Today, logic is taught not as a single, universally received system of rules observed from nature. Rather, logic is viewed formally as “one of many” systems of inference, which can be disproven by one or more other kinds of formal systems of inference. There is uncertainty concerning “where” our logical systems originate. On one hand, the formalism of epistemology assumes logic to be a “product” of the human mind, divorced from nature. According to this view, nature, being independent from the mind, has a logic that is not shared with humankind.
When we say “logic,” we mean the kind of ontology that governs a scientific system, not just the rules and inferences carried throughout its investigations. The logic of “trial and error,” methods for “formulating argumentation,” and the concepts of “valid” and “invalid” structures are said to be created by the human thinking mind. Therefore, they are methods that lead to discovery but are not themselves discoveries. The divide between formal and informal logic relates to the question of where logic resides in the world.
Definition of “formal”
The word “formal” means that thinking is a formalized system, created either to communicate things that are naturally ‘true’ or to ‘deceive’ away from naturally true things. The formal aspect of logic consists of the symbolism and terms used to communicate the truth, which is more fundamental than the language used to express it. The problem with a formal system is that sometimes the language itself can be used to manipulate the truth it was originally designed to clarify.
For example, this happens in rhetoric, where the art of persuasion may lead to the wrong truth or the wrong purpose. Reason has the power of “dissuasion,” which is the ability to dissuade, meaning to persuade in the negative or to convince someone otherwise. This can be done either by properly showing a valid argument or by virtue of the subject’s own fallacious inability to conceive a valid argument, leading them to act contrary to the natural course of action. We say “natural” because it is what would already happen if left unimpeded. To dissuade means to make someone refrain from taking a course of action they would otherwise have taken for the betterment of understanding the truth.
Rhetoric, on its own, is the skill of persuasive argumentation, which may argue for facts that are true or distort those facts away from the truth. Here, we associate that a formal system, although not inherently corrupt, can sometimes be very corrupt. In contrast, while an informal system may fail in formulating a logical structure of thought, when it succeeds, it is less prone to corruption than a formal system. The reason for this is that informal logic depends on nothing other than the thinker’s own organic systems of thought (his mind), which are given by nature and augmented by historical development. The informal thinker can reference ancient figures of the past as role models to guide his own logic toward the light of truth. However, in the end, an informal system is always shaped by the present time and becomes a “formal system”, which is meant to narrow the intellectual’s mind toward a certain way of thinking, rather than allowing his mind to align with truth in its natural formulations.
Informal Logic
An “informal” logic is self-evident if it is originally received from nature by the observer. A “formal” logic is not self-evident and requires demonstration because it is transmitted from one person to another. In other words, it is artificially formulated, meaning that the content of the truth is derived from a source that can manipulate the natural course of action into something it was never originally meant to be.
The supposition in either case is that there “ought” to be a fundamentally universal truth that represents itself. A man-made system must be proven, demonstrated, and argued for, either by appealing to informal logic, which is naturally found in the organic ability to reason (what we call “logic” as a naturally true universal set of rational relations, stripped of any content but capable of attributing any content to any proposition), or the formal system may appeal to its customs and traditions to propagate agreed-upon assumptions about the world, whether they are true or not—although, in some cases, they are true, and in almost all cases, false. The latter expresses external relations, which describe how the set of relations appear from the outside, as opposed to the former, which involves internal relations.
The internal relations are not “inside,” like something contained within another, but rather are the essence or form. The reason why essence is associated with the “internal” principle is that it does not exhibit one or two ways of being; rather, its measure does not have a definite manner but may exhibit an infinite number of possibilities with the same self-identical quality. The internal is the necessity that maintains any possibility for there to be a relation in the first place. The possibility for a thing to exist must be presupposed before its immediate observation in any given moment or specific way. For example, in ethics, the deontological idea is that, irrespective of whether a particular instance is good or bad, there must first and foremost be a standard that determines that. For instance, whether “I stubbed my toe and that is bad” or “I won the lottery and that’s good,” independent of these individual instances being good or bad, more fundamental is the universal axiom that there is necessarily good or bad, regardless of any single scenario being good or bad. This is not a mere language game because it applies to instances that we say are undoubtedly bad, such as killing. Even in this case, there are instances when it is right or wrong—e.g., in war, killing is made legal and therefore encouraged and praiseworthy, but on the same token, there are instances of “war crimes” where killing is wrong, even in cases when it is made acceptable.
Logic is rooted in man, but man is part of the natural logic of the world that made him into the kind of being that conceives the internal rational essence within himself, which is at the same time the universal for everything else outside of him. He uses logic itself to convolute the essence of logic, which is a passage of nature between the observer and the phenomena.
