Laws Of Discourse

In Poul Anderson's Is There Life On Other Worlds? (New York, 1963), Chapter 7 is "Other Minds." After two introductory paragraphs, the first section of Chapter 7 is "Laws of Discourse."

I agree with Anderson that human and non-human beings should be able to communicate about mathematics, science and practical matters. There should be no "incomprehensibly alien." (p. 130) Carl Sagan suggests in his sf novel, Contact, that someone who transmits a single beep followed by an arbitrary symbol, then a second single beep followed by a different arbitrary symbol, followed by two beeps has taught anyone who receives the signal his symbols for "plus" and "equals" and can then proceed to the rest of mathematics and engineering.

Instincts will differ but "...intelligence is, by definition, liberated from instinct." (ibid.) Mutually incompatible world views should not matter:

"A Christian, a Hindu, and an atheist...if they are all reasonable men...can follow each other's trains of thought and reach agreement on just what the areas of disagreement are.
"Moreover, they could all be scientists, in complete accord about their work." (p. 129)

"...if they are all reasonable men..." I have discussed the New Testament with a Presbyterian minister who was a fellow philosophy graduate. No problem. When I remarked that there are Christians with whom dialogue is impossible, he agreed with me. Some Evangelicals merely assume the truth of their belief and cannot establish any common ground for discourse with anyone else. They see no difference in meaning between the propositions "According to my belief, you are damned," and "You have consciously chosen damnation." I find that frightening. If aliens encountered a human community of that mind-set, then there would certainly be communication problems.

Anderson rightly defines "logic" as formal principles for symbol manipulation. (p. 128) He says that logic has four postulates but only tells us the first: "p or p implies p." I studied only a very basic course in symbolic logic a long time ago. I would have thought that "p implies p" or "if p, then p" was sufficient, other such propositions being:

not (p and not-p);
either p or not-p;
if p, then not not-p;
if (if p, then q) and p, then q.

Anderson rightly says that anyone who denies the principle of non-contradiction, i. e., not (p and not-p), can prove anything and therefore nothing:

1 p and not-p
2 p                from 1
3 p or q         from 2
4 not-p          from 1
5 q                from 3 and 4

q can be any proposition, even one known to be untrue.