Jamesian Philosophy Refreshed

 For fans of the original Star Trek .  Let us remember for a fleeting moment an episode in which Captain Kirk, with some help, defeats a robot that had been holding him prisoner. In part at least this victory is won by telling the robot "I am a liar." The paradox is too much, the robot blows its fuses, and Kirk gets back to his ship.  This is of course a tight version of the old Cretan paradox. The original version was just "All Cretans are liars" spoken by a Cretan. Not much of a paradox at all, actually.  And St. Paul makes a brief reference to it without mentioning its paradoxical nature.   There are lots and lots of Cretans.  For any one Cretan to say "we're such a lying bunch" is not paradoxical. It may seem like to speaker is giving himself too much credit as a supposed exception to that generalization: still, no paradox.  A Cretan might even say " all Cretans are liars" and be considered to have spoken hyperbolically.  Perhaps a commun...

  I quoted, yesterday, the Ivyberry passage from Tennyson's 1880 poem, De Profundis. Today I'd like to say something about what it means, which I will do beneath the image of (21st century) London at Christmas.  Ivy berries (the phrase is not typically written as one word outside poetry) are symbolic of an ability to thrive even in difficult conditions.   In the context of this poem, ivy berries appear right after a reference to grapes. Tennyson is writing from out of the depths of his own experience as, at this time, a man of 71.  "Out of the depths," of course, is the literal English language meaning of the title. Anyway: young folk, strike out into the world! It is your own responsibility to choose between a life of leisure, drinking the fruit of the grape, and a more rigorous challenging life, symbolically drinking of the Ivyberry. W hatever you do, you will help express the fullness of God who is the fountain of which we are all but droplets.  Soon t...

This is a puzzle created by the mathematician Augustus De Morgan. He offered this as a "proof" that 2 = 1, which is (as he understood) absurd, and dependent on sophistical reasoning. Can you spot the flaw?   1. Let  x  = 1.  2. Clearly,then,   x 2  =  x.   3. So  x 2  - 1 =  x  - 1.  Now, divide both sides of THAT equation by x-1.  That 'should' turn it into the following 4. x + 1 = 1.  But since we started by saying that X equals 1, we have now concluded that 5. 2 = 1.  QED.  That plainly cannot be.  But where is the sophism?  The answer begins with remembering a critical point in number theory: don't divide anything by zero.  Ever.  Any chain of inference that involves the division of anything by zero at any point is invalid.   The first proposition above tells us that x = 1. Later we are instructed to divide both sides of a certain equation by x-1.  This...

Had things worked out a little better for him on Tuesday, Bernie Sanders would be in a position to regret his participation in the last round of Democratic Party rule making. There is a paradoxical tone to the situation that I have not seen anyone in print pick up on yet. So I guess I'll have to do it. Sanders is the most Rawlsian candidate in the race. Yet though the Rawlsian notion of justice works for him, the Rawlsian notion of a social contract that depends on a veil of ignorance works at the expense of a procedural position he has taken. To get this, we have to distinguish those two parts of Rawlsian social theory: the idea of the social contract, with of course traditional Lockean roots but filtered through game theory; and the suggested content of the contract, which the contractors supposedly agree to in the Rawlsian model. [That's a portrait of John Locke you're looking at, BTW. ] As to the contract: Rawls said that justice should be understood as the set...

I recently came across the following abstract of a paper on the notorious Liar paradox: The Liar sentence is a singularly important piece of philosophical evidence. It is an instrument for investigating t he metaphysics of expressing truths and falsehoods. And an instrument too for investigating  the varieties of conflict that can give rise to paradox.   It shall serve as perhaps the  most important clue to the  shape of human judgment, as well as to the   nature of the  dependence of judgment upon language use. I don't know what the author of the paper is saying about the sentence "This is a lie," but I am struck by the phrase "piece of philosophical evidence." At law, an utterance is often evidence.  Or a text. But the say that a "sentence" is "evidence" is, fittingly, more abstract.  What does "evidence" mean in that sentence? And is it the same as the usage of "evidence" in the following sentence: "The ...

Grandfather paradox The “grandfather paradox” is an argument used to prove the impossibility of time travel. The idea is that an individual (usually called "Tim" because the name looks a lot like "time") who could travel backwards in time, could kill his grandfather, prior to the conception of his father. But this would imply that Tim’s father would never have been born, and that in turn would imply that Tim would never be born. And if Tim was not born, Tim could not go back in time. This situation leads to a contradiction. Tim both could and could not kill his grandfather. He could (because he would by hypothesis be in the right time and place with a weapon) yet he could not (because he would have to have been born!) And since our “Tim” could be anyone this means that nobody could - that time travel is impossible. Syllogistically, the macro argument is this: Premise 1. If time travel is possible, then contradictions are possible. Premise 2...

There is a new anthology out, a collection of essays by philosophers addressing in their various ways the "Liar Paradox."   I'll discuss the paradox myself today, and then say something about the new book in tomorrow's post. Most people, surely most people likely to be reading this blog, are familiar with most of the following material. I trust you will read on regardless. We begin, as is conventional, with the semi-legendary Cretan seer Epimenides, who is supposed to have said "all Cretans are liars." This is a rather fuzzy non-paradoxical comment, actually. Our tendency is simply to say that even liars don't generally lie all the time. A "liar" is someone who lies out of habit, pathological need, or to take advantage of other people. There is no logical inference that every sentence from the mouth of a "liar" in the ordinary language sense be a lie. So Epimenides may well have been telling the truth.  Over the next couple o...