The Laws of Thought

On the nature of thoughts and the laws of identity and non-contradiction

TD;LR: The "laws of logic/thought" don't apply to reality (which is in flux) or language (which is conventional), but to thoughts, which are truly definite. As such, thoughts are subject to the law of identity, the law of non-contradiction, and the law of excluded middle. A thought can't be contradictory but must have a defined identity to be classified as a thought. As defined entities, thoughts are the units of analysis in philosophy, rather than the physical world or language.

If we accept that matter is changing and language is illogical, as I have argued, then why should we accept thought as absolute and definite? Why are thoughts so special?

Thoughts¹ are definite, unlike reality or language. As such, they are subject to what are known as the "Laws of Logic." Yet this article will refer to these laws as their alternative name, the "Laws of Thought." For a thought to qualify as a thought, it must satisfy the three "Laws of Thought." These are the Law of Identity (LI), the Law of Non-Contradiction (LNC), and the Law of Excluded Middle (LEM).

The LI states that each thing is identical to itself. “A = A.” The LNC is the logical equivalent of the LI, which states that two contradictory propositions cannot both be true. Certain propositions necessarily exclude propositions they are in conflict with. Therefore, we can think of the LNC as stating that each thing is not what it is not. “Not A = Not A.”

The LEM only affirms that what something is and what it is not exhausts how that thing can be defined. Therefore, either “A” or “not A” must be true; there is no third possibility. As an illustration, if “A” is a defined space, there is an area only inside its boundaries and outside the boundaries of that space. There is no further space with respect to “A” (not so long as “A” is defined); there are no "gluts" or "gaps."

These laws don't apply to things in the world. As "Liebnitz's Law," states, there are no true identicals in the world. No two things out there have all the same properties as one another.

These laws do not apply to language either. The "Liar's Sentence" is not a counterargument to the Laws of Thought. As I had argued, a grammatical sentence like the Liar's Sentence doesn't have to convey a thought; it can still be meaningless gibberish.

Thoughts are not undefined or shadowy. Thoughts have a specified nature. Every thought you have has certain properties and lacks others. If a thought you had was vague, or unclear, then it was definitely vague or unclear. We couldn't even call a thought unclear unless it clearly possessed that property.

This is not to say that people don't hold contradictory beliefs. Some may believe that it is unacceptable to kill animals for food, but still believe that it is acceptable to eat meat. Yet, each of those contradictory thoughts is still specified. Otherwise, we couldn't say that these thoughts are inconsistent if we didn't know what they were. Just because they are mutually incompatible and in the same head doesn't make them less clear. But they would fail to convey a clear thought when they are expressed together.

This idea is uncomfortable for many who view the physical world as the only definite entity, as they may dismiss thoughts as too subjective and not publicly observable. However, thoughts are the unit of analysis in philosophy. We can't understand philosophy without understanding thoughts.

My previous article argued that because the world is changing and language is illogical, neither of these domains is absolute. This article will now show why thoughts are definite. So let's first examine why we should care about thoughts.

Thoughts in Philosophy

The units of analysis in philosophy are thoughts—not language or even the world. We express our thoughts through language, and we use our thoughts to understand the world. But thoughts, language, and the world are separate domains, each belonging to different fields of study. Philosophy lays claim to thoughts, and its aim is to develop thoughts that let us analyze the world best.

Many have asserted that philosophy is for learning about the world or analyzing language. Yet, as I've argued, the world is fragile, and language is conventional. They are each the domains of the sciences and linguistics, respectively. Philosophy studies thoughts, particularly those that can apply in all possible worlds (i.e., not contingent on the physical world).

Thoughts let us understand the world and give meaning to our language. Philosophy is about what thoughts we can use to understand the world, and what thoughts we express when we use language.

These proposed answers to big questions will be discussed later in this newsletter. Yet, for now, this article will only discuss why the Laws of Thought apply to thoughts.

To recap my prior article, thoughts are representations of the world and language is a representation of language. We can have different thoughts about the same physical entities (like "the Ship of Theseus"), and other thoughts can be represented by the same words (like the word "heap," as described in the Sorities paradox).

There is no direct relationship between language and the world. Both are mediated through thoughts. Failure to understand this relationship has created a lot of confusion in philosophy. As an aside, this is the problem with semantic externalism, the family of views that argues that meaning is determined by features external to the mind. Once we take meaning as something external in the world, we face a skeptical challenge.

