A high-altitude philosophical excursion into the importance of defining our terms—in this case, the concept of existence

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“Exist” can be a tricky word. Unless I define the term upfront, people often think I mean something other than I do.

When I am talking about the color red, or, the concept of loyalty or morality, I might say that these things don’t exist. What I usually mean is that they exist in our minds as concepts, but if all sentient creatures died, the universe would be left with no concept of these things.

Or, they don’t exist outside of our minds. Concepts require conceivers.

When humanity and sentient life dies off long before the heat death of the universe, of whatever outcome we can expect, the number 3 will no longer exist.

Even if we were to write them down in books, and those books continued to exist beyond our lives and sentience, the ideas—the concepts of red or morality—wouldn’t exist because there would be no minds to extract meaning or representation from those pages.

(For further understanding of my position, read the following piece: “The Foundation to My Whole Worldview.”)

I often use the term “ontic existence” or “objective existence” for the mind-independent kind of meaning for “existence.” There is no objective existence of abstract objects outside of our conceiving minds.

This piece has been inspired by a commenter, Ficino, who asked the following on my article “What is transcendence?“:

What is your reason for denying that abstract objects exist? I think this is a very important problem.

If I say, This is a faulty sentence form, am I not saying, There exists an x such that x is a sentence form and x is faulty? (we can play with how to monkey with natural language so as to be expressed in logical notation) If I assert things about that which has no spatial-temporal location or causal powers, and if my assertion is true or false, does not modern logic presume that some x exists, over which I am quantifying the relevant predicates? So how do abstract objects not exist? If they do exist, they don’t threaten much, since they have no spatio-temporal location or causal powers. But don’t we need them, for our statements about stuff like “the working class” to be true or false?

I may have mentioned back over on Patheos that I attended a panel at the APA [American Philosophical Association] where Peter van Inwagen argued for the existence of abstract objects, channeling Quine. What he said hit me like a bolt from beyond. To reject his position seems to require us to admit different senses of “exists,” and that’s a theory cost too high for me to want to pay at this point.

When we talk about existing and existence, we are talking about “ontology” (hence “ontic”). So to talk about what “exists” means, we need to thrash out our ontology. It’s necessary to understand how everything in existence is framed. Abstracts certainly exist, just “in here” rather than “out there.”

Thus there might well be different senses of “exist,” for example in saying “a chair exists.” One understanding is that of concrete existence—the matter that constitutes what an individual might understand as a given chair. That exists (under some version of physicalism) outside of the conceiver’s mind, and that matter would exist even if all sentient creatures died. Second, there might be objective (realist) existence of the chair as a concept. This abstract object, as a concept, for the Platonic realist, exists in some form outside of the mind, objectively. Or third, the conceptual nominalist might argue that the chair, as a concept, only exists insofar as a given conceiver might conceive of the arrangement of matter as “a chair” (but that the idea might manifest differently to different conceivers).

I would divide objects up into only two categories: inside human conception and outside human conception. We could, if we were a realist, divide those external objects into abstract or concrete. Either way, I would argue that stuff of mental abstraction exists only in our minds, subjectively, even if we do agree on things. You and I may agree that 2+2=4, or that this object is red. This agreement is just that: subjective mental agreement (given that we have similar brains, cultures, backgrounds etc.).

In the example above—”there exists an x such that x is a sentence form and x is faulty”—there is a lot to be unpacked. A “sentence” is an idea that we, as humans, have constructed to have certain properties. Defined as a verb with a subject (themselves concepts defined and agreed by consensus), there can be sentences and, strictly speaking, not-sentences. You can get gray areas, such as commands (imperatives). Is “Run!” a faulty sentence or a correct sentence? What is defined by the word “fault” in this sentence? A group of words that fails to be a sentence? “the long, green grass,” as a group of words, is a not-sentence as so defined. It might be what Ficino defines as faulty.

To me, this is all about coming to consensus agreements so that we can operate pragmatically. It is about setting up rules to heighten the practicality of language. These ideas don’t exist “out there” and will die with the death of sentience.

We create the rules, conceiving and constructing them to suit our needs.

When you get down to the nitty-gritty, the question is arguably really one about logic. This is perhaps summed up in other debates: a priori vs a posteriori knowledge, or analytic vs synthetic philosophy. Is logic a fundamental feature of the universe?

In the entry “Logic and Ontology” on the Stanford Encyclopedia of Philosophy, logic is split up into four different areas:

Overall, we can thus distinguish four notions of logic:

(L1)the study of artificial formal languages

(L2)the study of formally valid inferences and logical consequence

(L3)the study of logical truths

(L4)the study of the general features, or form, of judgements

Truth is something that would not exist without sentience. Indeed, in epistemology, philosophers still can’t agree on what truth means, let alone what the best theory of it might be.

