Is Logic Gibberish?

Is Logic Gibberish?

We are familiar with the standard notation of predicate logic in which we have what is called variable binding. Thus we have a symbol for (say) existence followed by an “x” and then a formula in which a predicate and bound variable occur (“Ex(Fx)”). How should we read this? It is common to hear it read as “There exists an x such that Fx”. What does this mean? The letter “x” is supposed to be replaceable by a singular term such as a proper name, a pronoun, or a demonstrative. So, a substitution instance might be “There exists a London such that London is crowded” or “There exists a him such that he is tall”. But these sentences are nonsense; it is not grammatical to place a singular noun in this position. What is wanted is clearly a predicate like “city” or “man”: then we can say “There exists a city such that that city is crowded” or “There exists a man such that that man is tall”. The correct logical form would then be something like “EF(that F is G)”, read as “There exists an F such that that F is G”, where “F” and “G” are predicate expressions. But this is not what logical notation says under the usual reading: this makes sense but that does not. Alternatively, we might try saying that the usual formula is to be read “There exists an object x such that x is F”, so that we have “There exists an object x such that x is a city and x is crowded”. That looks closer to the usual notation, but it contains a funny construction, viz. “an object x”. Put aside whether “object” is an adequate count noun and ask yourself what could be meant by following this word with an “x”. Presumably a substitution instance would be “an object London” or “an object it”: but these are also nonsense. That occurrence of “x” after “E” cannot be replaced by such an expression on pain of producing gibberish. It really doesn’t belong there at all; what belongs there is a count noun or predicate variable replaceable by a count noun, as in “There exists a city such that”. So, predicate logic should not be written in the standard way but rather along the lines of “EF(that F is G)”; otherwise the notation is gibberish. Even that formula has its drawbacks in the shape of the expression “that F”, since it is obviously not deictic and it has no anaphoric antecedent. One wants to say instead “There exists an F, x, such that Gx”, as in “There exists a city, x, such that x is crowded”, so as to have an antecedent to work with. But this also is gibberish, as can be seen by substituting a proper name or pronoun for “x” throughout. There is nothing wrong with saying “London is crowded”, but what is meant by “There exists a city, London”? Is this just a funny way of saying “London exists”? In fact, no one ever translates the standard formula this way, instead saying simply “There exists an x such that x is a city and x is crowded”—which takes us back to our first point. There is simply no intelligible way to interpret this initial occurrence of “x”. Hence predicate logic is gibberish and needs to be overhauled into something that actually makes sense. The whole quantifier-plus-variable symbolism is a mistake.[1]

[1] An Aristotelean might pounce and suggest that Aristotle’s subject-predicate logic is the way to go. Thus, we will have “Some men are philosophers” and “All men are mortal” where the first two words in these sentences are construed as logical subjects. Or else we will need to devise a whole new grammar and notation for expressing logical relations involving “some” and “all”.

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Oppenheimer

I went to see the film the other day. It is commendable in many ways. I liked the moment, surely lost on most viewers, when Einstein says to someone visiting the Institute in Princeton, “Have you met Dr Godel?”–who then disappears for the rest of the movie. But it irritated me that Oppenheimer was depicted as smoking in nearly every scene–when no one else was. Okay, he smoked a lot, but so did everyone else, so why only him doing it in the film? In general I disapprove of depicting smoking in movies, but presumably Christopher Nolan was making some sort of artistic point–but what point exactly? It gave the scientist a sleazy, obsessive appearance, but since heavy smoking was common in those days I’m not seeing that it has verisimilitude. It seemed like a lazy cheap way to suggest insight into character. Much better the high waistbands and western belt buckles.

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Goethe on Italy

I’m reading Goethe’s “Italian Journey”. He remarks during his visit to Rome: “The past year has been the most important one in my life; it does not matter whether I die now or last a while longer, in either case I am content.” People used to ask me whether there was anything about England I missed when I moved to the United States; I would reply, “Yes, Italy”.

