The semantic argument improved even more

The core premise of my semantic argument is an entailment consisting of an antecedent and a consequent. An early version of the core premise states that if two concepts have the same reference set, then they are identical. Over the last few years, I have been able to improve the core premise by weakening its consequent. By improving the core premise I mean rendering it more likely to be true. Introducing a weaker consequent indeed improves the core premise, since it renders it less demanding and thus increases its plausibility.

As I have shown in the linked paper, rather than claiming as a core premise that, for any two concepts, sameness of reference sets entails sameness of meaning, it suffices for the derivation of the semantic argument's conclusion—namely, that there are no contingent universal properties—to claim that sameness of reference sets entails that it is a conceptual (and thus necessary) truth that the references of the two concepts coincide. Moreover, I have shown that it is in fact already sufficient to claim merely that sameness of reference sets entails that, necessarily, the references of the two concepts coincide. This is the core premise in its current form. In all cases, the scope of the concepts is restriced to concepts with existential import that correspond to properties that are both positive and attaching.

A further way of improving the core premise is to strengthen its antecedent rather than weaken its consequent. Indeed, a stronger or more demanding antecendent further increases the plausiblity of the core premise. This is precisely the strategy I propose to adopt here in order to improve the core premise even more. Rather than requiring, as the current antecedent does, that two concepts have the same reference set, I introduce a significantly stronger antecedent condition. To this end, I first introduce some terminology.

Let S be a set of concepts. Define D(S) as the set obtained by replacing each complex concept in S with its component concepts. For example, D({object, blue car}) = {object, blue, car} and D({sandbeach, blue}) = {sand, beach, landform, blue}. Moreover, define R(S) as the union of the references of the concepts in S. The current core premise of the semantic argument can be stated as follows. Let S1 and S2 be two concepts. If R(D({S1})) = R(D({S2})), then, necessarily, the references of S1 and S2 coincide.

The proposed even more improved version of the core premise is obtained by replacing the current antecendent—namely, R(D(S1)) = R(D(S2))—with the following recursively defined infinite conjunction of propositions:

R({S1}) = R({S2}), and
R(D({S1})) = R(D({S2})), and
R(D(D({S1}))) = R(D(D({S2}))), and
R(D(D(D({S1})))) = R(D(D(D({S2}))))
and so on ad infinitum.

This new antecedent contains the current core premise's antecedent as its second conjunct and is thus stronger than the antecedent of the current core premise. It can be stated more compactly as

R(D^n({S1})) = R(D^n({S2})) for all natural numbers n,
where D^0(S)=S and D^(n+1)(S)=D(D^n(S)).

The resulting further improved core premise thus states that if the above more demanding antecedent condition obtains, then the references of S1 and S2 necessarily coincide. As can be shown by verifying the derivation of the semantic argument's conclusion in the linked paper above, this even more improved core premise still entails the conclusion of the semantic argument. Therefore, the semantic argument itself is improved even more.

Moreover, I take it that the intuition underlying the even more improved core premise is more compelling than the intuition underlying its predecessor. Consider two concepts that are not only compared at the level of their component concepts, but are recursively decomposed ad infinitum into their constituent concepts at every level of conceptual decomposition. Suppose that, at each such level, the unions of the references associated with the corresponding decomposed constituent concepts of both concepts coincide exactly. Under these conditions, it is plausible that the two concepts in question are identical, or at least necessarily have the same reference.

This is precisely the claim expressed by the further improved core premise. Shifting from a single-level comparison of reference sets to a fully recursive decomposition of constituent concepts at each level of decomposition, substantially reduces the space for potential counterexamples. Indeed, exhaustive referential coincidence at every level of conceptual analysis appears to leave no room for genuine conceptual divergence. Therefore, the intuitive reason to accept the newly proposed core premise is significantly stronger than the intuitive reason to accept its predecessor. The same thus holds for accepting the semantic argument's conclusion.

