|Doppler effect of water flow around a swan. [A]|
Suppose I tell you "Joe is a man". We can -- hopefully readers will agree -- abbreviate that sentence: M. (Think of stenography.)
Now, we may say: if Joe is a man, then he must have testicles and penis. Yes? This longer sentence is formed by "Joe is a man" and "Joe has testes and willy", joined by a connective ("then").
As we did before, let's abbreviate the sentence "Joe has testes and willy": T.
We could also write the compound sentence "if Joe is a man, then he has testes and willy" in our shorthand system [#]:
(1) M => T.
Hopefully, this should not confuse anybody. As magicians say: nothing on this hand, nothing on the other.
Would it be legitimate to conclude that "Joe is a man"? Don't rush, think things calmly.
Personally, I think it is perfectly legitimate and I trust you'll agree (or you may post a comment, arguing your opposition).
However, that means that the fact "Joe has testes and willy" implies that "Joe is a man"; in other words "if Joe has testes and willy, then Joe is a man":
(2) T => M.
"So?", you might ask. "That's trivial".
It is, isn't it? But compare (1) and (2) -- or the sentences in bold. Notice something?
In (1) we start in one sentence (M), move to the second (T); in (2) we do the opposite. Together, we have a cycle (from the Greek kuklos "circle"): we start with M and finish with M. It could go on and on!
"Wait a minute!", you might be saying excitedly. "That's a circular argument!"
Why, yes. Yes, it is.
That's when I ask: So?
"But, but, but, you are contradicting yourself. You just said this argument was 'perfectly legitimate'. Now, it turns out, you admit the argument is circular. Aren't circular arguments always fallacious?" you might ask.
Well, no, they aren't. Some circular arguments may well be fallacious, but there is no fallacy whatsoever in this particular circular argument: it's really trivial. That's its "magic".
When sentences convey the same information with different wordings -- as they do in this purposefully simple example: "Joe is a man" and "Joe has testicles and penis" -- they imply each other and are said to be equivalent; that situation is symbolised thus:
(3) M <=> T [*]
That's standard fare in logic.
One example -- apparently contentious -- is the redshift shown by light from astronomical objects moving away from Earth (an instance -- involving light or other electromagnetic radiation -- of the Doppler effect). A star approaching Earth, for instance, cannot present a redshift, anymore than a woman can have a penis and testicles (just look at the white swan, above). In other words, the redshift is a sufficient condition to infer increasing distance, just like Joe's junk suffices to infer his masculinity.
Conversely, knowing that a star moves away from Earth is enough to predict a redshift in its light, just like Joe's masculinity is enough to predict the presence of junk in his crotch: redshift, in other words, is equivalent to increasing distance, just like crotch-junk is equivalent to masculinity.
More briefly: redshift and increasing distance have a relationship symbolised by (3).
Come on, econosophers, this is neither that difficult, nor is it cutting-edge science -- if it were either, I probably wouldn't understand it.
Let me put it this way: New Horizons did manage to rendezvous -- within schedule -- with Pluto (4.7 billion kilometers from Earth), nearly 10 years after launch. NASA scientists and technicians thinking "funny" things scored one point.
[#] For the more demanding (or punctilious, depending on one's perspective) reader: the "arrow to the right" (=>) stands for "if … then … ".
[*] In the slightly more technical jargon of logic and mathematics: "Joe is a man" if and only if "Joe has penis and testes"; or "Joe is a man" is a necessary and sufficient condition for "Joe has his junk".
[A] "Doppler effect of water flow around a swan." Author: Zátonyi Sándor, (ifj.) Fizped. The author's endorsement must not be inferred from my usage of the file :-). Image licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Source: Wikipedia.