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A song for ill people everywhere (the rhyming scheme is the thing)

I Feel So Weak

 

Well, I feel so weak

There’s nothing I can do

I can’t even speak

Or come right over to you

 

I’m a-laying in my bed

Can’t stand on my own two feet

I feel half dead

It’s hard for me to breathe

 

Coz I’m weak

In my physique

Yeah, it’s bleak

 

I can’t play hide and seek

It’s been like this all week

I feel like a freak

I’m balsawood not teak

 

What happened to wear me down?

What entered my blood stream?

All I do is moan and frown

And cry in my dreams

 

Coz I’m weak

In my physique

Yeah, it’s bleak

 

So weak

In my physique

You know it’s bleak

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A short song about dead friends (inspired by Nellie Was a Lady)

Why Did You Die?

 

You were my dear old friend

That word is too short for you

Now you’ve gone and left me

And I don’t know what to do

 

I’d walk with you by my side

On summer days and winter nights

I thought you’d always be around

Like the clear blue sky

 

So why did you have to die?

And leave me here to cry

What harm did I do to you?

That you could ever justify

 

I asked what’s on your mind

I hung on every word

And you hung on every word of mine

We never went unheard

 

There was no doubt in our bond

I could see it in your eyes

But now it’s over and beyond

I’m left with only memories

 

So why did you have to die?

And leave me here to cry?

What harm did I do to you?

That you could ever justify

 

Why did you die?

Oh, why did you die?

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Higher-Order Desire

Higher-Order Desire

As we know from the work of Frankfurt, it is possible to have second-order desires directed at first-order desires. For example, the prudent alcoholic may decide, upon reflection, to reject or moderate his desire for alcohol: he desires not to desire alcohol, or to act on that desire. He thinks about his first-order desires and assesses their desirability, coming to the conclusion that they are not, all things considered, desirable desires to have. He might succeed in suppressing them, or at least reducing their hold over him. In this he exercises one kind of freedom (freedom from first-order desires). Apparently such higher-order reflection is not available to animals or young children—they are slaves to their first-order desires (for food, sex, aggression, etc.). They can’t distance themselves from their given first-order desires by reflecting critically on them.

            But that is not the end of the story. We can also reflect on our second-order desires: we might decide that too much second-order regulation of first-order desires leads to an unspontaneous and wizened life-style. We might think we need more Rousseau and less Kant in our lives, more D.H. Lawrence and less Saint Augustine. We might even decide that W.C. Fields would be a good role model (more fun, less gloom). We therefore undertake to lessen the impact of our puritan self and adopt a more childlike persona. That is, we have a third-order desire to modify the power of our second-order desire to exercise more control over our first-order desires. We decide to “let it all hang out”, or at any rate more of it. Wouldn’t it be nice to live the life of a carefree unreflective beast? Better than some uptight cardinal or moral philosopher who has read too much Kant! So, we adopt the first-order life-style and enjoy it for a while, but then we tire of the hangovers and general lack of moral seriousness. After a period of reflection, we decide to let our second-order desires have freer rein; this requires us to suppress our previous third-order desire to inhibit our second-order desire to have more control over our first-order desires. That is, we now have a fourth-order desire, occasioned by reflection on our previous higher-order desires. And so on. There seems to be no end, in principle, to this ascension of levels, though no doubt it gets more cognitively cumbersome the higher it goes. Perhaps in the end the agent assumes a position indistinguishable from that of the child or animal but only after a long series of reflective higher-level desire formations. Evidently things are much more complex than the simple binary distinction of first- and second-order desires. It isn’t just that humans can ascend from first-order desires to second-order desires; they can also scale a whole hierarchy of desires directed at other desires.

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Bob Dylan’s Philosophy

I just finished reading Bob Dylan’s The Philosophy of Modern Song. There is no philosophy in it but plenty about song. He clearly has never read any philosophy of music, or perhaps any philosophy at all (bit of Nietzsche maybe). I don’t know what he means by “Modern Song”: certainly there is nothing classical in it, though it ranges from 1849 onwards. Folk, rock, blues, Broadway, country–it’s all there. For me the biggest takeaway was the song “Nellie was a Lady”, which I had never even heard of before. Written by a white man about a freed slave’s dead wife, it is as sad as songs get (as Dylan points out), but with a beautiful melody. The lyrics are problematic and could not be sung today without an uproar (modern renditions update them completely), but it is a great song. Thanks, Bob.