Refining the core premise of the semantic argument

The core premise of my semantic argument holds that two concepts that share the same reference set also share the same meaning. The first consideration I offer in support of this premise is that two concepts that share the same reference set cannot be distinguished by examining the references of their component concepts. In both cases, we encounter precisely the same set of objects in the world. So, both concepts relate to the objects in the world in the same manner, when considered in terms of their constituent components. Given that meaning and reference must, in any case, be related, this provides a reasonable indication that the meanings of both concepts are the same. This consideration implicitly assumes, of course, that both concepts do in fact relate to the world. The scope of the semantic argument is thus reasonably confined to concepts that actually relate to the world and hence refer to at least one object in the world. Therefore, the core premise is reasonably limited to concepts having existential import. Concepts whose extension is empty are thus excluded from the scope of the semantic argument. This scope limitation of the core premise rules out certain alleged counterexamples. Consider, for instance, the concepts 'humans with orange blood' and 'humans with yellow blood'. Assuming that neither orange nor yellow blood exists in the actual world, the reference sets of both concepts - namely, on the one hand the set of all humans and all occurrences of orange blood in the world and on the other hand the set of all humans and all occurrences of yellow blood in the world - are the same, while both concepts clearly differ in meaning. Nonetheless, alleged counterexamples such as these do not undermine my semantic argument, as both concepts have an empty reference and thus fall outside the scope of the semantic argument's core premise.

The Extended Semantic Argument

This week I finalized a new paper titled A Semantic Argument Against the Existence of Universal Properties and Its Implications for the Likelihood of Theism. In this paper, I bring together the research of the last years regarding my semantic argument, and disclose numerous consequences of the argument's conclusion - including the implication that God likely exists. A preprint of the paper on PhilPapers is here available.

Universal withdrawal?

Already from the title of his fascinating book Object-Oriented Ontology. A New Theory of Everything (2018) it's clear that Graham Harman considers his object-oriented ontology to be a unified theory of everything. As Harman writes: "In my view, the 'theory whose range of applicability is limitless' can only be found in philosophy, and especially in the type of philosophy called Object-Oriented Ontology (OOO)" (p. 23). According to Harman science cannot provide a theory of everything since science doesn't avoid the pitfalls of physicalism (according to which everything is physical), smallism (according to which complex composites as less real than their component parts), anti-fictionalism (according to which fictional characters do not exist), and literalism (according to which accurate literal descriptions can give us the things directly and completely). I agree with Harman that a theory of everthing can only be found in philosophy. Moreover, with perhaps the exception of anti-fictionalism, I agree with Harman that we have to avoid the aforementioned pitfalls in our search for a philosophical theory of everything.

However, there's another pitpall we must also avoid: universalism. A theory traps into the pitfall of universalism if it is committed to the existence of a contingent universally held property (i.e., a contingent property held by everything). Universalism is a pitfall to avoid because there are no contingent universally held properties, as my semantic argument shows.(*) That's why for example the theories of everything of Thales (everything is water), Heraclitus (everything is fire), Nietzsche (everything is will to power), Schopenhauer (everything is will to live), and Latour (everything is a hybrid) are untenable. And that's why for example materialism (everything is material), idealism (everything is mental) and pantheism (everything is divine) fail as well.

Now, unfortunately, Harman doesn't avoid the pitfall of universalism. First, Harman is a methodological universalist in spirit. As he writes: "In short, we expect a philosophy to tell us about the features that belong to everything [...]" (p. 55). But more importantly, his object-oriented theory of everything falls prey to universalism. On Graham Harman’s object-oriented ontology, all objects have an interior that remains forever hidden to all other objects. So, all objects withdraw from all other objects. This does not only apply to all real objects, but also to all sensual objects. For each sensual object is hidden to everything that's not its observer, while its real qualities, and thus the sensual object itself, withdraws from its observer as well. Harman is thus committed to 'withdrawal' being a universally held property. Since 'withdrawal' is also a contingent property (e.g., it does not follow from the laws of logic that all objects withdraw from all other objects), Harman's thesis of universal withdrawal is a form of universalism, rendering his object-oriented ontology in its current form untenable. There are objects that do not withdraw from all other objects.

