In elementary logic the first steps mark out how normal (for my purposes, English) speech is used in deduction. Propositional logic discusses the ways in which complex (or compound) statements are constructed from atomic (or simple) statements. One of the ways this happens is the “conditional.” A conditional combines two statements like “the sky is blue” and “the grass is green” by connecting them with “if” and “then” as “If the sky is blue, then the grass is green.” Statements, compound or simple, such as these are thought to have a “truth value.” That is, they may be assigned one of the values, True or False. One can argue about this (and make money doing it) but I’d like to narrow the focus a bit and assume away some of the complexity.
When absolute precision is important in language, where consistency must be guaranteed and where jargon is fixed without nuance, the conditional is usually defined by the adjective, “material.” This gives a careful way of determining the truth value of a conditional, based on known or assumed truth values of the parts of the conditional, known as the antecedent (the “if” part) and the consequent (the “then” part).
For a material conditional, expressed symbolically as “if A then B,” the conditional’s truth value is determined by the following table:
|A||B||If A then B|
Some people are puzzled by the last line in the table, but it makes the conditional consistent with natural truth values of related compounds formed like “A or B,” or “A and B.”
This is all very beautiful as a system and is self-consistent, not yielding to inherent contradiction for example. In the very precise speech environments found in logic or mathematics, this is the foundation of discourse. But it is not the only way of doing things, and it is by no means a complete description about how conditionals occur and are used in ordinary or disciplinary situations. Poetic usage, or historical discussions can make a hash of this and it clearly does not fit in many such situations where flexibility and purposeful confundity may be useful and even necessary.
Specific to the conditional, outside the material version, is the “contrafactural” or counterfactual. A contrafactual in conditional form is a conditional like this one:
If the Nazi’s had won World War II, then American citizens would speak German.
How do we judge the truth value of such a statement? It does not seem dependent on the truth value of the antecedent or consequent in the same way as the material conditional scheme. On the other hand, we might feel comfortable arguing for it somehow, via discussions of Nazi policies, the nature of continental politics, or some such. We might argue that more precision is required to judge the truth of the statement. Should we assign this statement a truth value? The antecedent and consequent seem obviously “false” in terms of the facts. The contrafactual conditional seems to require a causal relationship between antecedent and consequent for its validity. It’s truth seems determined by that validity of causality, although we might be somewhat uncomfortable assigning the value “True” (or False) to the statement above.
Enter, Lehi (2 Nephi 13):
13 And if ye shall say there is no law, ye shall also say there is no sin. If ye shall say there is no sin, ye shall also say there is no righteousness. And if there be no righteousness there be no happiness. And if there be no righteousness nor happiness there be no punishment nor misery. And if these things are not there is no God. And if there is no God we are not, neither the earth; for there could have been no creation of things, neither to act nor to be acted upon; wherefore, all things must have vanished away.
The text supplies us with a string of contrafactuals that are designed to logically point to an absurdity, appealing to Reducito ad Absurdum. In other words, the text assumes the correctness of the Law of Excluded Middle, apparently.
The string of statements in verse 13 is a part of a larger chain of statements, each of which claims a metaphysical causality. The chain is linear and appears like this.
1. if ye shall say there is no law, ye shall also say there is no sin.
This and the other conditionals are exhibited as oral statements “if ye shall say” but might be rephrased as “if you would say.”
1. if you would say there is no law, you would also say there is no sin.
2. If you would say there is no sin, you would also say there is no righteousness.
3. if there be no righteousness there be no happiness.
4. if there be no righteousness nor happiness there be no punishment nor misery.
5. if these things are not there is no God.
6. if there is no God we are not, neither the earth;
for there could have been no creation of things, neither to act nor to be acted upon;
wherefore, all things must have vanished away.
Only conditionals 1 and 2 appear explicitly in contrafactual form, though they might be stated otherwise, and some of the others seem to be somewhat disguised contrafactuals. Note that the argument appeals to the Cosmological Logic: there has to be an antecedent cause for any “thing.” On that score alone, I think the argument fails, but it probably felt good to the people who heard it.
A Calvinist in Mormon Clothing
One of the more puzzling contrafactuals in Mormonism appears in the recital of a vision experienced by Joseph Smith. Some decades ago, parts of it became canonical. The text of the vision report comes from Joseph Smith’s diary under the date January 21, 1836. Smith did not make the diary entry himself, but that was not unusual. He rarely kept his own diary.
The heavens were opened upon us and I beheld the celestial kingdom of God, and the glory thereof, whether in the body or out I cannot tell,— I saw the transcendant beauty of the gate
that enters, through which the heirs of that kingdom will enter, which was like unto circling flames of fire, also the blasing throne of God, whereon was seated the Father and the Son,— I saw the beautiful streets of that kingdom, which had the appearance of being paved with gold— I saw father Adam, and Abraham and Michael and my father and mother, my brother Alvin [Smith] that has long since slept, and marvled how it was that he had obtained thisan inheritance <in> this<that> kingdom, seeing that he had departed this life, before the Lord <had> set his hand to gather Israel <the second time> and had not been baptized for the remission of sins— Thus saidcame the voice <of the Lord un>to me saying all who have died with[out] a knowledge of this gospel, who would have received it, if they had been permited to tarry, shall be heirs of the celestial kingdom of God— also all that shall die henseforth, with<out> a knowledge of it, who would have received it, with all their hearts, shall be heirs of that kingdom, for I the Lord <will> judge all men according to their works according to the desires of their hearts
(josephsmithpapers.org has facsimiles and transcriptions for the diary.)
Joseph is surprised by this experience, seeing his long dead idolized brother Alvin in a Heaven clearly marked out by an 1832 vision as reserved for those who are strict adherents to the rules and commandments of that early vision, including baptism into the new and everlasting covenant (of Mormonism). The end case for Alvin, and apparently for all who have ever lived on the earth, is determined by (perhaps not in a resultant sense, but in an absolute sense) the foreknowledge of God. Joseph never explicitly retreats from this, but he does change things up a bit. No, you can’t really bypass the liturgy, but you can get it by proxy. It’s interesting that his 1836 vision seems to have had little circulation among Latter-day Saints of the era. He also never retreats from his compatibilist position on free will, though he holds on to it in a fashion that is logically inconsistent–he never explored that logic.
Contrafactuals appear in many other religious contexts, and at times their logic seems baffling. Look for some others if you will.