts appreciated.

This is what Unger says:

This quote is from a small book that Bertrand Russell wrote, from 1912, which is still used as a textbook today: a little book called The Problems of Philosophy. He talks here about the value of philosophy:

Thus, to sum up our discussion of the value of philosophy; Philosophy is to be studied, not for the sake of any definite answers to its questions, since no definite answers can, as a rule, be known to be true, but rather for the sake of the questions themselves. Because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation; but above all that because, through the greatness of the universe which philosophy contemplates, the mind also is rendered great, and becomes capable of that union with the universe which constitutes its highest good.

The second part, after the ‘above all’ seems like complete nonsense. What the heck does all that mean? It’s mystical nonsense, no? This from one of the two founders of modern logic, second only to Gottlob Frege in laying down the foundations of symbolic and mathematical logic.

Let’s go to the first part, before the ‘above all’. He says that these questions, and not questions about, say, chemistry, or ornothology, enlarge your conception of what is possible. I hardly even know what that means. But he goes on and says things which are less hard to understand, like, it enriches your intellectual imagination. And a second thing it does, which I take to be distinct, is it diminishes your dogmatic assurance.

These are things that can be tested for, as I said before! Whether it’s a treatment effect, or a selection effect. There are tests for how creative people are, or how dogmatic they are. You test them, at the end, the day after they graduate. And you see whether this is true.

Bertrand Russell never even bothers to think about whether, or what, these things might have to do with any test you can give to human people, or what’s going on. It’s so full of nonsense, the guy was always full of nonsense. He read up on relativity theory, but you would think he would think of some psychological testing that had some bearing on the smoke he was blowing. He never gave it a thought.

BV: In dismissing mysticism as nonsense, Unger merely advertises his own ignorance and spiritual vacancy and falls to the tabloid level of an Ayn Rand who displays no more understanding of mysticism than he does. Mysticism is a vast field of ancient yet ongoing human experience and endeavor and one that earlier American philosophers such as Josiah Royce, William James, and William Ernest Hocking, to mention just three philosophers of high distinction, took very seriously indeed. See, respectively, The World and the Individual, First Series, 1899, lectures II, IV, and V; The Varieties of Religious Experience, 1902, lectures XVI and XVII; Types of Philosophy, 1929, chapters 30, 31, 32, 33. It is worth noting that all three luminaries were professors at Harvard University.

In those days Harvard was still far from the over-specialization and hyper-professionalization of philosophy that breeds people like Peter Unger, who though "terribly" clever — to use one of his favorite adjectives –appear to view philosophy as a highly rarefied academic game without roots in, or anything to say about, one's life as an "existing individual" (phrase from Kierkegaard, but I am thinking of all the existentialists, as well as Augustine, Pascal, the Stoics, the ancient Skeptics, and indeed all philosophers from Plato to Aquinas to Kant and beyond for whom philosophy has something to do with the search for wisdom).

The institutionalization of philosophy in the 20th century, though not without some benefits, has led to the following. Empty gamesmanship without existential anchorage. Hypertrophy of the critical and analytic faculty with concomitant atrophy of the intuitive faculty. Philistinic dismissal of whole realms of human experience and endeavor. Technicality and specialization taken to absurd lengths not justified by any actual results. (If extreme specialization and narrowing of focus led to consensus among competent practioners, then that might count as a justification for the specialization. But it hasn't and it doesn't. See here.)

Bertrand Russell, you will recall, published a collection of essays in October 1910 that in the second edition of December 1917 were given the title Mysticism and Logic. The lead essay, "Mysticism and Logic," which originally appeared in the Hibbert Journal of July 1914, displays a serious engagement with what Unger the philistine dismisses as "complete nonsense." What Russell writes about mysticism is penetrating enough to suggest that he may have had some mystical experiences of his own. In the end Russell rejects the four main tenets that he takes as definitive of mysticism, but his rejection is reasoned and respectful. He grants that "there is an element of wisdom to be learned from the mystical way of feeling, which does not seem to be attainable in any other way." (p. 11)

But of course that essay dates from the days of our grandfathers and great grandfathers. Times have changed, and in philosophy not for the better. The analytic philosophy that Russell did so much to promote has become sterile and ingrown and largely irrelevant to the wider culture. There are of course exceptions, Thomas Nagel being one of them.

There is a lot more to be said. But for now I will simply oppose to Unger's nauseating view the following quotations:

The absolute things, the last things, the overlapping things, are the truly philosophic concerns; all superior minds feel seriously about them, and the mind with the shortest views is simply the mind of the more shallow man. (William James, Pragmatism, Harvard UP, 1975, p. 56)

Maximae res, cum parvis quaeruntur, magnos eos solent efficere.

Matters of the greatest importance, when they are investigated by little men, tend to make those men great. (Augustine, Contra Academicos 1. 2. 6.)

See here for a different critical response to Unger.

Van Inwagen on Russell’s Teapot

I thank Jannai Shields for referring me to Peter van Inwagen's Russell's China Teapot and Andrew Bailey for making van Inwagen's papers available on the Web.