Abstract Objects

We have repeatedly alluded to the notion of abstract objects, as we have talked about, for example, propositions underlying information. As our last point of consideration in this seminar, we will now take a closer look at the necessary existence of abstract objects and what their existence means for the naturalistic paradigm upon which evolutionary theory rests.

Please note that we are here undermining the naturalistic worldview itself, showing that naturalism/empiricism cannot in principle be an adequate account of all there is. That worldview is the foundation for evolutionary theory. If that worldview can be shown inadequate, both the motivation and the basis for evolutionary theory will be removed. Furthermore, if there really exist various abstract objects, these are non-empirical entities that can never be pulled into the rubric of empiricism. So these entities can never be accounted for empirically; they are forever outside the purview of science (and, by extension, evolutionary theory). Thus, if abstract entities really exist, then they are entities that cannot be said to have emerged by any process that is scientifically accessible.

That result indicates that science cannot in principle be doing metaphysics, as it turns out that reality is populated by entities that are in principle not accessible to science. And that result indicates that evolutionary theory cannot in principle account for all that we are and all that we experience.

Do these results prove that evolutionary theory is false? No. Perhaps some version of evolutionary theory can account for adaptation and even minimal speciation. As we have seen, thus far we have no reason to think that present evolutionary theory can accomplish even that much. But the above results will prove that no version of evolutionary theory can ever be a comprehensive and adequate account of human existence and experience. Thus, the door is flung open wide for an array of “intelligent design” theories, including Christianity, to make their case as being a more comprehensive account of human existence and experience. And the merits of those theories will necessarily be evaluated philosophically rather than scientifically.

So, let us now turn to the reasons for believing in the existence of abstract objects. We will argue here for one sort of abstract objects: propositions. The same sorts of argumentation can be applied to other sorts, such as mathematical, logical, and geometrical objects (such as numbers and triangles). But first, let’s be clear about what an “abstract object” even is in general.


Abstract Objects

The word “abstract” can have many meanings in various contexts. For example, “abstract art” consists of paintings and other representations that don’t look like anything real. Wikipedia has as good a definition as any:

Abstract art uses a visual language of shape, form, color and line to create a composition which may exist with a degree of independence from visual references in the world…. Abstraction indicates a departure from reality in depiction of imagery in art. This departure from accurate representation can be slight, partial, or complete.

Notice in this definition that “visual references in the world” can only mean: empirically-accessible reality. So, abstract art, then, consists of representations of what is not (empirically) real. The above passage even flatly says: “Abstraction indicates a departure from reality in depiction of imagery in art.” But this sort of definition cannot be what we mean by “abstract objects,” because if such entities really exist, they certainly are not a departure from reality! They are part of reality, even if they cannot be empirically known.

Indeed, if you look up the term “abstraction” online, you will find many definitions, all of which will in one way or another build in a departure from (empirical) reality, such as:

The quality of dealing with ideas rather than actual objects or events.

But all references to “actual” or “real” in these definitions indicate how pervasive (and incorrect) is the prevailing empiricist metaphysics. Essentially, this approach to the term “abstraction” differentiates between “objective reality” (as it is necessarily known empirically) and “ideas” or “concepts” that are purely subjective, fictional, and unreliable, such as: “Jim had some vague notions of how his trip would go, but these proved to be mere abstractions, as the reality was much different.”

So, in the common vernacular, the phrase “abstract objects” has connotations of: vague, fictional, incorrect, subjective, and unreal. However, we mean none of those connotations when we talk about abstract objects in analytical philosophy!

The vast divide is between metaphysical nominalism and metaphysical realism.

Nominalism is the metaphysical position that we do have concepts of abstract objects, but these concepts do not refer to anything in the objectively real world.

Realism is the metaphysical position that our concepts of abstract objects do refer to objectively real entities, just as our empirical concepts do.

So, for a nominalist, the meanings of sentences inhere in concepts in people’s minds. For a realist, the meanings of sentences inhere in propositions, which are real entities that are picked out and conveyed by sentences. So, for a nominalist, propositions just are the concepts in people’s minds, while for a realist propositions are the entities that give the concepts meaning and content. Nominalism holds that there are no such things as propositions except as they are subjective mental entities, while realists hold that propositions are objectively existing abstract (non-empirical) entities.

Thus, what we mean by “abstract objects” in analytical philosophy is that certain non-empirical entities really exist, hence the “realism” about such entities.

Now, how could we ever demonstrate the existence of abstract objects? After all, you can’t point to one, like a dog, and say, “Look. A dog.” You can’t expect people to share in your empirical experience, so no empirical argument (nor scientific experiment) is going to reveal the existence of propositions. How, then, can we discuss what they are and show that they do really exist?


Church’s Translation Argument

Much of a graduate seminar I took from Nathan Salmon concerned this argument, so we can truly only scratch the surface of it here. However, the “Cliff’s Notes” version will suffice for our purposes. I have mentioned the credentials of Alonzo Church and Nathan Salmon before, so I won’t reiterate that discussion here. We are not appealing to authority anyway, and this particular argument is so obscure that only a tiny subset of philosophers (who are a tiny subset of society) have even heard of it, much less understand it. That said, often we have to search for truth as for hidden pearls. And Church’s Translation Argument is indeed a pearl.

