Zen Notes: A Language Only Describing Sensations

On William Todd's "Analytical Solipsism"

For many, “solipsism” is a novel word. As for the philosophically persuaded, the term “solipsism” is radioactive. Yet neither response is enough to disregard William Todd's Analytical Solipsism. His work is not an advocacy for solipsism, but merely an exploration for the sake of deeper comprehension. In Williams Todd’s book, he outlines a view on solipsism wherein all our words, thoughts, and ideas can thereby be defined purely in terms of sensations.

Solipsism

You are reading my words and understanding that they were set out by another real person. But how do you truly know that I am real? A Cartesian Demon could be feeding you the sight to convince you of this. Not only that, but such an argument would apply to all people in your life. The view related to the lack of existence of other people is called “solipsism.”

I only say “related” here because I find the use of solipsism to be inconsistent save for one aspect; showing that an argument has solipsistic strains is enough to disregard the view in its entirety. An argument may have a solipsistic strain if you can possibly infer a world where other people do not exist or some other similar condition. And fair enough, given that the idea that other people are (or may be) fictional is repulsive, unintuitive, and disheartening. Here you may have noticed the variable uses of solipsism: possibility and actual proposition.

Depending on the context, solipsism either can mean that it is possible for others to not exist or a proposition that people are not real. In Todd’s book, he is using the former sense by outlining a position where other people need not exist.

Background for the Position

Todd seeks to demonstrate the construction of a language that is theoretically, but not necessarily practically, able to replicate any statement in a traditional language. He lays out the language in a mathematical fashion. This makes sense because that is what mathematics is: a series of symbols defined in terms of each other to demonstrate some meaning. This elucidates the first step: any language of mathematics needs axioms defined with primitive terms.

Axioms are the lowest level of rules for the language with which all other rules are derived. These axioms are dictated using primitive terms, words that you fill in with intuited concepts. For instance, let us construct a language for talking about addition with the integers. We will start with the axioms:

a + b is an integer. (Closure)

a + b is b + a. (Commutativity)

a + (b + c) is (a + b) + c. (Associativity)

a + 0 is a. (Identity)

a + (-a) is 0. (Inverse)

Now, do not worry about remembering the names. Those are just there for whoever is interested. What is critical is the properties of the axiomatic system we just laid out. The most obvious application of this system is adding up numbers. If we define 1 + 1 as 2, 1 + 2 as 3, etcetera, then we have all that we need to do addition with integers. Now this may not seem apparent as all that is explicitly given are trite equations like 3 + 5 is 5 + 3 and 5 + 0 is 0. Remarkable. But, using these axioms, we can prove theorems like “-(-a) is a” and “if a + b is 0 and a + c is 0, then b is c.” And these are just the first steps, without even getting into more complex topics like multiplication. What is phenomenal about certain mathematical systems is the complexity you can develop from a few simple axiomatic laws.

But do not be misled, these rules by themselves are not sufficient for comprehending addition with integers. When we interpret these axioms, we bring our own primitive terms to the table. In this example, we automatically understand these rules to be about combining numbers in the traditional sense. If instead we understand “a” and “b” to be stand ins for people’s names, “a + b” to mean “a and b’s common ancestor,” and “0” to be nobody, then we are able to construct the same system but with an entirely different application. With these primitive terms, we can make some statements that make sense like “a + b is b + a” meaning “the common ancestor of a and b is the same as the common ancestor of b and a.” This does not apply for all statements; we can also say legal sentences in our language like “a + (-a) is 0” where we have no real way to define “-a.” What would the opposite of a person even mean? This is because these axioms were not chosen with this interpretation in mind, but we could feasibly choose axioms that would engender a system allowing for these primitive terms to make more sense.

The Position

We have established how one can construct languages with axioms that have an intended interpretation using specific primitive terms. Let us return to Todd’s overarching goal. He wants to create a language that our actual languages can be translated into while being only dependent on subjective terms. If he does this, then he will show that we could only be talking about our own experiences and thus has created a framework where you only know yourself to exist.

As has been seen, Todd’s first step must be to set out his axioms. These have two requisite conditions: (1) have an intended interpretation such that the primitive terms are subjective and (2) create a structure that contains all the ideas we could express.

Todd achieves the former by assigning some arbitrary marker (he uses a set of dots) to every possible sensation. For instance, one could assign “.” to having a swatch of red in the upper right corner of your field of view. Likewise, “…” could be hearing a clicking noise with some volume and frequency. The practical specifics are irrelevant. We need only concern ourselves with the theoretical feasibility.

Todd determined that sensations are not the only primitive terms we need; our subjective experiences have a temporal component. He adds terms like “now,” “is simultaneous with,” “precedes,” and so on to incorporate time. And last but not least, he introduces mathematical concepts to allow the use of logic. For instance, he adds “If [some event] then [some other event] will occur.” Thus, condition (1) has been completed.

Now for condition (2), we must ensure that we have axioms that allow a full recreation of our practical languages. This step is much more difficult, so I will save you the particulars. I would highly suggest reading his book for those interested. In short, Todd strategically crafts axioms related to the organization of our temporal and experiential concepts to allow direct translation into his theoretical solipsistic language.

Thus our axioms’ conditions are fulfilled and we can now apply his system to sentences. The example Todd provides is translating “There is a gray cat under the white car.” He does this as follows, “If I were to have the sensation of walking towards the white car and then the sensation of bending down to look under it, then I would see the cat.” Notice that in this sentence we use logic to provide structure with content that is exclusively temporal and experiential. Therefore, this is a successful translation, bar one aspect.

Todd clarifies that he would have to make his translation a compound sentence because there are multiple ways to sense the cat. For instance, one could sense the cat by laying out catnip to lure it out or by starting the car and scaring it. This is not a significant issue as you can simply append every possible way to sense the cat. The sentence will be unwieldy, but again we are only concerned with theoretical possibility.

Language in Terms of Sensations

Now the position has been laid out. We can express any stated idea purely in terms of our subjective reality. As for the complete implications of such a language, that question has less certain answers. Sure we have shown that we could only be talking about our personal reality, but is that enough for the feasibility of a solipsistic reality? Todd elaborates further on such a view while also combatting critiques in the rest of his book. This is where any solipsistic theory shows its true mettle and is better left for another day.

Thanks for reading, if you have any comments or critiques please let me know.