The laws of logic presuppose God?

[JontheMaronite]

I came across this interesting argument, developed by James N. Anderson and Greg Welty, which I condensed into this and thought I’d share and listen to your opinions/criticisms/analysis. I’ll start off with an overall description, followed by the syllogism, followed by an explanation of each premise, lastly followed by some concluding thoughts.

The laws of logic are necessary truths about truths; they are necessarily true propositions. Propositions are real entities, but cannot be physical entities; they are essentially thoughts. So the laws of logic are necessarily true thoughts. Since they are true in every possible world, they must exist in every possible world. But if there are necessarily existent thoughts, there must be a necessarily existent mind; and if there is a necessarily existent mind, there must be a necessarily existent person. A necessarily existent person must be spiritual in nature, because no physical entity exists necessarily. Thus, if there are laws of logic, there must also be a necessarily existent, personal, spiritual being. The laws of logic imply the existence of God.

1: The laws of logic are truths
2: The laws of logic are truths about truths
3: The laws of logic are necessary truths
4: The laws of logic really exist
5: The laws of logic necessarily exist
6: The laws of logic are non-physical
7: The laws of logic are thoughts
8: The laws of logic are divine thoughts
C: The laws of logic presuppose God

Definition: It should be clarified at the outset what is meant by “the laws of logic”. We are referring to those axiomatic principles of rational thought that govern how truth-valued statements or ideas can be related in truth-preserving ways. Prime examples of such laws would be the three classical principles whose earliest formulations are attributed to Aristotle:

• Law of Identity: that every true statement is true and every false statement is false
• Law of Non-Contradiction: that no statement can be both true and false
• Law of Excluded Middle: that every statement must be either true or false

This argument does not require acceptance of these particular logical principles or any specific system of logic (whether classical or non-classical). While there may be debates over which laws of logic hold, there is no serious debate over whether there are laws of logic. (How could one rationally debate the point without assuming that there are rules of rational debate?)

1. The laws of logic are truths
   What then are the laws of logic? What kind of things are they? Perhaps the least objectionable observation we can make is that the laws of logic are truths. That is to say, they are things that are true; among the qualities they exhibit is the quality of being true. When we state that the Law of Non-Contradiction is true—in other words, when we say it is true that no statement can be both true and false—we are affirming that the Law of Non-Contradiction is true in just the same sense that the statements “Paris is in France” and “2+2=4” are true.
2. The laws of logic are truths about truths
   So the laws of logic are truths. But what are they truths about? The truth that Paris is in France is about Paris—obviously enough. The truth that two plus two equals four is about certain numbers and the mathematical relations between them, at least on the face of it. But what exactly is the Law of Non-Contradiction about? What is its subject matter?

The simple answer here is that the Law of Non-Contradiction is a truth about truths.
Specifically, it is the truth that no truth whatsoever can also be a falsehood. (Strictly speaking, the Law of Non-Contradiction is also a truth about falsehoods, viz. that no falsehood whatsoever can also be a truth. But this is a trivial point, since any truth about a truth can be recast as an equivalent truth about a falsehood by use of the logical operator ‘not’.)

In other words, the Law of Non-Contradiction is a truth about propositions: those primary bearers of truth-value. It is a truth about which truth-values a proposition can and cannot bear: if a proposition bears the value true, it cannot also bear the value false, and vice versa. So the Law of Non-Contradiction is about propositions. And the same may be said of the laws of logic in general. They are truths about propositions and the truth-value relationships between them. It is for this very reason that our knowledge of the laws of logic enables us to infer from the
truth-values of some propositions, the truth-values of other propositions.

1. The laws of logic are necessary truths
   Not only are the laws of logic truths, they are necessary truths. This is just to say that they are true propositions that could not have been false. The proposition that the Allies won the Second World War is a contingent truth; it could have been false, since it was at least possible for the Allies to lose the war. But the laws of logic are not contingent truths. While we can easily imagine the possibility of the Allies losing the war, and thus of the proposition that the Allies won the Second World War being false, we cannot imagine the possibility of the Law of Non-Contradiction being false. That is to say, we cannot imagine any possible circumstances in which a truth could also be a falsehood.

In the standard terminology of possible worlds, we are observing here that the Law of Non-Contradiction is true not only in the actual world but also in every possible world. There is no possible world in which that logical law is false (or fails to be true in any other way). However this world might have turned out, regardless of the course of the Second World War or any other series of events, the Law of Non-Contradiction would still be true. We cannot imagine a possible world in which the Law of Non-Contradiction is false.

