Does the Fact that Something Exists mean that Nothing is Impossible?

Great Debates
81

Why, sure it does. Open a thread to have a debate about the Prime Minister of the United States. You will be told two things straighaway: (1) that there is no Prime Minister of the United States, and (2) that as a consequence, the position doesn’t even mean anything here.

Well, you were a bit more civil this time, I must say. Still, you are hereby assigned to read Dale Carnegie’s eternal best seller, How to Win Friends and Influence People, linked to herein. Quine, incidentally, was a self-indulgent hack.

Pardon me for interrupting your train of writing, but now that you mention Russel, I see that it looks like you attempted to adapt Russel’s extension of Frege’s theory of descriptions to your assertion about the south pole.

Russel’s whimsical observation about France’s King is formulated something like this.

Let there be a current King of France, called x:
(∃x(Fx))

NB: it is important to note that there was no King of France by that time

And let it be the case that there is not more than one King of France (i.e., if y is the current King of France and x is the current King of France), then:
(∀x(Fx → ∀y(Fy → y=x)))

Aver further that for every King of France (x), the King of France is bald.
(∀x(Fx → Bx))

Russel held that because the first statement is false, then a conjuction of the three statements must also be false (in FOPL, but not necessarily in other logical systems, where the truth condition is more controversial).

In your case, there was no need for biconditionality, nor all the flopping about with respect to xs and ys, because by definition there is only one South Pole. (In Russel’s case, there could have been two Kings of France. Henry VIII of England, for example, took on the title for a time.)

Be that as it may, it just doesn’t come across well in an informal setting like this. The whole purpose of logic is to examine statements for truth. We can talk plainly here, like people in a room. Just because we do so does not make what we say horseshit.

82

You have grossly misapprehended the importance of Russell’s accomplishment. It was not to make some casual observation on the hairiness of the chimerical present King of France.

It was to demonstrate that names (definite descriptions) could be eliminated and all that was needed for a robust logical system was variables, predicates, quantifiers, and identity. (A system, Russell would later endeavor to show in the Principia Mathematica, that is powerful enough to produce all elementary arithmetic.*) Additionally, it asserted the meaningfulness of statements that had names which lacked referents (such as “the present King of France” or “Pegasus”). These statements are false to the extent that they require something in the world which makes the predicate “is-the-present-King-of-France” or “Pegasizes” true. They are just false, and it is quite a thing to say that all false statements are meaningless.

Thus, instead of having to repair to metalinguistic constraints on our sentences (such as your aside that there is only one place called the South Pole) we can instead express those constraints as sentences within the object language itself, as given upthread (which statement would be read “There is an x such that for all y and all z, y is a South Pole iff y=x and no z is more southerly of x.”)

This was Russell’s objective, not any concern with the historical accidents of European royalty.

83

Yes, I know. And with only a few hundred pages of symbology, he (and Whitehead) proved that 1 + 1 = 2. (Never mind Godel for now.) And that’s all fine and dandy. But to be clear, I didn’t say that “there is only one place called the South Pole”. I said that there is only one place that can possibly be the South Pole. It was a straightforward modal claim, not a “metalinguistic constraint on our sentences”. (Speaking of horseshit.)

Since the assertion is modal, there is a much easier way to prove that there is one and only one South Pole. Simply invoke the CD modal axiom. It is already widely accepted, and given that its combination of convergient and serial accessibility relations directly implies a condition on frames such that (wRv&wRu) -> v=u, where w is some possible world, R is an accessibility relation, and v and u are free variables.

So, on any given sphere, a lattitudinal mapping assures us that <>S -> S (CD Axiom). If follows, then, by the modal axiom that S -> S. QED.

84

You use phrases like “modal logic” and you apparently know the shape of the “necessarily” and “possibly” operators (although most logicians just use “L” and “M” respectively) – was this in Gödel, Escher, Bach or something (like “teaching” yourself modal logic through the combined resources of the Wikipedia and Mathworld)? Because I have a difficult time believing you would be exposed academically to that but not the metalanguage/object language distinction, which is pretty rudimentary.

85

Even if Liberal did teach himself, if he’s using it correctly, and his logic can be understood, what’s wrong with that?

86

Here’s a hint: when you say “There is only one place that can possibly be the South Pole” you are not asserting the possibility (the diamond operator Liberal uses), you are asserting the necessity of something (the square operator).

In possible worlds semantics, to say “There is only one place that can possibly be the South Pole” is to say “In any possible world w, there is not a place x that is the South Pole and a place y that is the South Pole and x and y are different places.” This is the form of the necessary operator.

The fact that he misanalyzed something this basic (notice in his exposition, he purports to begin with a diamond statement) sets off my poseur alert, regardless of the fancy (and irrelevant) talk of accessibility relations.