By accepting meaning as purely internal—in the form of a thought, we can better understand the nature of meaning as a type of thought. And these thoughts have a nature.

The Nature of Thoughts

Thoughts can take any form, so long as they're produced by mental activity. We can have thoughts of images, historical events, mathematical equations, future plans, etc. The only requirement for thought is that it be logical; it must obey the three Laws of Thought. I can't think of colorless green ideas sleeping furiously or a sentence that is both true and false.

Language (and communication broadly) is how we can transmit these thoughts. There are no limiting principles to "thoughts." There can truly be infinite thoughts. So long as something is logically possible (adhering to the LI and LNC), then it exists as a thought. Logical possibility isn't limited to anything in the world.

Thoughts can include all possible truths about the game Chess and all truths about the games Chmess (to use Daniel Dennett's example), or Chmmess, or Chmmes, or Chmmesss, ad infinitum. And all of these thoughts are definite. Useless, but definite.

Although a thought can't be contradictory, it doesn't mean we can't hold contradictory thoughts. For example, say we believed that "All birds can fly," and "Penguins are birds and they cannot fly." These statements are contradictory, but to understand them as contradictory, they must at least be definite. Each of those beliefs expresses a clear thought—but when that clear thought is paired with another conflicting thought—the two clear thoughts taken together become incoherent. If you were to state both beliefs in the same sentence, for example, you wouldn't be expressing a thought on whether or not all birds can fly.

Nonetheless, these conflicting beliefs are still definite and can still be used to express a thought—so long as they're not used together. In other words, the fact that we hold contradictory thoughts doesn't mean that thoughts themselves are not definite.

Definite thoughts may not always fit coherently in a set of beliefs—but to even judge a belief as incoherent, it must at least be definite. Otherwise, there is no thought, and a non-thought is compatible with anything (since "nothing" doesn't conflict with the existence of anything).

A thought must still obey two laws: the LI and the LNC. Satisfying both would then imply the LEM.

The Laws of Identity and Non-Contradiction

The LI and LNC are two sides of the same coin. A definite entity is what it is, and is not what it is not.

The LI and LNC are the intrinsic and relational properties of all definite things, respectively. The two laws are logically equivalent.

The LEM then follows from this feature of definitions as an implication, which states that either a proposition or its negation is true. A proposition and its negation exhaust all the possibilities with respect to a thought; there is only space within the thought and outside the thought. All the possibilities are exhausted, and one or the other must be true.

"Thoughts" that violate the "Laws of Thought" could not exist as thoughts. You may be able to say the words "This sentence is false" or "married bachelor," but those words don't express a thought.

To summarize, the LI defines absolutes by what they are. The LNC defines absolutes by what they are not. If an entity is not definite, it violates the Laws of Thought and, therefore, cannot exist as a thought. And the LEM affirms that either the thought or its negation must be true, as there is no other space that is not within the thought or outside the thought.

It is strange to see some people accept one or two of these laws but not all three. Really, once you accept just the LI, then the LNC and the LEM naturally follow. A thing couldn't be identical to itself if it was a contradiction. The LI, LNC, and, the LEM all go together.

If one "Law of Thought" is violated, then all the laws would be violated. In those cases, the issue would be with the violator—not the laws. Otherwise, they wouldn't be "laws." I'll now go into more detail about the LI and LNC.

Law of Identity

The LI only states that everything is equal to itself. But what use is this law? You may think that describing something "as itself" is a meaningless tautology, as noted by Ludwig Wittgenstein. Moreover, there are no true identicals out in the world. You'd be hard-pressed to find two separate objects in the world that have all the same properties (according to Leibniz's Law).

But LI doesn't apply to things in the world. Rather, it applies to the properties of things in the world, which are thoughts.

A property is only a way of understanding a thing. And properties are the adjectives we're all familiar with (soft, blue, quiet, etc. - which are all “thoughts” about things). They are the senses or "modes of presentation" of things. While some things can share some of these properties, they can't share all of them. Otherwise, they wouldn't be separate.