 

[JontheMaronite]

1. The laws of logic necessarily exist
   If the laws of logic exist, as we have argued, we must ask whether they exist contingently or necessarily. A moment’s reflection should make clear that they exist necessarily. We have already seen that the laws of logic are necessary truths—that is, they are true not only in the actual world but also in every possible world. There is no possible world in which (to use our standard example) the Law of Non-Contradiction is not true. But if the laws of logic are true in every possible world, it follows sensibly enough that they exist in every possible world. So the laws of logic not only exist, but exist necessarily.

This point can be reinforced by extending two of the four arguments given in the previous section so as to encompass not only the actual world but all possible worlds. Consider the first argument, from ordinary language. It would be quite correct to say, for every possible world w, “There are laws of logic in w.” (If it makes no sense to say, “The laws of logic are truths, but there are no laws of logic,” how could it make any more sense to say, “The laws of logic are truths in w, but there are no laws of logic in w”?) If such world-indexed statements are true, then ordinary language considerations should lead us to conclude that the laws of logic really exist in every possible world. The fourth argument, from the ontological preconditions of property attribution, can be extended similarly. If only existents can bear properties, and the laws of logic are propositions that bear the property of truth in every possible world, then we can only conclude that the laws of logic exist in every possible world, as the bearers of that property.

1. The Laws of Logic are Non-Physical
   The laws of logic really exist, and necessarily so. But what kind of things are they? Whatever they are, they cannot be physical or material entities, such as sentences written on paper or neural configurations in brains. It makes no sense, for instance, to ask where the Law of Non-Contradiction is, because the Law of Non-Contradiction quite evidently lacks any location in space. The question commits an obvious category mistake. Nor does it make any sense to ascribe physical properties to the Law of Non-Contradiction, such as mass or velocity or electric charge. It simply isn’t that kind of thing.

In fact, the decisive argument against the physicality of the laws of logic has already been given. Physical entities are, by their very nature, contingent entities. Any physical object we care to consider (whether it exists in fact, like the Empire State Building, or in fiction, like the planet Krypton) is such that its non-existence is possible. Even if that object exists now, it might not have existed. (This is this case not only for every physical object within the universe, but also for the physical universe as a whole, as the age-old question “Why does the universe exist at all?” takes for granted.) But as we have seen, the laws of logic are not contingent entities; thus, whatever the laws of logic are, they cannot be physical entities.

1. The Laws of Logic are Thoughts
   ‘Intentionality’ is a philosophical term of art derived from the Latin verb intendere: “to be directed toward some goal or thing”. Intentionality is routinely (albeit roughly) characterized as aboutness: X exhibits intentionality if and only if X is about something or other. In particular, propositional items (i.e., truth-bearers) such as statements and beliefs exhibit intentionality. The statement “Tokyo is the capital city of Japan” is about something: the city of Tokyo. In the same way, your belief that Elizabeth I was the daughter of Henry VIII is about the woman also known as the Virgin Queen.

Reflecting more closely on the phenomenon of intentionality, we can distinguish two important characteristics. The first characteristic is directedness: an intentional entity is directed toward something else, viz., whatever it is about. Thus the statement “Tokyo is the capital city of Japan” is directed toward Tokyo (and perhaps also toward Japan). The second characteristic is aspectual shape, which can be thought of as the particular way in which the object (i.e., that to which the intentional entity is directed) is apprehended. For example, the two statements “Mark Twain wrote The Adventures of Tom Sawyer” and “Samuel Clemens wrote The Adventures of Tom Sawyer” are both directed toward the same object: the man who was born “Samuel Clemens” but later adopted the pen name “Mark Twain”. However, the two statements exhibit different aspectual shapes in their intentionality; they are directed toward that one man in different ways. We might say that they reflect different perspectives on their object. And for this very reason, a person could believe the first statement but not the second,even though the two statements express the same historical fact. They assert the same fact by means of two different propositions.

-continued-

 

[JontheMaronite]

So propositions, construed as primary truth-bearers, are intrinsically intentional; they possess both directedness and aspectual shape. Indeed, it is precisely because they are intentional that they can be truth-bearers. If propositions were not about anything (just as, for instance, a puddle of water is not about anything) it would make no sense to ascribe truth or falsity to them.

