- Induction is "the process of deriving general principles from particular facts or instances." That is how scientific theories are developed, in principle. That is, a scientist begins with observations and devises a theory from them. Or a scientist may begin with an existing theory, note that new observations do not comport with the theory, and devise a new theory to fit all the observations, old and new.
- Deduction is "the process of reasoning in which a conclusion follows necessarily from the stated premises; inference by reasoning from the general to the specific." That is how scientific theories are tested, in principle. That is, a theory (a "stated premise") should lead to certain conclusions ("observations"). If it does not, the theory is falsified. If it does, the theory lives for another day.
One realm into which scientists often venture, with equally invalid effect, is the realm of theology. It seems that scientists can't resist atheism, which is an utterly unscientific stance because it assumes an empirically untestable fact, namely, that there is no God.
At least one scientist has tried to work around the empirical obstacle to atheism by trying to prove with logic that there cannot be an omniscient God. After all, he probably said to himself, if God isn't omniscient, then He's not much to reckon with. Now, I have no problem with agnosticism (being an agnostic myself), which is perfectly defensible from a scientific viewpoint, but I do have a problem with scientists who try to sneak unscientific atheism into their science, so I must expose the error of this particular scientist's ways.
John D. Barrow, an English astronomer, wrote a book called Impossibility: The Limits of Science and the Science of Limits (1997), which I recently began to reread. I encountered this on page 13:
We [pompous ass: ED] began this section by introducing the familiar idea of a god who is ominiscient: someone who knows everything. Ths possibility does not immediately ring alarm bells in our brains; it is plausible that such a being could exist. [Note that he says "plausible" and not "possible": ED] Yet, when it is probed more closely one can show that omniscience of this sort creates a logical paradox and must, by the standards of human reason, therefore be judged impossible or be qualified in some way. To see this consider this test statement:If that's too convoluted for you, here's a more straightforward version:THIS STATEMENT IS NOT KNOWN TO BE TRUE BY ANYONE.
Now consider the plight of our hypothetical Omniscient Being ('Big O'). Suppose first that this statement is true and Big O does not know it. Then Big O would not be omniscient. So, instead, suppose our statement is false. This means that someone must know the statement to be true; hence it must be true. So regardless of whether we assume at the outset that this statement is true or false, we are forced to conclude that it must be true! And therefore, since the statement is true, nobody (including Big O) can know that it is true. This shows that there must always be true statements that no being can know to be true. Hence thaer cannot be and Omniscient Being who knows all truths.
1. Statement X -- which is either true or false -- asserts that no one knows it (the statement) to be true. In plainer words than those used by Barrow:This is all verbal sleight of hand. Here's the trick:X: NO ONE KNOWS THAT THIS STATEMENT IS TRUE.
2. If X is true (that is, if no one knows that X is true), and an omniscient God knows that X is true, then the omniscient God cannot be omniscient because the true statement is that no one knows of its truth. If no one knows of its truth, there cannot be an omniscient God.
3. If, however, X is false, then someone knows that X is true. And if X is true, no one knows that it is true. And if no one knows that it is true, there cannot be an omniscient God.
1. Barrow's statement is really a variant of the Epimenides paradox: Epimenides was a Cretan who made one immortal statement: "All Cretans are liars." Accepting, for the sake of argument, that Epimenides was a Cretan and that all Cretans are liars (all of the time), one reaches two contradictory conclusions:
a. If Epimenides was lying, as he must have been as a Cretan, then all Cretans are not liars.2. One problem with the Epimenides paradox, as with Barrow's statement, is its self-referentiality. This can be shown by restating it properly:
b. But if all Cretans are not liars, then Epimenides was telling the truth, which is that all Cretans are liars.
EPIMENIDES SAYS THAT ALL CRETANS ARE LIARS (ALL OF THE TIME).Therefore, nothing. Epimenides, as a Cretan, could not assert a possibly truthful statemtent about Cretans ("All Cretans are liars") because he called himself a liar to begin with. Barrow's statement is more obviously self-referential:
EPIMENIDES IS A CRETAN.
THEREFORE, . . .
BARROW SAYS THAT THERE IS A STATEMENT "X" THAT IS NOT KNOWN BY ANYONE TO BE TRUE.Therefore, according to Barrow, there is a statement X that says that it (statement X) is not known by anyone to be true. That's all Barrow has "proved."
STATEMENT "X" IS "THAT THERE IS A STATEMENT THAT IS NOT KNOWN BY ANYONE TO BE TRUE.
THEREFORE, . . .
2. Barrow's statement suffers from more than self-referentiality. It is nonsense. It asserts that "this statement is not known to be true," without specifying what it is about the statement that is not known to be true. A statement that purports to be either true or false has no meaning if it does not assert something that can be adjudged true or false.
3. But Barrow's statement is worse than nonsense because it also asserts an unprovable fact, namely, that "this statement is not known to be true by anyone." One can never know if a particular thing is not known by anyone.
Consider this equivalent piece of nonsense:
BARROW SAYS THAT THERE IS A STATEMENT X THAT IS NOT KNOWN BY ANYONE TO BE TRUE.Barrow's statement, in sum, is a piece of nonsense, deployed in an attempt to proved the unprovable (the non-existence of an omniscient God) through flawed (self-referential) logic, which hinges on an unprovable premise ("this statement is not known to be true by anyone").
STATEMENT X IS JABBERWOCKY.
THEREFORE, THERE IS A STATEMENT X THAT IS JABBERWOCKY, AND WHICH BARROW SAYS IS NOT KNOWN BY ANYONE TO BE TRUE, ALTHOUGH SAYING THAT A STATEMENT IS JABBERWOCKY IS NONSENSE AND NOT A MATTER OF TRUTH OR FALSITY. AND SAYING THAT A STATEMENT IS NOT KNOWN BY ANYONE TO BE TRUE IS AN UNPROVABLE ASSERTION.
Barrow, in his anxiety to disprove the existence of an omniscient God, chose to doff his scientist's hat and put on his atheist's hat. As a scientist, Barrow should have known better than to try to prove the unprovable -- or I should say, to disprove the undisprovable: the existence of an omniscient God.