Ontological Manicheism

 I. Introduction

Before he reached his mature metaphysical view of being as gradual in the Republic (Allen 1961), Plato claims that neither can negative facts explain positive facts, nor vice versa (Phaedo 103b) (this is very likely a corollary of his principle of opposites according to which if A and B are of opposite ontological categories, A cannot explain B (González-Varela and Barceló 2023). Paulo Sergio Méndoza just informed me (on January 2024) that Kant held a similar ontological principle in his A New Explanation of the First Principles of Metaphysical Knowledge (September 27, 1755).

Yet, it seems obvious that we explain positive facts by appealing to negative facts and vice versa, all the time. We say things like "Pat must be sick, because she would not have missed the party otherwise", "The Plant died because we forgot to water it", "The suitcase was so large, it did not fit in the trunk", etc. So this seems like a strange and obviously wrong take on the limits of metaphysical explanation. Yet here I will defend that this counter-intuitive metaphysical thesis has been unjustly dismissed and will argue that, instead, it is a plausible metaphysical principle.

My defense of this metaphysical principle can also be seen as part of a larger defense of an under-explored metaphysical hypothesis, Ontological Manichesim, according to which positive and negative facts, if both belong in our ontology, are separate realms of being with no interaction whatsoever.  When debating the ontological status of negative facts it is usually assumed that our ontology is unproblematically constituted by positive facts and that if negative facts are to be granted ontological citizenship it must be because of their indispensability in accounting for the existence and behavior of positive facts. This means that the question of the ontological status of negative facts relies heavily on the answer to the broader question whether it is possible to metaphysically explain a positive fact by a negative one or viceversa. This means that those who believe that there are no negative facts must be even more interested in the question of why we have the strong intuition and many prima-facie examples of negative facts being involved in metaphysical explanations, for if, like me, they want to defend a negative answer to this fundamental question, they also need to explain away these intuitions, as I will try to do here. 

My defense will proceed in three stages. In the first one I will offer a couple of motivating reasons as to why we must at least entertain the possibility that negative and positive facts are metaphysically isolated in such a way that only negative facts can be involved in the metaphysical explanation of negative facts and vice versa. Then, I will offer two arguments, one positive, one negative, in favor of this claim. On the positive one, I will argue that negative facts cannot be relevant to positive facts (and vice versa), and thus cannot feature in their metaphysical explanation. On the negative one, I will take alleged examples of explanations that seem to be counter-examples to my general hypothesis) and try to deflect them. 

A couple of preliminary caveats: I will consider as negative facts, facts about non-existent beings, absences, lacks, excesses, differences and non-obtaining states of affairs. I know there is debate as to whether these different sorts of facts are native in the same sense, yet I will not venture a definition of what makes a fact positive or negative.

As I have already mentioned, many people think that there are no negative facts, and for most metaphysicians, even if they exist, they are not fundamental and thus cannot metaphysically explain positive facts. I do not want to get in these arguments (even if I have done in depth elsewhere), so a couple of clarifying remarks are in order. First of all, I assume, as it is traditionally assumed within the neo-Aristotelain framework, that metaphysical explanation is not just the explanation of the non-fundamental by the fundamental, but also the explanation of some non-fundamental facts by other more fundamental, but not necessarily completely fundamental, facts. Thus, even if there are no fundamental negative facts, these can still be featured in the metaphysical explanation of other less fundamental facts.

 I. Motivation

An important motivation to think that the principle is not absurd is that, in general, the best known relations that underlie our most commonly accepted explanations such as logical consequence, causation, grounding, etc. all are understood as transmitting some property, as Plato himself had already recognized. Thus, logical consequence is customarily conceived as truth-transmission, just as grounding is seen as transmitting being, and causality as transmitting the obtaining of facts. In general, what explains why something X has some property P must be something else Y that is already P (and not not-P) and from which X obtains its being P by some form of transmission of P-ness. Thus, only obtaining facts can cause other facts to obtain, only existing entities can generate other entities, etc. In general, since an object X cannot receive its being P from Y unless Y itself is also P, it is impossible for something that is not P to explain why something is P through relations of this sort.

