Is Reality Consistent with First Order Predicate Calculus?

The whole of science is based on answering yes to that question. But what about religion? At least from Augustine to Aquinas, people hoped the answer was yes. Of course, they wouldn’t have used the same terminology.

First order predicate calculus (FOPC) — if you don’t know what it is, I suppose we could summarize it as the model for deductive reasoning — it is a complete system. Self-consistent. Not decidable, but perfectly reliable. You can’t derive contradictory statements in it. It’s deductive logic.[1] Whitehead and Russell[2] learned by sad experience that not everything we may think is fundamental in human thought can be derived from FOPC. You need extra assumptions to do that. And those extra assumptions may introduce paradoxes. Shudder.

Many thoughtful human beings tend to organize human knowledge (perhaps knowledge is too strong a word) step-wise, based on perceived reliability. We might think in terms of concentric circles, one inside the other, growing ever larger. The inside, the most sure, the most reliable is logic itself, the theorems of FOPC if you like. Now *that’s* reliable. Then (I can hear the squeamishness) mathematics. What’s more reliable than 2+2=4?[3] Then the hard sciences. I’m bundling them together. Physicists may dither. Then whatever is left, perhaps I should say whatever “truths” (things accepted as fact, say) are left over from the other various branches of human endeavor. Does religion fit in this outer circle? Can it? In particular we may ask, does Mormonism fit there? Is reality characterized by this list? The answer is surely no, unless we somehow expand it to some kind of potentially discoverable truth. Is known truth? (Well by definition, right?) A list that somehow includes black holes and “Winged Victory” should be fairly comprehensive nevertheless.

For Mormons, and many religious believers, revelation from God must count as truth in the strongest of ways and therefore must fit in at least the largest circle. But perhaps it belongs in the innermost circle. Right up there with FOPC. Is it *more* reliable than FOPC? An obvious problem with that is revelation is not given in symbolic logic formulae. It appears in the lingua franca of the day. Spoken by non-logicians, often unaware of the subtleties of communication. So then finally, can FOPC and prophetic communication (assuming it’s from God) circumscribe paradox? My guess is that believers aware of the meaning here would say NO. (This might raise the ugly question as to whether God is not ruled by reason but freely indulges in true contradiction – I think there is enough evidence from Mormon teachings to suggest this is not worth considering as an option for Mormonism — apparent paradox is often explained by a simple lack of knowledge of the purpose and plans of God). As we move to circles broader than that of FOPC, may revelation and those “truths” circumscribe paradox? I would venture to say that most folks would allow the possibility.[4] Things in the broader circles may be “less sure,” i.e., their status is often contingent on further evaluation. After all, what else keeps the humanities and social sciences in business?

Now, revelation may be thought of as sitting in its own set of circles. What might come in the next circle up from revelation? Perhaps axioms of belief derived (hopefully by valid if informal use of FOPC) from the revelatory circle. We have to admit though that the step into this next circle is one fraught with danger. Paradox lurks again: for example, despite Campbell’s axiom about the bible speaking for itself, it can’t really do that. Translation and interpretation are required. Long tradition may prescribe what’s in the next circle, rather than pure logic (or revelation). God may even expect human beings to work this out to some degree.[5]

Many people tend to separate one set of circles from the other: preferring not to think of possible intersections. But if known reality is circumscribed by the first set of circles (the one which starts with logic), then the second set of circles, the revelatory one, must fit securely in the first set somehow, if we believe revelation describes reality in some way. Indeed, for Latter-day Saints, we probably have to conclude that it was there all along.[6] Hence the relevance of the original question to the blog charter.