(*) Let me provide a concise formulation of my semantic argument. If two simple or primitive terms (i.e., terms having unanalysable meanings) have the same reference, then they have the same meaning. From this it follows that there are no contingent universally held properties. For suppose there is a contingent universally held property. Its reference is thus everything that exists. Now, that property is a conjunction of simple terms all having the same reference and thus also the same meaning as the simple term 'exists'. The alleged contingent universally held property is therefore 'existence'. But ‘existence’ is not a contingent property, so we arrive at a contradiction. Hence, there are no contingent universally held properties.

Dual forms in metaphysics

Suppose that in true metaphysical propositions the concept of ‘object’ and ‘relation’ are convertible, so that for each true metaphysical proposition about objects and relations, there is a dual propositional form that holds as well. For example, the true dual form of “Objects participate into relations” would be “Relations bind to objects”. In that case the conclusion of my semantic argument (“No relation binds a quality to all objects”) would be the dual of Graham Harman’s core premise of his object-oriented ontology (“No object reveals its quality to all relations”).

Papers in Acta Philosophica and Sophia

My semantic argument has been published in Acta Philosophica and is thus available as of now. Recently also my reply to Wintein's critique of my modal-epistemic argument has been accepted for publication in Sophia and will be available in due time.

Yet another implication

Here is yet another implication of the conclusion of my semantic argument. Take the positive property of being numerically finite. An object is numerically finite if and only if it has finitely many parts. Now, if this property is universally held in the actual world, the conclusion of my semantic argument (i.e., universally held positive properties are necessarily universally held) entails that all objects in all possible worlds are numerically finite. That is to say, if there is no numerically infinite object in the actual world, it follows that a numerically infinite object is in fact metaphysically impossible. Note that the absence of a numerically infinite object in some possible world does not entail that there is no actual infinite in that world. For there might be an infinite set of objects in a possible world whose members do not compose an object in that world. One thus needs a further premise - such as mereological universalism being necessarily true - in order to conclude that there being no actual infinite in the actual world entails the impossibility of such an infinite.

It's metaphysically impossible to be alone

Years ago I argued in this brief paper that the empty world is not a possible world. That is to say, total nothingness is metaphysically impossible. Now, the conclusion of my semantic argument, namely that all positive universally held properties are necessarily universally held, entails that it is also metaphysically impossible to be the only object in the world. In other words, there are no possible worlds that contain only one object. I briefly show how this follows. Consider the property 'being together with others'. This property is clearly positive and universally held. But then it is also necessarily universally held. Hence it is universally held in all possible worlds. So it is indeed metaphysically impossible to be alone in the world.

The origin of being is freedom

If existence is not a property, then there are no universal properties. That's what I show in this special version of my semantic argument. The absence of universal properties reveals that reality as such does not let itself be constrained or corseted in any way whatsoever. But then the ultimate origin of being is freedom. Free at last.

UvA Seminar on my Semantic Argument

The Institute for Logic, Language and Computation (ILLC) of the University of Amsterdam (UvA) organizes a seminar on my new semantic argument. The seminar is entitled "There are No Positive Universally Held Contingent Properties" and will take place at Friday 19 February from 16:00u till 17:30u in ILLC Seminar Room F1.15 at the ILLC building on Science Park 107 in Amsterdam. This building is right behind the building of Amsterdam University College at Science Park 113. Everyone is welcome!

Fitch, Aristotle, Lovejoy and the semantic argument

The conclusion of my semantic argument has it that there are no contingent universally held positive properties. This comes close to the more general thesis that there are no contingent universally held properties whatsoever, either positive or negative. This thesis results in a collapse of the distinction between universality and necessity. For it entails that if a property is universally held it is necessary, while clearly all necessary properties are universally held. So the semantic argument has an effect that resembles the effect of Fitch’s famous proof that if all actual truths are knowable, then all actual truths are known, leading to a collapse of the difference between possible and actual knowledge. The effect of the semantic argument also resembles the effect of Aristotle’s dictum that each possibility is actualized at some point in time, leading to a collapse of the distinction between modality and time.