A second motivation is that, in general, trans-categorial relations have always been mysterious and thus, many philosophers have tried avoiding them. The fundamental contrast here is between non-mysterious intra-categorial relations like causal relations between material facts, or inferential relations between mental states, or logical relations between propositions, etc. and the mysterious relations that are supposed to cross across categories, like how Descartes postulated the pineal gland to bridge between the internal and external worlds, or the participation relation that is supposed to relate universal forms and particulars in Plato, etc. As a matter of fact, many of the most recalcitrant problems in philosophy are precisely problems about how it is possible for entities from one category to be related with entities of a different one. So, for example, the very challenging problem of mental content is none other but the problem of how it is possible for a mental state to be about a non-mental state of affairs or entity. In a similar sense, one of the basic problems of political philosophy is to make sense of the normative relation between individuals and collectivities. In philosophy of mathematics, the phenomenon of mathematical knowledge defies explanation precisely because it requires explaining how us, as concrete entities can get epistemic access to the behavior of abstract entities, while the problem of mathematical application is the analogue problem of explaining how the abstract facts of mathematics can have concrete applications in the physical world. In general, there is a recalcitrant explanatory gap between any two different ontological categories. Thus, it must not be surprising to find that the very possibility of interaction between positive and negative facts is also full of obscurities and paradoxes.

These two arguments do not give us indefeasible reasons to reject the possibility of negative/positive grounding relations, but are enough to warrant the claim that it is a hypothesis worth exploring.

II. Argument from Relevance

In classical logic, most basic inferential rules go either from positive premises to a positive conclusion – like modus ponens, simplification, addition, conjunction, etc. – or from negative premises (i.e., from premises that contain at least one negative premise) to a negative conclusion – like Modus Tollens or De Morgan. Yet, there are a few others that allow us to get positive conclusions from negative premises: disjunctive syllogism, ex falso quod libet aka the paradox of implication, reductio ad absurdum, addition, etc. Interestingly enough, except for the rules governing double-negation, these rules are all rejected in relevance logic and/or intuitionistic logic. This means that despite their broad acceptance as part of logical orthodoxy, many consider them counter-intuitive. Consequently, if we restricted ourselves to logical rules that are acceptable in classical, intuitionistic and relevance logic, then no inference that makes essential use of at least one negative premise with a positive conclusion, or vice versa, would be valid.

[By "negative" premises or conclusion, I mean propositions whose logical form is expressed in formulas with explicit negations. I will not get into the very interesting discussion of whether there are other negative operators besides negation. For example, there are good logical reasons to consider implications (and good linguistic reasons to consider conditionals) as negative.]

Thus, we can borrow from intuitionist and relevant logic to generate a metaphysical argument for the claim that metaphysical explanations that appeal to negative facts to explain positive facts, or vice versa, fail because negative facts lack the proper relevance necessary to explain positive facts, and vice versa.

Of course, in their justification for rejecting these rules, neither relevantists nor intuitionists mention anything like the Platonic principle that we cannot get something positive out of something negative (or vice versa). However, there is widespread agreement that one of the underlying issues, if not the underlying issue that makes these rules problematic is negation and in particular how negative propositions are logically related to the propositions they are negations of (Restall 1999). 

    Now, we can build an argument for ontological Manichaeism out of the relevantist and intuitionist arguments against classical logic: Broadly construed, relevantists claim that for an inference to be logically valid, premises must be relevant to the obtaining of the conclusion. Presumably, this restriction can be extended to metaphysical explanations: in good explanations, the explanans must be relevant to the explanation. Thus, if the relevantists are right that inferences of these forms violate this restriction for inference, explanations of these forms would also violate the analogous restriction for explanation. Therefore, negative facts cannot play an essential role in explaining positive facts and vice versa.

It is true that the relevantist and intuitionist claim is not that no inference of these forms can be relevantly valid, but only that not every inference of these forms is. My claim, in contrast, is universal: I claim that no explanation of these forms can be acceptable. Thus, it seems that I cannot derive my universal claim from their existential ones. 