So, here we go. Joseph Smith was an inveterate reasoner. Not always a correct reasoner, or an obvious reasoner (those can be exclusive categories). There were at least two Joseph Smith’s in Mormonism. The one not afraid (usually) to ask God, and the one not afraid to run with what he was told by God or could learn on his own–Joseph could be rather credulous. I believe a perfect example of this sort of behavior is the Book of Abraham. I think it is really beyond dispute that Joseph got the text of the Book of Abraham by precisely the same means that he used with his previous translation of the Book of Mormon. I’ve argued this elsewhere in this blog and I won’t go further with it here. It came through use of his white stone, I take that as an axiom here. Believers then, would place the results in the category of revelation. This revelation probably for the most part happened during a few weeks, perhaps less, in Kirtland, Ohio, 1835. Probably most of that in July.[7]

That was the prophetic Joseph. What did he do with it? I think there is considerable evidence to show his and others curiosity regarding the “textus receptus.” They tried matching the received text with portions of the papyri. The most logical matching exercise would be with material surrounding what is now called Facsimile No. 1 of the Book of Abraham. The text makes reference to a drawing like this. If you know how Joseph used the seer stones he had, you know why there was some thinking about this issue of which portion of the papyri to look at. I won’t go into that now, that’s for another day perhaps. He and his companions in the effort tried matching the received text with hieratic characters. They gave up the exercise after it appeared to go nowhere. But Joseph was all for it I believe. That was the thinker Joseph. By study and by faith was actually a principle he lived and valued. Another example of this is Facsimile No. 3 of the Book of Abraham (the facsimiles and Joseph’s treatment of them must be done individually for a number of important reasons I won’t touch on here).

Facsimile 3 sports a remarkably detailed explanation of the participants in the drawing. I think this matches Joseph’s vision of some episode in the life of Abraham during his translation effort, probably while he worked at the project in Nauvoo. But the Egyptian text on the top and bottom has no relevance at all to these explanations. Joseph saw the drawing attached to the “Hor Document of Breathing made by Isis” with Facsimile 1 at another position on the same scroll and assumed it matched his revelatory experience, given the similar (if also oddly different) figures in his explanation, and used it to complete his text (it is important here that Facs. 3 was published more than a month after the text). This sort of thing also almost surely occurs in the “translation” of the bible effort, so productive of revelation itself. A considerable number of the text changes in the biblical effort suggest simple reasoning about the meaning of a passage, or perhaps a correction of a repugnant concept (God doesn’t repent!). The Book of Abraham suggests other examples of this kind of thing. For example, Joseph’s use of Hebrew words in the book. It is certain that these were added to the text in Nauvoo, probably perhaps before publication. These words were probably added by Joseph, still a student of Hebrew,[8] because the book was about Abraham, who, as virtually all biblicists of the time believed, spoke Hebrew. It made sense to employ some Hebrew terms to amplify the text and give it an Abrahamic flavor. Surely he (Abraham) used Hebrew in his original composition? This does not cover all the unusual words in the book-but I won’t go into that here. Prophets just don’t know everything beyond what they get in revelation, and they don’t usually get everything. That is a proposition that should be obvious to Latter-day Saints and other readers of biblical and related texts.

I should say here that the prophetic Joseph always took the revelatory claims of others seriously, unless or until he learned otherwise. A good example was the “boy prophet” of Kirtland who produced a book. Joseph actually considered the book, he took it seriously, until his own revelatory insight gave him confidence to declare it a spiritual fraud. When one woman said she had seen an angel with red hair, Joseph declared it a false vision or one from the dark side, based on his own experience with the nature of divine beings.

An earlier example occurs in D&C 20:1-36 which is a production of Joseph and Oliver (see D&C 18:1-5), based on Book of Mormon texts, but designed in part to state how Mormonism fit in with Protestantism. How did the Church of Christ stand with the much discussed issues of the time? For example verses 30 and 31. The Saints were named as believers in justification and sanctification, key words that divided Protestantism along various lines. That the “Articles and Covenants”[8] named sanctification, or as it was otherwise known, “the doctrine of Christian perfection,” the step by step progression in perfection as a doctrine, placed Mormonism in a definite camp of Christians, with of course, certain deeply important distinctions.[11]

Joseph often used his own revelations as tools to think about religion in general. His frequent return to hot religious issues of his time shows this. For example his discussion of grace. He offers his own view by contrasting the prevailing Presbyterian view and the Methodist view as he understood them.[10] He suggests his own view as a compromise between them. Wilford Woodruff, in his typical style, reports Joseph as saying:

This spirit of Elijah was manifest in the days of the Apostles in delivering certain ones to the buffitings of Satan that they may be saved in the day of the Lord Jesus, they were sealed by the spirit of Elijah unto the damnation of Hell untill the day of the Lord or revealtion of Jesus Christ . . . The doctrin that the Prysbeterians & Methodist have quarreled so much about once in grace always in grace, or falling away from grace I will say a word about, they are both wrong, truth takes a road between them both. for while the Presbyterian says once in grace you cannot fall the Methodist says you can have grace to day, fall from it to morrow, next day have grace again & so follow it, but the doctrin of the scriptures & the spirit of Elijah would show them both fals & take a road between them both for according to the scriptures if a man has receive[d] the good word of God & tasted of the powers of the world to come if they shall fall away it is impossible to renew them again, seeing they have Crucified the son of God afresh & put him to an open frame shame, so their is a possibility of falling away you could not be renewed again . . . [12]

Joseph’s use of “grace” here is related to his temple theology and “calling and election made sure.” That for him is true grace, the highest manifestation of grace. Falling from that state can happen, (see D&C 20 again for an early manifestation of this belief) but there’s no going back. Truly perdition. Hence his point of taking a path between the views. It is rather interesting that Joseph identifies this grace with the grace of these versions of Protestantism. Room for discussion there, but this is already way too long and besides I escaped with bringing it back to a funeral sermon (possibly).



[1] There are other brands of logic (modal, multivalued, higher order, etc.), some perhaps important in religion, I want to avoid that for now. The way we discuss those other forms is essentially by informal FOPC and arithmetic anyway and for some important cases at least, they are reducible to FOPC. One of the best readable introductions to logic for the completely ignorant is Willard Quine’s Methods of Logic (still in print I believe). For a fantastically quick development see the opening sections of Paul Cohen’s The Independence of the Continuum Hypothesis. The questions of insanity, use of counterfactuals, etc. come up, but let’s not mess with that.

[2] See their magnum opus, Principia Mathematica. University libraries probably still keep copies around. A magnificent, but doomed quest. What could be more romantic. Better than twilight!

[3] Actually, if you throw in multiplication axioms too, you’ve got trouble. Paradoxes might be lurking. In ordinary language, paradoxes may appear to exist by virtue of a lack of information about context. For example, “I am 40 years old and I am 30 years old” appears paradoxical, but may simply represent computations in different calendars.

[4] NO seems reasonable. If valid reasoning from valid premises can be violated by revelation, it’s easy to feel a stronger connection to amoebae. See here, you amoebae. I think those who might be tempted to cry “philosophies of men!” here are not really thinking very deeply about what’s at stake. For Christian non-Mormons, note that even the doctors of the church blanched at the thought that revelation might defy logic. That is not to say God can’t ask people to do things they may question, think Abraham, or Nephi. But those things do not represent defiance of logic. Joseph Smith learned this the hard way too. None of that requires or allows that we run from paradox. Indeed, in our heart of hearts, we expect God is logical, much more precise in his thinking than human beings. But the logical rules are the same. The known theorems are not. But we have a chance to understand them. God presumably has a much better grasp of which premises may be added to FOPC to avoid flushing the system. (Keep in mind, Mormonism probably does not allow the absolutist God of Anselm). Theorems are usually “if … then” statements. To make such statements useful one must have some knowledge regarding the “if” portion of the statement. When does assumption = fact? Many old chestnuts of theology fall into this category. We simply don’t know enough about premises. The classical conflict of free will and foreknowledge comes to mind. Such questions can generate vigorous if sometimes puzzling discussions. Stated precisely with enough caveat and definition, the free-will foreknowledge question forms a genuine paradox. Most would be led to conclude that something about the premises is not valid, rather than conclude that God lives paradox somehow (hence the vigorous debates). People that actually make those kinds of (paradoxical) statements are usually assigned the title of poet. But one should be careful about dismissing such problems. How they may be dismissed logically, by modifying premises in such an argument is important, if we are to take Joseph Smith as any guide.