The argument itself appears in a few-page article from the journal Analysis, 10, 5 (1950), pages 97-99. It is entitled: “On Carnap’s Analysis of Statements of Assertion and Belief.” It is short, it is very dense, and our “Cliff’s Notes” version will be best here. In his seminar, Dr. Salmon distributed his own one-page synopsis of propositions, entitled: “The Very Possibility of Language.” This cannot be emphasized enough, because Dr. Salmon argues in various articles and book-length publications that there can be no language at all (including the sense we mean when we’ve talked about information) without reliance upon propositions as abstract entities in the metaphysically realistic sense.

Let us consider some example sentences, which we’ll number for later reference. The numbers followed by the “prime” apostrophe will be the French versions.

(0) The world is round. (English version)

(0′) Le monde est rond. (French version)

(1) Chris believes that the world is round.

(1′) Chris croit que le monde est rond.

(2) Chris accepts “The world is round.”

(2′) Chris accepte “The world is round.”

(3) Chris accepts “Le monde est rond.”

(3′) Chris accepte “Le monde est rond.”

Now, notice some facts about these sentence pairs and their relations to the whole set of sentences.

First (0) and (0′) are synonymous. They convey the same meaning (the same propositional content) in both English and French, although they are not the same sentence. (0′) is a French translation of the English (0).

Next, note that (1) and (1′) are synonymous. Again, these are two different sentences conveying the same propositional content. Translation between the two sentences is possible (and correct) because they both convey the same propositional content.

Already, nominalism is in trouble, because it must account for how two different “concepts” in the minds of two people who do not share even the same natural language can possibly be shared between them. The typical “answer” is a la Michael Dummett: The propositional content in (1) and (1′) refers to itself. In other words, the syntax of the sentences points the English and French thinkers “inward” to their own meanings in their own languages. A thinker that knows both languages can look at both sentences, be directed inward to her own concepts in both languages, and recognize the “sameness” of the proposition (which just is a concept, a la nominalism). Church, however, says that this account won’t do, and he argues further….

Compare (2′) with (3′). Most translators would use (3′) rather than (2′), as Dummett says. The French-only speaker would “look inside” and recognize his/her own concept as being the propositional content of the quoted part of (3′). However, Church notes that (3′) does not preserve the same meaning as (2′) and is in fact a mistake. This can be seen by comparing (2) and (3) for we English-speakers who do not know French!

Let’s make it even more clear by inserting your own name in place of “Chris”. So, I would have:

(2) Richard accepts “The world is round.”

(3) Richard accepts “Le monde est rond.”

On Dummett’s nominalism, I “look inside” and see my own concept in (3). But wait! I cannot do that, and now the problem becomes apparent!

I agree that (2) is true of me, but I do not agree that (3) is true of me. I don’t know French, and when pressed am not going to trust Google Translate for such an important assertion. So, really, I have no idea what I would be supposedly be agreeing that (3) is true of me! The French-only speaker in (2′) and (3′) is in the same boat and should not agree to the truth of (2′) for the same reason I do not agree to the truth of (3′).

So, these facts already demonstrate the the “internal reference” of the propositional content asserted by nominalism is not a correct account of how these various sentences have the meanings that they do. And a nominalist translator is actually making a huge mistake to claim that I agree with (3) and that French-only-speaking Chris agrees with (2′).

The reality is that these sentences are synonymous, but nominalism’s “internal reference” account of the synonomy falls flat.

Before we continue, let’s codify what we know rigorously:

(1) = (1′) — Synonomy from (0) and (0′)

(2) = (2′) — Synonomy from (1) and (1′)

(3) = (3′) — Synonomy from (2) and (2′)

(2) ≠ (3) — Richard agrees with (2) but does not agree with (3)! He does not even recognize the meaning of (3)!

But (2) means the same thing as (1), and (3) is an “internal reference” translation of (2), so Richard should agree with (3) if he agrees with (2).


(1) ≠ (2) — But this is an absurd result, because if I agree with (1) then I cannot fail to have (2) be true of me.


The “internal reference” approach that claims that (3) picks out the same concept in Richard as does (2) is flatly incorrect.


So, then, what is actually going on here, given that “internal reference” isn’t going to work? Where does propositional content reside, if it is not “just inside” as nominalism claims? How is correct translation possible at all?

Church says that anybody who ascribes believing, knowing, asserting, or any other “attitude” clause to another thinker is metaphysically committed to the real existence of propositions. The only way that (3) can be true of Richard is by appealing to objective reality rather than some “internal reference.” Another example will help:

Ketchup = Catsup — This is just an objective fact; they are just two names for the same substance.

James does not know that these are just two names for the same substance. James has tried both, and he has concluded that he likes ketchup but does not like catsup. Here is what follows from these facts:

(4) James likes ketchup.