What more can be said about this quality of intentionality? There is good reason to regard intentionality as the distinctive mark of the mental. Mental items—what we might generally term ‘thoughts’—are distinguished from non-mental items by their exhibiting intentionality. Beliefs, desires, hopes, fears, and intentions (of course) all exhibit intentionality: they’re all about things (directedness) and they’re all about things in particular ways (aspectual shape). Non-mental items—rocks, clouds, oil slicks, toe nails, flutes, electrons, etc.—are not intentional in this technical sense. At any rate, they cannot be intrinsically intentional. There is certainly a sense in which physical marks on a page (such as this one) can exhibit intentionality. But it’s equally evident that this intentionality is derivative; it is dependent on the prior activity of a mind. The physical marks exhibit intentionality only insofar as they express thoughts. Without minds conferring meaning upon them, no physical structures would ever be about anything else, for only a mind has the intrinsic power to direct thoughts.

In a universe without minds and thoughts, no physical structures could be ascribed truth-values. It is the mental—and only the mental—that exhibits intentionality intrinsically. It is the mental that confers intentionality on the non-mental. Thoughts, then, are the paradigmatic category of intentional entities. And the existence of thoughts is uncontroversial. (At any rate, we trust that thoughtful readers will grant this point.)

In summary: the laws of logic are propositions; propositions are intrinsically intentional; the intrinsically intentional is none other than the mental; therefore, the laws of logic are mental in nature. The laws of logic are thoughts.

1. The Laws of Logic are Divine Thoughts
   Now an obvious question arises. Just whose thoughts are the laws of logic? There are no more thoughts without minds than there is smoke without fire. Our first inclination might be to say that they must be our thoughts. After all, we’re the ones who think about the laws of logic and apply them to our other thoughts. But the fact that we have thoughts about the laws of logic no more entails that the laws of logic are just our thoughts than the fact that we have thoughts about the Eiffel Tower entails that the Eiffel Tower is merely a product of our minds. In any case, the laws of logic couldn’t be our thoughts—or the thoughts of any other contingent being for that matter—for as we’ve seen, the laws of logic exist necessarily if they exist at all. For any human person S, S might not have existed, along with S’s thoughts. The Law of Non-Contradiction, on the other hand, could not have failed to exist—otherwise it could have failed to be true. If the laws of logic are necessarily existent thoughts, they can only be the thoughts of a necessarily existent mind It doesn’t require much further thought to see whose mind this must be. A necessarily existent mind must be the mind of a necessarily existent person. And this, as Aquinas would say, everyone understands to be God.

Concluding thoughts:
This argument hardly constitutes an incontrovertible proof of the existence of God. But then few if any philosophical arguments amount to incontrovertible proofs. If a deductively valid argument that (i) has premises that appear to be true and (ii) is not vulnerable to obvious objections is a good argument, then we submit that this argument is a good argument. Still, it could be challenged at a number of points. The sub-arguments for the real existence of propositions and for the identification of propositions with thoughts are likely to draw the most fire. That said, if the overall argument is cogent and defensible, two significant implications should be noted.

First, the argument doesn’t merely show that the laws of logic can be understood as divine thoughts. Rather, it shows that the laws of logic should be understood as divine thoughts; more precisely, as divine thoughts about the essential relations between divine thoughts. The laws of logic are nothing other than what God thinks about his thoughts qua thoughts. Secondly, if the laws of logic are metaphysically dependent on God, it follows that every logical argument presupposes the existence of God. What this means is that every sound theistic argument not only proves the existence of God but also presupposes the existence of God, insofar as that argument depends on logical inference. Indeed, every unsound theistic argument presupposes the existence of God. And the same goes, naturally, for every antitheistic argument. The irony must not be missed: one can logically argue against the existance of God only if God exists

 

[Barbkw]

In fact, the decisive argument against the physicality of the laws of logic has already been given. Physical entities are, by their very nature, contingent entities. Any physical object we care to consider (whether it exists in fact, like the Empire State Building, or in fiction, like the planet Krypton) is such that its non-existence is possible. Even if that object exists now, it might not have existed. (This is this case not only for every physical object within the universe, but also for the physical universe as a whole, as the age-old question “Why does the universe exist at all?”

The laws of physics indicate a creation event (Big Bang) through technological advancements and the ability to now map residual cosmic radiation.