Aristotle’s dictum is a temporal version of the principle of plenitude, which holds that all possibilities are actualized. The actual world is so full and diverse that there are no unrealized possibilities. It was Arthur Lovejoy who formulated this principle explicitly for the first time. There is in fact a deep connection between the above mentioned thesis and the principle of plenitude. For each one implies the other. To see that the principle entails the thesis, assume for reductio ad absurdum that there is a contingent universally held property P. Since P is contingent there is a possible world in which there exists something that is not P. But then ‘being not P’ is a possibility. So the principle of plenitude entails that there is something that is not P, which contradicts the fact that P is universally held.

To see that the thesis also entails the principle, let X be some possibility. If ‘being X’ is a necessary property, then there exists something in the actual world that is X. So in that case X is actualized. On the other hand, if ‘being X’ is a contingent property, there exists something in some possible world that is not X. But then ‘not being X’ is a contingent property. Given that there are no contingent universally held properties, it follows that ‘not being X’ is not universally held. But then there is something that is X.

The general thesis that there are no contingent universally held properties is thus in fact nothing more than a different formulation of the principle of plenitude. It simply is the principle of plenitude. As said, this thesis is obtained from the semantic argument’s conclusion by removing the positivity restriction. In other words, the conclusion of the semantic argument is a restricted version of the thesis. But then the semantic argument is in fact an argument for a restricted version of the principle of plenitude. As such it alludes to the principle itself. It suggests its truth.

An improved version of the semantic argument

The third premise of my semantic argument can be improved significantly. I realized this a few days ago while preparing my talk on the argument for the upcoming OZSW conference on 11 and 12 December at VU University in Amsterdam. Premise 3 of the argument can be stated as follows. If M1 and M2 are the meanings of two positive predicable generic expressions E1 and E2 such that RefSet(M1)=RefSet(M2), then M1=M2. In my paper I provide an elaborate defense of this premise. But in fact I do not need this premise. All I need for my argument to go through is the following weaker modified premise. If M1 and M2 are the meanings of two positive predicable generic expressions E1 and E2 such that RefSet(M1)=RefSet(M2), then 'x is E1 iff x is E2' is necessarily true. This modified premise is indeed weaker, since the original premise entails it but not vice versa. After all, E1 and E2 having the same meaning obviously entails that 'x is E1 iff x is E2' is necessarily true, while it is not the case that the necessary truth of 'x is E1 iff x is E2' suffices to conclude that E1 and E2 have the same meaning. Now, I suggest to replace the original premise 3 of my argument with the modified weaker premise. By doing so the conclusion of my argument, namely that there are no positive contingent universally held properties, still follows. Therefore, by doing so we have obtained a stronger version of the semantic argument, making its conclusion even more plausible.

Pruss on my semantic argument

Earlier this year I shared my semantic argument with Alexander Pruss. In response he suggested an interesting simplified version of it. I find his suggestion both helpful and promising. Here it is:

1. All the pairs of elementary positive predicates that we know to differ intensionally also differ extensionally.
2. So, probably, all elementary positive predicates that differ intensionally also differ extensionally.
3. Suppose F is an elementary positive universal predicate.
4. Then F and "is something" do not differ extensionally.
5. Therefore F and "is something" do not differ intensionally.
6. Thus, necessarily, something is F if and only if it is something.
7. Necessarily, everything is something.
8. So, necessarily, everything is F.

My new semantic argument (abridged version)

In this post, I propose a deductive argument for the claim that positive universally held properties are necessarily universally held. I take properties to be whatever can be attributed by a predicate that uses no or one leading noun qualified by zero or more adjectives, such as ‘being Aristotle’, ‘being red’, ‘being a table’, ‘being a red table’ and ‘being a large red table’. What I say about positive properties is compatible with various available accounts of positive properties in the literature. My argument consists of three premises. The first premise is the Frege-Russell-Quine view of existence. On this view there are no things that do not exist. I take the first premise to state a necessary truth.