(4′) James likes catsup.

(5) “James likes ketchup” is true.

(5′) “James likes catsup” is true.

But (5) ≠ (5′)! (5) is an accurate account of James’s “internal reference,” while (5′) is not.


On the “internal reference” theory, (4) is true of James, while (4′) is not. But that is also absurd. The two substances are objectively the same. The only way to recognize the absurdity of the “internal reference” account of these sentence-pairs is to appeal to the objective fact of what ketchup and catsup really are! And any acceptance of the “internal reference” account, while biting the bullet by saying “For James it really is true that he does not like catsup,” is ridiculous because in that account the objective fact of the synonomy between ketchup and catsup is entirely lost!

To be able to recognize “the same thing” presented in different formats, including “the same meaning” in different sentences, presumes and logically requires an appeal to an extra-human, objective reality. We can, of course, be mistaken in our perceptions of that reality. But the only possible way to ever be correct is to be “in touch” with that reality. So, meaning-correctness logically necessitates being “in touch” with an extra-human, objective set of propositions.

Empiricists are howling now (even though their own accounts cannot be correct). They say, “Being ‘in touch’ with these strange things! What can that possibly mean? By what means can anybody be ‘in touch’ with such entities?”

Notice that Church, Salmon, and others who understand the force of Church’s Translation Argument are not offering any account of how we are “in touch” with propositions. They are only arguing that we necessarily are (by some means). As most of them are atheists, and most of them do not also understand Kant, they have no account of how we are “in touch” with propositions; they can only accept that we are.

We, however, can offer an account of how we are “in touch” with such propositions.

Kant demonstrated that space and time are “in us” but are also really objective and “out there” for all creatures that are “in the same box” as we humans are. He accomplished the same thing regarding his so-called Categories. Now, Kant only listed 12 categories, and he offered no philosophy of language. But we can “extend” Kant without doing any violence to his arguments by saying that there are more than the 12 categories he listed. We can also say that these “axioms of pure thought” can be built upon, just as the axioms of logic can be built up to a vastly robust set of theorems that can all ultimately be derived from the axioms.

“Learning a language,” then, amounts to “building up” from the Categories using the sentences that are taught to us in that language. The “building up” process is empirical, but it ultimately appeals to entities (propositions) that are either Categories or are derived from Categories. All human natural languages appeal to the same objective set of propositions, just as all human experience appeals to the same objective space and time, because we are all “in the same box.” So, the “objective facts” of meaning (and information itself) rely upon real abstract entities we call “propositions,” and we all share in and are “in touch” with these abstract entities because we all share “the same box.”

Remember that that “box” did not appear for us empirically, because all empirical experience necessarily presumes it. Just so, our many and varied languages did not emerge for us empirically (like shared grunts that finally became full-blown sentences), because, as Salmon says, “The Very Possibility of Language” presumes a preexisting and very robust set of shared and objective propositions. And to correctly translate between two languages presumes an appeal to objective facts that cannot be accounted for empirically or nominally.


Abstract Objects Besides Propositions

The same points can be made for a wide range of informational content, including the facts of mathematics, logic, and geometry (Kant even argued for the same thing regarding moral facts).

All empirical “similarities” (universals) do not emerge empirically, because they cannot. To recognize two properties as “the same property” presumes understanding of the property! So you can never detect a similarity from empirical exposure to similar objects. Instead, to recognize two objects as similar presumes that you have already categorized the universal that you detect in the two similar objects.

Another problem faced by empiricists/nominalists is that there is absolutely no reason why the world should conform to our mathematics, geometry, and logic! In fact, if nominalists are correct, we would be shocked to discover that even one of these fields cohered with the real world at all, much less all three! And we would never imagine perfect conformity at all. Yet, perfect conformity is exactly what we find. Only Kant has offered a solid account of how this conformity can come to be. And his account is no nominalism!

So, yes, we are awash in abstract objects. They really exist. They are objective, and we all share in referencing them. And they are this way for us because we all share in the “same box” of space, time, and the Categories. And all of these features of reality are pre-empirical and utterly inaccessible to science, because all of experience, all of information, indeed all of “real world content” already presumes these features. Thus, these features of reality make up what reality is for us, yet these features are forever beyond our understanding.

Why are these fundamental features of reality forever beyond us? Simply because we are not gods! We are not “box makers”.

Thus, the utter arrogance of Science is revealed. Some philosophers are aware enough of the limits of Science and Reason to realize that some facts of reality will be forever beyond our capacity to explain, and necessarily so. But committed empirical scientists, lacking this core philosophical awareness, are committed to their arrogance and will continually tilt at windmills, never realizing the futility of their efforts.

And we applaud them and urge them on, because by rejected the fact that some things can never be explained by us, they keep striving to explain. And in that process we do get better and better technology, which is just really, really cool! I love having the equivalent of an 80’s supercomputer in my pocket! So, gooooo Science!

But Science is not doing metaphysics, and it cannot.