    However, notice that by rejecting the universality of these rules, relevantists are committed to accepting that if there is any relevantly valid inferences with the form of a non-universally valid rule like, say, disjunctive syllogism, then such inferences cannot derive their validity from their having that particular logical form. This means that, if an inference with the form of a disjunctive syllogism is valid, it has to be because of some other logical reason, different from it being a disjunctive syllogism (or having any other not relevantly valid logical form), but because of some other logical reason in which the negative premise is not essential to the positive conclusion.

Vanilla and Chocolate Ice Cream Cones

    Let me illustrate this idea with a simple example. Imagine you go with a friend for ice cream and she gets a cone of chocolate. You ask her why and she responds that she always gets vanilla or chocolate, but this time they had ran out of vanilla. For the classical logician, the explanation is flawless and does explain why your friend got a chocolate ice cream. However, for the relevantist, the explanation does not actually reveal why she got chocolate. That there was no vanilla ice cream left is irrelevant to this. It might be relevant to why she did not get vanilla, but not to why she did get chocolate. The traditional relevantist argument states that since vanilla is not even mentioned in the conclusion that your friend got chocolate, nothing about vanilla could be relevant to this conclusion. 

    To actually explain why your friend got a cone of chocolate ice cream, one has to skip the irrelevant disjunctive syllogism to see why she always gets vanilla or chocolate. Maybe she likes them both very much and, if this is so, this positive fact would be what actually explains the positive fact that she got chocolate now: she got a chocolate ice cream because she likes chocolate ice cream. 

    The disjunctive syllogism seems relevant because it brings up an important contrast between vanilla and chocolate: one was available but the other was not. Thus it is not that vanilla was unavailable and, therefore, she did not get it, that is relevant; what is actually relevant is that chocolate was available. Thus, no negative fact, like the unavailability of vanilla, is involved in the explanation of the positive fact that your friend got a chocolate ice cream cone. 

    In general, as we shall see later, many times, when negative facts seem to be relevant in the explanation of a positive fact (or vice versa), it is because they point to a contrast with an opposite positive fact that is the one that is actually relevant. In the previous example, the unavalability of vanilla ice cream seems relevant 

    Of course, one can always say that the unavailability of vanilla is relevant to explain why your friend got chocolate instead of vanilla, but this is a completely different explanandum. Most importantly, this later is no longer a purely positive fact because it involves the negative fact that she did not get vanilla. Thus it has a positive component, that she got vanilla, which has a positive explanation – she likes it and it was available – and a negative component, i.e., that she did not get vanilla, which has a negative explanation: that it was unavailable. Either case, we get neither positive fats explained by negative facts nor vice versa. 

III. Apparent counter-examples: 

There seem to be many cases where we seem to intuitively explain positive facts by appealing to negative ones or vice versa, such as:

1. Rationality explanations: Pat must be sick, because she would not miss the party otherwise. Pat must have missed the party, because we would have heard about it already otherwise
2. Causal explanations: María stayed because she could not leave. / María did not stay, because she could leave.
3. Analytic explanations: That John is not married explains that John is single / That John is married explains that John is not single.
4. Existential explanations: The flaws in Ishtar explain its imperfection / The lack of flaws in La Gioconda explain its perfection.
5. Explanations by excess: The load was so heavy, it sank the boat.
6. Distributive explanations: I missed the guy in the gorilla suit, because I was concentrated on the basketball / I cannot come to your party, because I will be at the beach.

But if we look one by one to these cases where negative facts seem to explain positive facts, we would see that there is something else happening instead.

1. What is explained is a belief and what explains it is another belief, so both are positive facts of the same ontological sort, even if their content is, in one case, positive and another negative. Or what happens here is an inferential link, not a metaphysical one.
2. Analogously, in causal explanation what is explained is why something happened and causes and effects are always either both positive events, states or actions, or both absences (of events, states or actions) and again staying is not an action but an inaction thus it is an impossibility (the absence of a state) that explains an inaction (the absence of an action).
   