The second premise is a statement of the Fregean theory of meaning. I call the meanings of the meaningful subexpressions of an expression the meaning elements of that expression. If a meaning lacks meaning elements, it is called elementary. A complex meaning is a meaning that is not elementary. Since everything is a ‘being’, the meaning expressed by ‘being’ does not add anything to the way a reference is presented or thought about. But then the meaning expressed by ‘being’ is not an additional meaning element of a meaning.

For the third premise I need the notion of a reference set for a meaning. First, the reference set of an elementary meaning is defined as the reference of that meaning. So, the reference set of the meaning expressed by ‘red’ is the set of all red things. Similarly, the reference set of the meaning expressed by ‘being’ is everything that exists. Second, the reference set of a complex meaning M is defined as the union of the reference sets of the meaning elements of M. Note that a meaning element can itself be a complex meaning and thus have meaning elements. The definition of reference set is therefore recursive.

Consider the following example. The reference set of the meaning expressed by ‘unicorn’ is the union of the reference sets of its meaning elements. The meaning elements of the meaning expressed by ‘unicorn’ are the meanings expressed by ‘horn’, ‘forehead’, ‘tail’, ‘hoof’, etc. So, the reference set of ‘unicorn’ is the set comprised of all horns, all foreheads, all tails, all hooves, etc. Unless, of course, these elements are themselves complex. In that case, the reference set of the meaning of ‘unicorn’ is the union of the reference sets of the meaning elements of our original meaning elements. And so on.

I now state the third premise. Let M1 and M2 be two meanings expressed by positive predicable generic expressions, then M1 = M2 if and only if RefSet(M1) = RefSet(M2). If M1 and M2 are elementary, the criterion trivially reduces to M1 = M2 if and only if Reference(M1) = Reference(M2).

Why should we accept the criterion? The ‘only if’ part follows straightforwardly. I shall offer two reasons to accept the ‘if’ part of the criterion. First, if the reference sets of two meanings coincide, then these meanings are entirely indistinguishable in what their meaning elements refer to, all the way down to their most elementary parts. Both meanings are thus entirely similar in how they map onto the world. But then, given the close connection between meaning and reference, it is plausible that these meanings are themselves identical.
The second reason is constituted by an induction over the collection of meanings of positive predicable generic expressions. It is very easy to come up with different meanings that have different reference sets. Just pick any two meanings that are so different from each other that it is obvious that their reference sets do not coincide, e.g. {‘motorcycle’, ‘bicycle’}, {‘red’, ‘blue’} and {‘house’, ‘rock’}.

It becomes more interesting once we consider pairs of different meanings with the same reference. Take the meanings expressed by ‘three-sided’ and ‘three-angled’. Clearly, they differ. This provides us with another confirmation of the ‘if’ part of the criterion, since the reference set of the meaning of ‘three-sided’ is not identical to the reference set of the meaning of ‘three-angled’. The former, but not the latter, includes all sides.

Consider also the meanings expressed by ‘water’ and ‘H2O’. On Fregean semantics the mode of presentation of both expressions differ. The meaning of ‘water’ is thus not the same as the meaning of ‘H2O’. But what about their reference sets? The meaning expressed by ‘water’ has as meaning elements the meanings expressed by ‘transparent’, ‘potable’, etc., whereas the meaning expressed by ‘H2O’ has as meaning elements at least the meanings of ‘hydrogen’ and ‘oxygen’. But then the reference set of the meaning expressed by ‘water’ is not the same as the reference set of the meaning expressed by ‘H2O’. We thus obtain further confirmation of the ‘if’ part of the criterion.