87

Before either of us gets much more snotty about all this, let’s back up and regroup, because you are slinging around quite a lot of, frankly, made up shit. It was I, in my discussions with you who first suggested you sounded like a mixture of Kant and Wittgenstein, and had expressed some good ideas. Let us set aside that it was a compliment that you ignored.

Then, someone began asking or talking about what was south of the South Pole. Obviously, the answer to that question is the empty set. There is nothing south of the South Pole. Later, I remarked that, on any latitudinally marked sphere, there is only one place that can possibly be the South Pole. And at each step in the discussion, you’ve droned on and on, tossing out the ideas put into your head by your teachers and have applied them, as best you can I’m sure, to the topic at hand.

If it is your object to demonstrate that you are smarter than I, then allow me to make that concession if it will facilitate an actual discussion about actual things that actually matter.

I do realize that when I assert a singular possibility which is actual, that I am asserting a necessity. Why you would carry on as though I thought otherwise is a mystery. Why you make the assumptions you do is known only to you. However, one must prove that what is possible is necessary. One cannot simply declare the necessity of a South Pole or anything else, and call that a proof. That’s not a proof; it’s a premise.

Your protestation that a proof of necessity cannot begin with a diamond operator is utterly Neanderthal in its conception. Given <>E, for example, it is almost trivially easy to prove E, where E is defined as the supreme existence. Even the notion of necessity itself is derived from the notion of possibility, inasmuch as is equivalent to ~<>~.

Just because I do not dwell on your particular fixations on linguistics and meta-linguistics does not make me an idiot. I hate to be the one to inform you, but you do not possess the objective point of view, nor is it necessary that your analysis be accepted by anyone else. If you want to make a point then make it.

It has been my experience that autodidacts often have a clearer view than those whose heads have been muddled by academics who have taught the same crap for ten or twenty years for which they have lost all passion. Ramanujan was a self-taught mathematician. Avicenna, Socrates, Abraham Lincoln, George Bernard Shaw, Feodor Chaliapin, Benjamin Franklin, Descartes, Thomas Alva Edison, and Malcolm X — these were all autodidacts. Karl Popper taught himself the philosophy of science. Friedrich Wilhelm Nietzsche never was formally taught philosophy. Leibniz was mostly self-taught.

The list of autodidacts is long, and it would be a foolish thing to look down one’s nose at them. Frankly, your condescension is, I believe, a symptom of your frustration with me, and your inability to beat me down with stating some vague premise about the identity principle with universal and existential qualifiers and declaring, “Voilà! I have proved that I am smarter than everyone!”

And while I’m at it, I wish you would use the expression “more southerly than Y” rather than “more southerly of Y”. What is required is a subordinating conjunction, not a preposition.

Upon review, I apologize for the tone of this post. But you seem to demand confrontation rather than seek a productive discussion among respectful peers. If you are willing to tone it down, then so am I. Let us respect one another.

Your call.

88

Okay, I wasn’t following that he was in error in the modal stuff he was doing, hence my question.

But even still, he never said he was formally educated in the matter (and he just might be, I dunno?), so the way you’re condescending just about everyone in this thread is coming off a tad arrogant (even if you can back it up with your logic skills).

ETA: I composed this before Lib’s reply, FWIW.

89

I was NOT in error about “the modal stuff”, CMYK. Kimmy seems to think he can declare a thing and so mote it be.

And while I’m at it, Kimmy, let me add that the talk about accessibility relations was important because convergient and serial relations combine to form the unique relation, which is what your y=x is.

90

After reading your post, Lib, you have nothing to apologize for. Well said. (speaking as an autodidact myself, in my own profession. A quite successful one at that.)

91

Granted, I felt you were not. But I don’t know two shits about that logic, so I was hoping you’d respond. :wink:

92

I know that your artistic and writing talents are second to none. I’m confident that whatever you pursue, you will always succeed.

Speaking of writers, Mark Twain said, “I have never let my schooling interfere with my education.”

:slight_smile:

93

Ha, a man after my own heart.

94

You’re a poseur.

95

So, I have to know… what’s north of the north pole?

96

And you deserve to be pitted, but I don’t have the time. So let’s just skip what such a thing would degenerate into, and draw your own conclusion about what I think of you.

97

According to Wikipedia, citing a dictionary, the term you have used is a pejorative.

98

Just stick to arguing the logic, and leave the name-calling for the Pit.
If you can persuade the audience, (or, better, your opponent), of your correctness, you will have established your point.
Otherwise it is just name-calling.

[ /Modding ]

99

Meta-pittings do nothing to improve the quality of arguments.

[ /Modding ]

100

It’s a trick question; there’s no such thing as either.

Or to put it another way; if the poles flipped, would “North” then be where “South” was, or would we just call the new alignment “North” and “South”… assuming there was anyone left to name them??