Univocal
For Aristotle, logic is univocal because the logical system is meant to grasp abstractions concerning the fundamental relations in the world. The laws of thought for Aristotle are not just correct inferential rules for proving an argument against an opponent or showing how some axioms follow from other axioms. Even these processes are based on the actual ways substance operates. This means that while language for us is written and uses symbolism—something other than the idea itself—to communicate the idea itself, the “language” of reason in nature uses matter as the content to mold into the forms and geometry of its expression.
Aristotle is interested in logic not only because it establishes the correct conduct for reasoning, but also because he believes that logic deals with the nature of substance, which generates the forms essential for physics. For Aristotle, logic is not only a product derived from human thinking, but it also belongs naturally to the world. Logic is univocal because the logical system is meant to grasp real abstractions concerning the fundamental relations in the world. For example, the laws of thought for Aristotle are not just correct inferential rules; they are “correct” because they reflect the actual ways substance operates. The most fundamental principle, for instance—the law of non-contradiction—describes the most basic nature of substance by stating that it is impossible for the same thing to have and not have the same feature at a single time. This is a fundamental logical property of elementary physics, but we find it is not entirely true in quantum physics, where a phenomenon may occupy the same and not the same feature at the same time. In fact, the ability to do that constitutes the essence of spacetime as a continuum.
Aristotle introduces logic to the science of metaphysics. Logic does not only deal with the right conduct of thinking, but it is also the structure of consciousness, which is realized by consciousness. The deeper claim here is that logic, being the science of thought in general, speaks precisely to the metaphysical question of what being is. The affiliation of logic to metaphysics is primarily the affiliation of thought to nature (Aristotle, Metaphysics IV.3).
The term “logos” for Aristotle defines the concept of reason or thought, which is a living, ultimate mind in nature, of which all the objects we perceive are abstractions. The form of any mind is logic, meaning that the content of thought consists of physical objects structured along and around the relations and activities of some definite determinations of being. The ordinary understanding, on the other hand, sees the laws of thought as just another system of inferences that can be disproven by other kinds of formal systems of inference—i.e., modes of argumentation. As the adversarial legal motto goes, “It’s not what is true… it’s what can be proven.” What this understanding fails to grasp is that the laws of thought are actual abstractions taken from the world; they are true whether they are grasped by a single observer or not. Once separated from the world, they are taught as valid ways of reasoning, yet their origin lies in the way the world operates.
According to Aristotle, metaphysics is the fundamental science because it is the thinking that wonders about its own foundation—much like the expression in the Bible, “what you seek… you shall find” (Matthew 7:7). Metaphysics seeks the fundamental truth and, in doing so, eventually found it. Metaphysics discovered logic. Logic is the most fundamental of the sciences, and for other reasons, it has proven itself to be the most complex one because, “informally”—which is another meaning for “primarily”—it does not have a pre-formalized basis. Yet, it is the formal basis for every other science, if we mean by “formal” the true start of a systematization and structure of science. The science of logic goes beyond the ordinary systems of formal logic. Formal logic is simply a subcategory of logic in general. According to Aristotle, logic is not only abstract, but it is also concrete structures we observe in nature. Even animals, although they are not logical by their thinking facility, still act in accordance with a logic natural to the world.
“logica utens & logica docens”
Peirce distinguishes between what he identifies as logica utens and logica docens. The latter explains logic learned as a formal system, whereas the former explains the “pre-theoretical innate faculty” that thought naturally applies (informal).
Logica docens is a formal system of logic taught in schools.
The formal side of logic is the method of cognition that extracts all content, and the so-called second constituent belonging to thinking—namely its matter—is said to come from somewhere else. Since matter is absolutely independent of logic, logic teaches only the rules of thinking without reference to what is thought about, that is, the object. Formal logic, in this way, sees the rules of thinking as something distinct from the other important element of thought, namely matter, which is what thinking is confronted with in the first place.
This is ironically a materialist doctrine, but in an inverted form. The materialists separate all matter from substance that is not measured physically, which they call “abstract,” and claim that thought is a product of matter, i.e., dead matter comes first, and a living mind comes second. The materialists say that thought is also measured by physical means by reducing it to the chemical level and balancing it in the brain. The materialist psychologist claims that thought is non-physical because it is a blank slate facility, an empty nothing, that receives the object. Upon receiving it, the faculty fills the empty space with content. For example, in the case of perception, light particles are supposedly received, the taste buds get stimulated, or the nose detects pheromones, and so on.