[5] Hopefully, one could touch base with God about derived truths, but of course one might believe that is unwise, unreliable or that He only speaks once and we fumble or score. I didn’t note it above, but there are somewhat analogous dangers in using FOPC. You have to encode your argument in FOPC. Precision of that sort requires standards of interpretation that can be difficult to meet and could create false issues.

[6] They might even offer (for aesthetics) that the first set sits inside the second. That is my own view and one suggested in sacred of Mormon spaces as well as statements by some LDS authorities.

[7] “Translation” also occurred in Nauvoo. The scare quotes are there to simply say that Joseph, on these occasions did not translate in the sense we use the term in foreign language courses. No dictionaries, grammars, etc. It was between him and what the Deity wanted to say.

[8] Joseph formally studied Hebrew in the early part of 1836.

[9] The popular title for what is now LDS Doctrine and Covenants section 20.

[10] While, unlike Baptists, Presbyterians and Methodists were openly “creedal,” their doctrinal explication could vary somewhat from congregation to congregation. Centralization was not a big idea among Protestants, refusing to go too close to Catholicism was a powerful driving force in Protestant doctrine and practice. See for example the previous post on “Joseph Smith and Catholicism.”

[11] That D&C 20 was a work of reason (with divine acquiescence in the result apparently) and revelation is clear from the internal structure of the text, as well as several items of external evidence. For a nice introduction to the cratering of Protestant unity over such issues, see Danial Walker Howe’s What Hath God Wrought.

[12] Journal of Wilford Woodruff, March 10, 1844. Woodruff had the habit of leaving off the “e” in doctrine, but did not always do so. He took notes of Joseph’s sermons, then later expanded them in his journal, connecting his notes with text from usually accurate memories (often not of precise words but generally correct ideas).

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8 Responses to Is Reality Consistent with First Order Predicate Calculus?

  1. J. Stapley says:

    Strong write-up, WVS. I think that there have been fits and spurts in Mormon history – particularly manifest in certain individuals – to circumscribe, if you will, all truth into one whole, with variable degrees of success.

    I think your outline of revelation and subsequent interaction is helpful in looking at JS. I would add that his interaction was not in vacuo. It was fairly collaborative, I think (even some of the revelations themselves).

    • WVS says:

      Thanks, J. Yes the idea that Mormonism includes all truth has seen variations. Collaboration was certainly a hallmark of JS’s approach in many cases.

  2. Ben Pratt says:

    Thanks, WVS. This is good stuff.

    It seems to me Mormonism has sometimes been equated with all that is true. That works for me, since my religious views color virtually all that I do anyway.

  3. Mark D. says:

    First Order Predicate Calculus is perfectly applicable to the domains that it describes. The difficulty with applying FOPC to the real world is epistemological and metaphysical. We have to start with certain assumptions that we cannot logically establish, only at best have strong reasons to believe.

    For example, the first thing to understand about quantum mechanics is that nobody understands quantum mechanics. In addition, no one can establish that any scientific theory is strictly true, we only know that some of them have been demonstrated to be false, i.e. less than completely faithful representations of reality.

    If the sun doesn’t come up in the morning, we will definitely have second thoughts about the law of gravitation. I don’t think anyone will worry about the first order predicate calculus though, because there are a million things that could go wrong before the latter comes into question.

    • boaporg says:

      Exactly. Most everything is less reliable than FOPC. But when religious discussion devolves into questioning “logic,” most questioners don’t clearly know what they’re giving up. Or perhaps we may say their use of language is faulty.

      There are certainly contested interpretations of quantum theory. Quantum mechanics is a lot of fun mathematics involving 2nd order partial differential equations. The fringes of which are not completely resolved. The relativistic version(s) are more iffy.


  4. Mark D. says:

    I think that most people are sufficiently acquainted with incorrect applications of logic (without knowing why or what went wrong) that they have lost faith in its general applicability.

  5. Mark D. says:

    At least they (most of them anyway) haven’t descended to the point yet where they think that logic is a subjective artifice of the Western mind…

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