True, the Big Bang doesn’t now exist as it once did, but the radiation it created remains, even after 13.7 billion years.

 

[Alan_Wostenberg]

Thanks for an interesting post, and an occasion to reread a similar argument from Plantinga, over here, item A, as well as an occasion to reread Maritain’s introduction to philosophy chapter titled “Logic”, in which he introduces us to the topic:
“logic studies reason as the tool of knowledge…what are the rules which we must obey to reason correctly?”.

Now it seems to me that if reason is contingent, so are the rules governing it. For God does not know what He knows by process of reasoning from true premise to true conclusion. God knows everything knowable immediately. Omnisciences makes no deductions, no inferences, uses no syllogisms, nor any truth tables. However God created us, who know what we know, by reason. Had God created no rational creatures, there would be no rules they must obey to reason correctly, because “they” don’t exist.

So it seems to me the fifth premise

5: The laws of logic necessarily exist
is mistaken.

Granted the law of non-contradiction in logic is a corollary to the first principle of being: a thing cannot be and not be. This law is necessary, not contingent. Would the argument be better if limited to this alone?

 

[NonServiam]

The Laws of Logic are Thoughts

This is, if I do say so myself, the huge and gaping hole in the argument: you assume that these laws are thoughts in order to claim that they have a thinker. But you ignore the possibility that these laws are just our statement of our understanding of the way things are.

Take, for example, the law of identity: A=A and not not-A. If there were a universe with no minds in it (no supernatural minds, no human minds, nothing), the law of identity would still apply: in that universe, a rock would still be a rock and not not-a-rock. Now, of course, without any minds, there wouldn’t be anyone around to label it a rock or formulate a statement of the way things are and call it “the law of identity”, but a rock would still be what it is and not not-what-it-is. Even in a universe with nothing at all, the law of identity would still apply, because it would be nothing and not not-nothing.

The point here is that you’re thinking of these laws backwards: they’re not things that have a nature: they are statements of our understanding of the nature of things.

In other words, they are – like the “laws” of physics – descriptive, not proscriptive. Once you realize that, this argument becomes nothing more than an amusing word game.

 

[WinterLight]

Take, for example, the law of identity: A=A and not not-A. If there were a universe with no minds in it (no supernatural minds, no human minds, nothing), the law of identity would still apply: in that universe, a rock would still be a rock and not not-a-rock. Now, of course, without any minds, there wouldn’t be anyone around to label it a rock or formulate a statement of the way things are and call it “the law of identity”, but a rock would still be what it is and not not-what-it-is. Even in a universe with nothing at all, the law of identity would still apply, because it would be nothing and not not-nothing.

First, a disclaimer: I’m not defending the OP’s argument. With that said, I object to your claims.

I’ve never seen an axiomatization of first-order logic in which the “Law” of Identity is derived rather than assumed. Moreover, identity is not without controversy in philosophical logic: it’s not quite as obvious as it initially appears. For example, in set theory, we say that two sets are identical if and only if they contain the same elements. But is this the only way to conceive of set identity?

Usually, the “Law” of Double Negation is derived from the axioms, but only because the system is axiomatized to guarantee double negation. In intuitionistic logic, double negation is neither assumed nor derivable from axioms.

Two good textbooks on these topics (and much more) are Computability and Logic by Boolos, Burgess, and Jeffrey and Mathematical Logic by Shoenfield.

 

[Perplexity]

I don’t think it’s clear that ‘the’ laws of logic are true.

Take for instance the law of excluded middle (LEM): Every proposition is either true or false. This is also the principle of bivalence.

Does this hold of things like failed presuppositions?

Observe the proposition: 1. Perplexity stopped beating his dog.

According to LEM, (1) is either true or false. Suppose it’s true. Then, apparently, I’ve beaten my dog. But that’s not true. So, (1) must be false. But, then it’s not the case that I’ve ceased beating my dog. But, I’ve never done that! etc. It seems clear then to me, that propositions like (1) are neither true nor false, yet…they’re propositions.

There are many other counter-examples to ‘the’ laws besides failed presuppositions but perhaps this is an interesting place to start.

The understanding of propositions you seem to advocate is strange to me, but on it, I don’t think it’s clear that (1) isn’t a proposition. So it seems to me you must admit (1) is a proposition and therefore to defend LEM must show why it’s either true or false even though it doesn’t seem to be.