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Ordering Philosophy

Ordering Philosophy

Does philosophy consist of a bunch of more or less unconnected problems or is there a pattern to its problems? Is it possible to order philosophy in a natural and illuminating way, with some areas leading naturally to others, or is it that there is just a loose association of problems that historically we label “philosophy”? Is there a root from which it all springs or is philosophy like a garden made up of different plants (metaphysics, epistemology, logic, ethics, etc.)? I will argue that there is such a root, so that there is a natural order to the various sub-departments of the field. This thesis should shape the way philosophy is taught: it provides a philosophy of philosophical education.

            Let me begin with what I shall call the “confident error problem”. This is very familiar to all human beings: not only are we sometimes (often!) wrong about things, we are also very confident that we are right. It isn’t just that we are fallible (it’s a big world and our powers are limited); we are mistaken even when we are totally convinced, supremely confident, and completely certain that we are right. And we are not just wrong but embarrassingly wide of the mark, not even close to being right. This is bad. We are aiming at knowledge, we are sure we have achieved it, and yet we are in complete error. Chagrin is the only reasonable reaction—shame, humiliation. Socrates could make people see this all the time.[1] It is not desirable; it is not admirable. It should be avoided. We therefore need to understand why it happens and take steps to prevent it from happening. But that isn’t easy: the world is full of illusions, people tell lies (or make honest mistakes), we harbor many prejudices, our reasoning ability is limited. Thus, the field now known as epistemology begins—not with a bang but with a whimper (why-oh-why do we fall into such errors?). It seems part of the human condition, but it’s also possible to correct it. We just need to think harder about the problem.

            It is easy to see how this problem could lead to inquiries familiar to us from the history of philosophy. First, we need to know what knowledge is; then we will know what it is that is so prone to error. If we have an analysis of knowledge, we will have a breakdown of what needs to be achieved to gain real knowledge. Second, we need to understand perception (including perceptual errors), because this is our primary way of acquiring knowledge of the natural world. Third, we need a good account of reasoning so as to ensure that error does not creep in because of faulty reasoning. This will usher in the study of logic in the broadest sense (induction as well as deduction). We need a general theory of justification. This will include a theory of irrationality—what leads people to irrational beliefs. Inevitably this will lead us to general considerations about the relation between mind and world, since knowledge clearly is some kind of relation between the mind and the world outside the mind. The confident error problem is obviously some kind of mismatch between our mind—our thoughts—and the world we think about—objective reality. If we made no such errors, we would not be compelled to make this distinction; we could lazily acquiesce in a kind of monism of mind and world, since the two never diverge. What we think there is would always be what there is. Epistemology occurs to us because of the possibility (frequency) of error; without error it wouldn’t have the same urgency.

            But these epistemological questions quickly raise other questions typically expressed in other words (we shouldn’t assume that philosophy always felt as fragmented as it does today, what with specialization and university curricula). It gives rise to the discipline we now call metaphysics (or ontology). For we now need a description of the world if we are to understand its relation to human knowledge. To what extent is the world dependent on the mind (the issue of realism)? Might it be a projection of the mind (idealism)? Is it such as to be knowable at all? Does perception reveal its full nature? What if it consists of atoms in the void? What if it is ultimately spiritual? For example, we think we have knowledge of causation, but what is causation such that it is knowable by our minds as they are constituted? How do we know about necessity? Well, that depends on what necessity is. What about mathematics, or other minds, or our own mind? We need an account of reality in order to understand how our minds grasp it, or fail to. Thus, epistemology brings metaphysics in its wake; or better, a single field is created that combines inquiries into knowledge and reality. Notice that according to this picture epistemology comes first: it is what gives rise to metaphysics as we historically find it. We don’t just start thinking about metaphysics for no particular reason; we do so because epistemology can’t proceed without it. If we want to know whether perception reveals the objective nature of physical objects, and hence enables knowledge of their properties, we need some idea of what these properties are, and this is the subject matter of metaphysics. The original impetus for metaphysics comes from epistemology, as shaped by the problem of error.