For instance, take two separate white cats who are identical in all possible respects. They share the same anatomy, genetics, and even personality. However, because the cats don't share all the same properties (being in separate places, for one), the cats themselves are not true identicals. They nonetheless have identical properties: their anatomy, genetics, and personalities are the properties of the cat by which we understand each cat. Although the physical cat and its physical genes are not actually identical (they are in separate bodies), we still understand the cats as being physically and genetically identical. Again, the LI doesn't apply to things in the world, it applies to properties or ideas we have about things.

We can explain thoughts through a visual metaphor. Cartoons often illustrate a character's thoughts by placing an image in a “thought bubble.” The audience has a clear sense of the image that the character is thinking. This image could be anything—a memory, a counterfactual, an imagination, etc. The image is definite; the audience can see it and comprehend it.

Now, imagine our thoughts as visuals in thought bubbles. It is clear what the thought is and what it is not. It's subject to the LI and the LNC. Yet, this metaphor is incomplete. Thoughts are more expansive than just pictures. They include words, sounds, abstract ideas, and even emotions. Anything produced by the mind is a thought, and each of these thoughts obeys the LI, the LNC, and the LEM by consequence.

Some may argue that thoughts are still undefined. The contents of these thoughts may be vague, ambiguous, or unclear—even to the thinker herself. How can a thought satisfy the LI if it's so unspecified?

Yet these are definite features of the contents of one's thoughts. A blurry thought is still a thought, and it has the property of "blurry." Importantly, for the LI, the "thought bubble" still has boundaries that separate the thought from its non-thought counterpart. The LI encompasses the thought bubble. That specific thought bubble has certain properties and lacks others. It's definite. And when we both have this definite thought, we can say that our thoughts are identical, as if we're sharing the same thought.

Law of Non-Contradiction

LNC states that two contrary propositions cannot both be true. There cannot be both "A" and "not A." If you expressed both "A" and "not A," you wouldn't be expressing any thought about A. Saying both "A" and "not A" is equivalent to gibberish in ordinary language.

This is why statements like the "Liar's Sentence" are meaningless; they fail to express a thought because they assert two contradictory propositions.

The LNC is the flip side of the LI. Where the LI says something is what it is, the LNC says something also is what it is not. You can define a thought by both the properties it has and the properties it lacks.

Of course, we can have contradictory thoughts. And each of those conflicting thoughts is definite, obeying the LNC. However, the thought that both contradictory statements relate to would not exist.

For example, if I say both, "The car is red all over and is a Honda," and "This car is blue all over and is a CR-V," I have expressed definite thoughts about a car's make and model. However, I have failed to express a thought about the car's color since "red all over" and "blue all over" are contradictory properties.

While each of these statements is definite (as we only understand them to be contradictory because they are each a thought) together, they fail to express a thought on the car's color.

The "thought" on the car's color has no identity. Is it blue all over or red all over? Because, logically, it can't be both. And if you can't identify a thought, it can't exist. So, although saying that the car is both entirely blue and entirely red appears to express two thoughts about the car, they don't express even a single thought!

Meanwhile, the two statements on the car's make and model were each both (1) definite and (2) not contradicted by any further statements. Each statement expressed a clear thought about the car's make and model, without contradiction.

While the two statements are contradictory overall, they still express thoughts outside of the contradiction (the contradiction being about the car’s color). These thoughts are definite and not contradictory (I’m still able to express thoughts on the make and model).

Again, this is not to say that two contradictory thoughts are not thoughts. The point is that we only understand such thoughts as contradictions because they are definite. However, two definite but contradictory thoughts together fail to express even a single thought. If so, what identity could this thought have? Take "square circle." We may think of a "square," and we may think of a "circle," but we can never think of a "square circle."

Absolute Thoughts and Fungible Reality

The number "1" is definite and absolute. Nothing in the world may exemplify the property of being "1," but this would have no consequence to "1" being a clear thought.

Whether something is "1" can vary with circumstances. We can even think of several real-world instances where 1 plus 1 does not equal 2. If I added a heap of sand to another heap of sand, I would still only have 1 heap of sand, even though I started with 2. But does this mean 1 + 1 = 1? No, because a "1 heap of sand" is an undefined property. Heaps of sand don't come with labels in the real world. "1 heap of sand" can mean however many grains of say we say they mean.

Meanwhile, basic arithmetic operates with defined variables (or thoughts). Whether or not a true absolute number "1" exists in the world is irrelevant. The laws of mathematics don't depend on the world; they depend on thoughts. The organization of the thoughts contained in mathematics helps us understand the world.

