Tuesday, March 31, 2009

Fallacy of the Temporary Name

This is a formal logical fallacy that many, many otherwise bright people fall into from time to time. In formal symbolic logic, of one has asserted or proven an existential quantifier, it is a valid line of arguement (known as E-elimination) to imagine an object that fulfills that existential quantifier.

For instance, I was riding the light rail yesterday. At that time, I could assert the premise, "Someone is driving this train." It would follow in a valid way that I could argue "Let's call the driver of this train 'Elvis'." Something similar happens in geometry: One begins (for instance) by asserting "A triangle exists", and then one can assert in a valid way "Let's call said triangle 'ABC'." So good so far.

How is E-elimination useful? Let's take a more comlex arguement. In our light rail arguement, we can accept another premise - a universal one this time - that "For all x, if x is a light rail driver, then x works for the MTCO." Taking our previous premise of "Someone is driving this train", or more formally "There is an y, such that y is a light rail driver". Then E-elimination allows us to say "We'll call y 'Elvis'. 'Elvis' is a light rail driver." This assertion then allows us to say "Since 'Elvis' is a light rail driver, and all light rail drivers work for the MTCO, then 'Elvis' must work for the MTCO." Then we wrap things up by asserting "There is an x, such that x is an employee of the MCTO" A valid arguement. If we had a more complicated arguement, we can continue to assert in a valid way that 'Elvis' is an employee of the light rail - that's a quality 'Elvis' has been proved to have working simply from already established premises. The limitation to 'E-elimination' or as it's sometimes called 'giving a temporary name' is that no other information can be asserted by the temporary name than what has already been proven from the arguement, and the choice of the temporary name should reflect that.

The fallacy of the temporary name is when that limitation is violated. Let's go back to our example. We could add another premise, "For all z, if z is Elvis, then z is the king of rock and roll." Wow! We've already named our light rail driver 'Elvis'! How convenient - we can use our new premise to prove that the light rail driver is the king of rock and roll. The king of rock and roll is alive and well, and driving light rail trains in Minneapolis.

Ummm.... not so much. That's the fallacy of the temporary name - an incorrect choice of the temporary name has led us from true premises to a false conclusion. We have an invalid arguement. With Elvis and the light rail train, it's pretty easy to see. But consider another arguement (sometimes known as the 'watchmaker arguement':

Premise 1) "For all x and n, if x is a system above a number n, then that system requires a designer" (We'll postulate that this is true)

Premise 2) "for all n, n is an arbitrary measure of complexity,"

Premise 3) "For all b and m, if b is the system of biological life on Earth then b has a complexity of m"

Premise 4) "There is a b, such that b is the system of biological life on Earth"

Premise 5) "Both m and n are numbers, and m is equal to or greather than n"

Premise 6) "For all y, if y requires a designer, then there must exist q, such that q designed y"

Premise 7) "For all z, if z is God, then z so loved the world that he sent his only begotten son."

What comes of this arguement? Well, Premise 3 and 4 together say 8) that there is a b* that has a complexity of m. (b* being a temporary name for the object whose existence is asserted in 4). Lines 8 and 5 say 9) that b* has an m larger than n. Lines 9 and 2 assert that 10) m is a measure of complexity. 10, 4, and 1 all come together to say that 11) the system of biological life on Earth requires a designer. 11 and 6 together say that 12) there is a q such that q designed the system of biological life on Earth. This is all kosher so far, and if one accepts the premises as true, then one has reached a true conclusion. But if we use E-elimination incorrectly and say "Let's call q 'God'", then we go on to argue "Since we've proven that there must have been a designer of biological life on Earth, and that that designer is God, and since we know God so loved the world that he sent his only begotten son, then God must exist as stated in John 3:16!"

This is a fallacy of the temporary name. The only thing we can use this arguement for is proof that something designed the system of biological life on Earth. We can say nothing else about that something unless we can prove that those qualities adhere to the something, and aren't predicates of whatever name we arbitrarily selected. If we had selected 'George' as the temporary name of the designer, then we would only be able to say that something exists that we've decided to name 'George', not that the God of Abraham, Jesus, and Mohammed must exist necessarily exist because of the complexity of life on Earth.

Googlebombing for a cause: www.minnesotangos.org 


phaedrus said...

Premise 1) "For all x and n, if x is a system above a number n, then that system requires a designer" (We'll postulate that this is true)

The argument lost my agreement there, but I got the point you were making - even if we took that premise to be true, the argument says there is a creator, but does not say that any particular version of that creator exists.

Thanks, I get what the "Fallacy of the Temporary Name" is referring to now.

I'd be interested in finding a situation where I'm likely to be taken in by it, because while _some_ people obviously think the watchmaker argument implies the god described in the bible exists, that's always seemed kind of silly to me. Handy to know what to call the mistake they're making.

Lord Carnifex said...

Some of the great names of philosophy run afoul of this one.

For example, there's Anselm's ontological proof of god: "I can imagine a being perfect in all ways including existence. Such a being must exist to generate the image of itself in my mind. We'll call that being God."

Buy this one or not if you like, but all he's proved is the existence of a being perfect in all ways, including existence. He has not proved is this being is the God of Abraham and Isaac, or divided into three parts, or sits in a lotus, or is Plato's ideal Form of the Good.
Similarly, both the Greeks and the Medievalists liked, "All phenomena have a cause. There must be an unbroken chain between effect and cause back to an initial cause that caused all others, including itself."

Handy enough. But they still haven't proved that their uncaused cause narrowly avoided being eaten by His father, or took up His prophet from the Temple Mount, or appeared to a half-Egyptian as combustive shrubbery.

phaedrus said...

It seems like the Greek and Medievalist example has both that fallacy and another weakness as it discounts the possibility of an infinite unbroken chain