I don’t want this piece to get too bogged down. Suffice to say that there is (unsurprisingly) debate about nominalism (the idea that abstract ideas don’t exist objectively) and Platonic realism (the idea that they do) in terms of various logics. In the context of mathematics, I would direct you to the Stanford Encyclopedia of Philosophy entry for “Nominalism in the Philosophy of Mathematics.”

What about other forms of logic, such as to say, as Ficino does above, that “there exists an x such that x is a sentence form and x is faulty.” To me, that looks the same as saying, “This is not ~this” (not not-this). How can A also be ~A?

It can’t.

This is the Law of Non-Contradiction (LNC). Is this built into the fabric of reality? Is it some kind of observational axiom that cannot fail to be true? Is this some kind of abstract law? How can a thing that exists as some thing (A) also not exist as that thing?

Is logic, like mathematics (as I would claim), merely a language we have invented and use to describe reality? We should not confuse the map with the terrain such that we think this language is not descriptive, but actual reality.

Perhaps another way to think about this, again, is imagining whether logic would exist if no minds or sentience existed in the universe. Would there be logic inherent in rocks? In grass? In a supernova? Is logic just a language, as mentioned, that we have constructed, using axiomatic systems, to understand reality?

When we look at physical laws, how do we understand these laws? Are they prescriptive (matter has to adhere to these abstract regulations) or are laws descriptive such that they are human descriptions of how matter behaves with regularity? We might then wonder what underwrites such regularity. (See “Philosophy 101 (philpapers induced) #11 – Laws of nature: Humean or non-Humean?“)

Finally, it is worth mentioning the Munchhausen Trilemma. How do we ground any claim, any knowledge? There are three options:

  1. An infinite regress. This is so because that is so, and that because that is so. Turtles all the way down. Forever.
  2. A circle. A is true because B is true, and B is true because A is true. Round and round we go.
  3. Axioms or self-evident truths. A is true because B is true, and B is true because C is true. End of. C is a brute fact. Get over it. It’s obviously true.

None of these unfortunately allow for rationality to properly ground any claim or knowledge at base. Oftentimes, option 3 is preferred because it gives some kind of grounding. It is actually how mathematical systems generally work. For example, the most basic one (using a Peano axiomatic system) is the system of natural numbers we use:

The mathematical system of natural numbers 0, 1, 2, 3, 4, … is based on an axiomatic system first devised by the mathematician Giuseppe Peano in 1889. He chose the axioms, in the language of a single unary function symbol S (short for “successor“), for the set of natural numbers to be:
* There is a natural number 0.
* Every natural number a has a successor, denoted by Sa.
* There is no natural number whose successor is 0.
* Distinct natural numbers have distinct successors: if a ≠ b, then Sa ≠ Sb.
* If a property is possessed by 0 and also by the successor of every natural number it is possessed by, then it is possessed by all natural numbers (“Induction axiom“).

“Axiomatic Systems”, Wikipedia

Those axioms are brute facts or self-evident truths that cannot be derived further down to other reasoning. And we often just use “brute facts” that cannot themselves be rationally grounded (otherwise the regress continues) that we just accept. I use logic like the LNC as an axiomatic conceptual building block to build up my map of reality in order to navigate it. Something cannot be ~not something at the same time or we have a paradox.

But I would argue that these ideas are still conceptual in nature, being semantically explained using language that is also conceptual in nature.

If something exists in here, in my mind, and I die then does that thing die? Especially if no one else can or does conceive of it?

This reminds me of the truly brilliant Disney film Coco, a movie that deals with existence, death, memory, and legacy. The core idea of the film is that people only really continue to exist after death when remembered by others. The legacy is in other people’s memories and thoughts. When we conceive of ideas, they live in our minds. But when we die, those ideas die with us—us as individuals or us as communities and societies.

When humanity and sentient life dies off long before the heat death of the universe, of whatever outcome we can expect, the number 3 will no longer exist. There won’t be 3 pebbles next to the boulder. There will just be some stuff near other stuff. And even that sentence is a conceptual reframing and interpretation of that reality. What is “near,” and who benchmarks that? What is stuff?

So, in the end, there will be: “________”.

A TIPPLING PHILOSOPHER Jonathan MS Pearce is a philosopher, author, columnist, and public speaker with an interest in writing about almost anything, from skepticism to science, politics, and morality,...