The truths of trigonometry are also not contingent on triangles being out in the world. If we live in a world with only heaps of sand, trigonometry would still be true and comprehensible. These geometric thoughts exist independently of reality. Trigonometry may not be very useful in a world without triangles, but that doesn't make them any less true even in that world.

In math, the idea of "1" is absolute. 1+1=2 is true because 1 is absolute, a definite thought with firm boundaries. 1 plus 1 could not equal 2 if 1 did not equal itself. The symbols in math must stand for definite ideas, abiding by the LI and the LNC. However, this absoluteness of thought does not necessarily have to correspond to reality. As mentioned above, adding two piles of sand together will create only one pile of sand.

The world is not clearly defined. It’s in constant flux. Reality is akin to a series of events rather than absolute properties. But our thoughts about the world—our representations of reality—must be definite.

Partially Defined Thoughts

An undefined thought is a contradiction. Something must be defined for it to be a thought. But a thought doesn't have to be fully defined (defined in all respects). Only reality is fully defined, which is why we can get caught in a lie but not in a truth. Fictions have contradictions that can be discovered, whereas truth only has complete explanations.

The universe contains a built-in order and reasons for its existence.² Thoughts, meanwhile, are self-contained. They only need to make sense in the particular thought bubble in which they occur.

For example, fictional characters may have some of their features explained, but not others. Although every person who exists in the real world has a birthday, that may not be the case for fictional characters, whose date of birth may be undefined.

And if there is inconsistency in the story, like Bart Simpson having two separate birth dates, then the date of the character’s birth would also be undefined. Having two separate birthdays is a logical impossibility, so no thought is expressed about the date of Bart Simpson’s birth.

There are necessary facts in reality that don't necessarily track onto fictional worlds, making such features in fictional worlds unspecified properties. While all persons have birthdays, and having a birthday is a necessary aspect of personhood, we can still imagine a person without also imagining their exact birthday. Because this is still conceivable and obeys the Laws of Thought, a birthday-less character is still a defined thought.

This is a response to Gilbert Ryle's example of imagining a speckled hen (as a critique of sense-datum).

We can think of a speckled hen, but our image of a speckled hen may have an indeterminate number of speckles. We can still have a general picture of a hen covered with speckles, without imagining how many. Although every speckled hen that exists in the real world has a defined number of speckles, that doesn’t stop us from imagining a hen with an indeterminate number of speckles. This thought is undefined concerning the number of speckles, but defined with what the image represents—a speckled hen. Therefore, we can understand this image as partially defined. Not fully defined, but still defined.

Having a thought that is only partially defined doesn't make it any less of a thought. A thought may define certain properties and not others (even necessary properties). Yet this thought still has an identity—things it has and lacks.

Take emotions. They may not be fully explained by language or by physical manifestations in behavior and psychology, but they're real and definite, regardless of their not being publicly observable.

In a way, all of our thoughts are only partially defined. If I ask you to imagine a "woman," we may imagine a person with feminine qualities like soft features, curves, long hair, and a dress for clarity. However, this thought may not include that woman's interests, life history, or emotional state, even though all women have such qualities. We only imagine a physical model of a woman—but leave the remaining features unspecified.

Again, this is why it’s so easy to get caught in a lie. When telling the truth, you can just take the facts of the world as they are. But when telling a lie, you're creating a new world that you haven't fully defined and may, therefore, contain contradictions, allowing for the discovery that your world doesn't exist.

Our thoughts are specified in some ways, but not others. How defined our thoughts should be is context-based, depending on how useful more definition would be. Thoughts are only maps of reality to help us understand reality; thoughts are not reality themselves. Maps do not correspond one-to-one to the physical world. To do so would make the map useless.

Conclusion

The Laws of Thought apply to thoughts. Every thought is at least partially defined and is, therefore, absolute. The Laws of Thought are often misapplied to reality and language, and therefore, thoughts are misunderstood. If we want to speak of things that are truly definite, we only have thoughts to refer to.

With this view of thoughts, we can now understand the mystery of meaning. Yet the next article will disprove the existence of God, and prove the existence of something higher.

1. I can refer to “thoughts” as “ideas,” “concepts,” “abstractions,” “mental representations,” or “propositions,” but for consistency, I’ll mostly refer to them as “thoughts.”

2. This will be described later in this newsletter.