Another class of examples are cases where both meanings have an empty reference, such as those expressed by ‘round square’ and ‘married bachelor’. Clearly these meanings differ. The reference set of the meaning expressed by ‘round square’ includes all round things and all square things. The reference set of the meaning of ‘married bachelor’ contains all married people and all bachelors. So both reference sets differ as well, confirming the ‘if’ part of the criterion. In the absence of counterexamples, the above examples – and many more like them – provide strong inductive support for the ‘if’ part of the criterion.

I shall now derive the conclusion that all positive universally held properties are necessarily universally held from the premises. Suppose for reductio that there is a positive universally held property that is not necessarily universally held. Let P be such a property. Since a property is whatever can be attributed to something by a predicate, it follows that P can be attributed by the predicate ‘being P’. Since property P is positive, the predicate ‘being P’ is positive. That is to say, ‘P’ is a positive predicable expression.

Furthermore, since P is universally held, ‘P’ is in fact a positive predicable generic expression. Let M be the meaning expressed by ‘P’. Since ‘P’, when used as a predicate, attributes a universally held property, the reference of M is everything that exists.

M is either elementary or complex. Suppose M is complex. If we recursively unfold M’s meaning elements, we find at some stage at least one elementary positive meaning element M*. But then the reference of M* is also everything that exists. And since M* is elementary, the reference set of M* is the reference of M* and thus everything that exists.

Hence, RefSet(M*) is everything that exists. Now, the reference set of the meaning expressed by the positive predicable generic expression ‘being’ is everything that exists as well. So, it follows that RefSet(M*) = RefSet(meaning of ‘being’). According to the identity criterion for meanings of positive predicable generic expressions, if follows that M* = meaning of ‘being’. This contradicts the fact that M* is a meaning element. For, as mentioned above, the meaning of ‘being’ cannot be a meaning element. There are no meanings that have the meaning of ‘being’ as one of their elements.

The only remaining option is that M is elementary. Recall that the reference of M is everything that exists. Since M is elementary, the reference set of M is the reference of M and thus also everything that exists. It follows that RefSet(M) = RefSet(meaning of ‘being’).

So, according to the identity criterion, M = meaning of ‘being’. Now, M is the meaning of a predicable expression that, when used as a predicate, attributes a property that is not necessarily universally held. But then the meaning of ‘being’ is the meaning of a predicable expression that, when used as a predicate, attributes a property that is not necessarily universally held. From this it follows that it is possible that there are things of which it cannot truly be said that they exist. In other words, it is possible that there are things that do not exist. But this contradicts the first premise of the argument – the Frege-Russell-Quine view of existence – according to which it is impossible that there are things that do not exist. We thus have to reject our reductio assumption. Hence the conclusion follows: All positive universally held properties are indeed necessarily universally held.

I’ll now point at a number of interesting ontological corollaries. Consider the positive property of being material. This property is positive and plausibly not necessarily universally held. For the existence of a thing that is not material seems at least possible. But then the property of being material is not universally held either. After all, according to the conclusion of the argument, if everything would be material, everything would be necessarily material. It thus follows that there are immaterial things, which is to say that materialism – the thesis according to which everything that exists, is material – fails.

Analogously physicalism and naturalism fail as well. There are non-physical and non-natural things. We can go on: The property of being contingent is positive and plausibly not necessarily universally held either. For a necessarily existing thing seems at least possible. But then it follows that this property is not universally held. So there is at least one non-contingent and thus necessarily existing thing. It can furthermore be shown that there is at least one contingent thing, which refutes fatalism – understood as the thesis that everything exists necessarily.

Take the positive property of being caused. It certainly seems possible that not everything is caused. So this property is not necessarily universally held. But then it follows that it is not universally held. That is, not everything is caused. There must be at least one uncaused thing. By now the recipe for deriving further interesting consequences will be clear enough.

Nieuw artikel

Onlangs heb ik mijn nieuwe argument - het semantisch argument - nader uitgewerkt in een artikel. Dit artikel is inmiddels opgeleverd voor peer review. Daarnaast is ook langs deze weg alle commentaar erop van harte welkom! Het artikel is bovenaan mijn site gjerutten.nl beschikbaar.