3. Being single seems to be positive, but it is negative and the analysis in (3) precisely reveals its negative nature, i.e., it is precisely because being single is nothing but being not married that it is a negative property.
4. Analogously for (4), flaws are actually negative features of a work of art, therefore being flawless seems negative but it is actually the contrary, i.e., positive, because the absence of flaws is nothing but perfection.
5. Here again, we are wrong in taking facts like the load being so heavy as positive, because what makes a load being too heavy, i.e., heavy enough to explain why the boat sank, is that the weight is not within (exceeds) the boat’s capacity. This excess is a negative comparative fact.
6. Here, even though the explicit explanandum is positive, an important element in the explanation is the background negative fact that the basketball is different from the gorilla, and that the party will not be at the beach. In this sense, the actual explanations would be “I missed the guy in the gorilla suit (negative), because I was concentrated elsewhere (also negative)” and “I cannot come to your party (negative), because I will be out of town (also negative)”, both of which are negative-negative.

In summary, when we pay closer attention to these apparent explanations, we can see that they are actually not so, because they are either based on misjudgments regarding whether a fact is positive or negative or the facts that are really doing the explanatory work are not those in the apparent explanation but others close by of the correct polarity.

IV. More difficult counter-examples:

Theaetetus:  One million dollars won't make you rich.

Socrates: It will, if it is the seventh or eighth one.

This joke illustrates Plato’s principle of contraries and is actually very close to the example Socrates actually uses in the Theaetetus (but without the extra-complication that comes from using a vague predicate like “rich”). The paradox is that something that is not large (one million dollars) seems to explain something being large (being rich). This suggest another apparent sort of counterexamples:

7. The bill reached a majority (an event of large size) because of the votes of Peter and Mary (just two votes, thus, not an event of a large size).
8. I mistook Elisabeth for Carmen (negative) because they are very similar (positive).

Here, I do not know what to say. Is the issue how big a difference is necessary to make a difference between big and small, and therefore is this just the sorites paradox under a new disguise?

Or maybe we ought to distinguish between two sorts of facts: facts of existence  and facts of  magnitude. That there is a difference between two facts or object is a fact of existence, independently of whether it is big or small is a fact of magnitude. That A is larger than B, just like that A is different from B, is a fact of existence, not of magnitude, since it only says that there is a surplus in A in relation to B, but does not say how big, and thus is not a fact of magnitude. 

That A being larger than B is not a fact of magnitude must have been obvious from the fact that it neither necessitates, nor is necessitated by either A or B being large (or small, for that matter). In other words, A and B can be both large and still A larger than B; they can be both small, and yet A can still be larger than B; A can be large and B small, and thus A would be larger than B. The only possibility that it excludes is that A be small and B large. Thus, since the fact that A is larger than B does not necessitate that A is large, that A is larger than B is not a fact of ‘largeness” and therefore there is no violation to the Platonic principle that opposites cannot explain opposites in this fact being explained by a small difference as in (7). 

In other words, what explains that the bill reached a majority is that the votes in its favour were more than those against it, i.e., that there were more votes in its favour than against it. This is clearly a fact of existence. That Peter and Mary voted in its favour is also a (conjunctive) fact of existence, and thus, there must not be anything strange in one explaining the other.

The same line of reasoning might apply to (8) as well. One might want to argue that Elisabeth and Carmen are very similar is a negative fact because it denies the existence of a noticeable difference between them. This difference is what is relevant for distinguishing between them and thus we have here two analogous negative facts, one explaining the other. 

I am not fully convinced by this later reply, because in the previous section I just claimed that differences are negative. Thus that there is a noticeable difference between, say, Elisabeth and Carmen, even if it seems to be a (positive) existential fact, I have committed myself earlier (in my response to apparent counterexample (6) above) to its being actually a negative fact. Therefore, that Elisabeth and Carmen are very similar, if we identify it with the fact that there is no noticeable difference between them would be the negation of a negative fact and therefore would be a positive fact, leaving (8) as still a counter-example of Plato’s principle.

References

R. E. Allen (1961) "The Argument from Opposites in Republic V", The Review of Metaphysics, Vol. 15, No. 2 (Dec., 1961), pp. 325-335.

Barceló-Aspeitia, A., & González-Varela, E. (2023). "Plato on False Judgment in the Theaetetus", Journal of the History of Philosophy 61(3), 349-372. doi:10.1353/hph.2023.a902875.

Restall, G. (1999). Negation in Relevant Logics (How I Stopped Worrying and Learned to Love the Routley Star) in Gabbay, D.M., & Wansing, H. (1999). What is Negation, Springer, pp. 53-76.