            But what about the mind-body problem—how does that fit into this genealogical picture? As follows: once we start thinking about the relation between mind and world, we cannot help wondering how the mind relates to the body. Thinking about perception will lead us to think about the brain as the terminus of sensory stimulation, but then we have to ask how brain events relate to conscious perceptual events. Is the mind really just the brain, so that the mind-world problem becomes the brain-world problem? We are thus plunged into the mind-body problem by reflection on how the mind relates to the world. The philosophy of mind naturally arises from the problems of epistemology; it is one aspect of those problems. It isn’t so much that we have to refute the skeptic, a la Descartes; rather, we have to produce an account of how knowledge works, which requires an account of the mind (and the world). Skepticism is just one response to the problem of confident error; that problem exists whether or not skepticism can be refuted.

            How about ethics—how does it arise from the error problem? It arises because ethical error is common and dangerous; it is the domain of confident error par excellence. How can we guard against ethical error? That question can’t be answered without an account of ethical truth—a theory of right and wrong. So, we get subjectivism, emotivism, relativism, and allied doctrines—as well as moral realism, cognitivism, etc. We need a moral psychology, and a moral metaphysics. Ethics is just one more example of how the problem of error can generate the subject we now call “moral philosophy”. Aesthetics is similar: how can we protect aesthetic judgment from the vagaries of human knowledge? For that we need an account of beauty (etc.) and an aesthetic psychology—more metaphysics and philosophy of mind. Ethics and aesthetics are not sealed off from epistemology but link to it in non-trivial ways; the confident error problem is the common thread.

            Theory of meaning and philosophy of language generally are natural offshoots of epistemology. Knowledge is a propositional attitude (or some of it is) and hence we need an account of propositions—contents of thought, meanings of sentences. Concepts are elements of propositional attitudes. Evidently propositions do not stand in the way of error; they conduce to it. We do well to understand them if we want to combat error. We may become interested in them in their own right, but they directly link to issues in epistemology; similarly, for spoken words (just think of Frege on sense and reference). The case of action and the will is something of an outlier, but even here we have links to epistemology: for (a) we have knowledge of our actions (a special kind of knowledge apparently), and (b) action results from knowledge (or what passes for it). The error problem is particularly acute in the case of action, because actions performed from error are unlikely to be successful actions. Actions need to be rational and based on knowledge not ignorance. Successful volition needs to be connected to competent cognition. Perhaps this subject (the “philosophy of action”) will come as an afterthought, but it is not completely removed from epistemological concerns. And let’s not forget philosophy of religion: it too is full of epistemological questions. Can we know that God exists and by what means? Is God all-knowing? What is the ethics of religious error? Is faith a way to gain knowledge? Fear of religious error is potent and difficult to prevent—wars have been fought over it! We are an error-prone species and we don’t like it (in ourselves and others); philosophy has its roots in error avoidance, and this concern permeates the field as a whole. It isn’t just a hotch-potch of unrelated problems (a list) but more like a tree structure. A natural way to teach it would be to proceed according the map sketched here, which is discernible in the history of the subject. Philosophy is what you do when faced with the problem of error, especially the persistent confident kind. Is this why philosophers are so obsessed with correcting each other’s errors?[2]

[1] Socrates’ treatment of Euthyphro is the prime example: the latter is completely confident that he knows what the “holy” is, but Socrates quickly demonstrates that he has no idea. Without such encounters Socrates might have avoided philosophy altogether. Plato, too, was obsessed with the existence of error, as with the cave analogy.

[2] Knowledge is very important to human beings, but error is its ever-present enemy. Philosophy arises from this tension—between the love of knowledge and its manifest difficulty. I myself have a visceral hatred of error; perhaps that of why I became a philosopher instead of a psychologist.

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