Ordinary Understanding
Thought without object and object without thought
(Science of Logic 35, 36, 37)
Hegel says:
“When logic is taken as the science of thinking in general, it is understood that this thinking constitutes the mere form of cognition that logic abstracts from all content. The so-called second constituent belonging to cognition, namely its matter, must come from somewhere else; and since this matter is absolutely independent of logic, this latter can provide only the formal conditions of genuine cognition and cannot in itself contain any real truth, nor even be the pathway to real truth because what is essential in truth, its content, lies outside logic. But, in the first place, it is quite inept to say that logic abstracts from all content, that it teaches only the rules of thinking without any reference to what is thought of or without being able to consider its nature. For as thinking and the rules of thinking are supposed to be the subject matter of logic, these directly constitute its peculiar content; in them, logic has that second constituent, a matter, about the nature of which it is concerned. But secondly, the conceptions on which the Notion of logic has rested hitherto have, in part, already been discarded, and for the rest, it is time that they disappeared entirely and that this science be grasped from a higher standpoint, receiving a completely changed shape.”
Hegel goes on to say:
§ 38
“Hitherto, the Notion of logic has rested on the separation, presupposed once and for all in the ordinary consciousness, of the content of cognition and its form, or of truth and certainty. First, it is assumed that the material of knowing is present on its own account as a ready-made world apart from thought. Thinking, on its own, is empty and comes as an external form to the said material, fills itself with it, and only thus acquires content and becomes real knowing.”
The content of thought is matter, but “matter” as a “content” is seen as separate from thought. Formal logic presupposes a separation between thought and the object. It assumes that the material of knowing (the content of thought) is merely “present on its own account as a ready-made world apart from thought,” and that thinking on its own is empty and external from the object. In this sense, thinking receives the material external to it and thus acquires content for its knowledge. Yet, at the same time, when thought completes itself with this external content, it excludes the object as playing a role in its forms of thinking.
This kind of hypocrisy that Hegel is talking about is implicit in our understanding of the world.
Hegel says:
§ 39
“Further, these two constituents — for they are supposed to be related to each other as constituents, and cognition is compounded from them in a mechanical or at best chemical fashion — are appraised as follows: The object is regarded as something complete and finished on its own account, something which can entirely dispense with thought for its actuality, while thought, on the other hand, is regarded as defective because it has to complete itself with a material and, moreover, as a pliable indeterminate form, it has to adapt itself to its material. Truth is the agreement of thought with the object, and in order to bring about this agreement — for it does not exist on its own account — thinking is supposed to adapt and accommodate itself to the object.”
The true business of science
Science is “the agreement of thought with the object.”
Today, the term “science” is often used as a synonym to justify narratives that mislead individuals away from being self-conscious of the truth.
The true definition of science is:
The “business of science is simply to bring the specific work of reason, which is in the thing, to consciousness.”
The ontology of science is the “consciousness” of the essential nature constituting the object. Comprehension is the way consciousness receives the truth.
The only way to arrive at the truth is to know what constitutes it because science, in a basic sense, does not create truth that is not already there; rather, it is the systematic inauguration of what already is true by bringing that into the light of consciousness. The methodological skepticism of Descartes produces a misapprehension of the purpose of science. Hegel says about Descartes: “To seek to know before we know is as absurd as the wise resolution of Scholasticus, not to venture into the water until he had learned to swim.”
“But the examination of knowledge can only be carried out by an act of knowledge. To examine this so-called instrument is the same thing as to know it.” And this will be what today we know as a fundamental principle in quantum mechanics. It assumes that there is knowledge prior to the act of knowing.
He goes on:
§ 40
“Thirdly, when the difference of matter and form, of object and thought, is not left in that nebulous indeterminateness but is taken more definitely, then each is regarded as a sphere divorced from the other. Thinking, therefore, in its reception and formation of material, does not go outside itself; its reception of the material and the conforming of itself to it remains a modification of its own self; it does not result in thought becoming the other of itself; and self-conscious determining moreover belongs only to thinking. In its relation to the object, therefore, thinking does not go out of itself to the object; this, as a thing-in-itself, remains a sheer beyond of thought.”
What the understanding fails to realize is that the laws of thought are actual abstractions taken from the world. Once separated from the world, they are taken as valid ways of reasoning that can, in turn, be applied to a multiplicity of other different objects in the world. For example, when an angle is abstracted from a table, the angle does not only belong to the table by being limited to it, but is rather applicable to an array of other objects with angles, like chairs, a human elbow, a corner of an edge, etc. All of these are different in physical composition but share the same dimensions and the same geometric forms.
The laws of thought, however, have their origin in the way the world operates. But if we say that the world is logical, then we also have to deduce that it is rational, and if it is rational, it must also be living — because living is the activity of the concept of logic and not just a mere concept as a rule, axiom, or empty abstraction. It is this very self-conscious thinking that is being exercised at this moment — reading, critiquing, thinking, etc. The relations abstracted from the world are not random; they exhibit complex and integral structures characteristic of a thought process, or rather a narrative of a thinking activity. Whether that thinking ultimately belongs to all Being or to some particular being is another important question, later on discussed.
The concept of a successful theory derives exactly from the concept of phenomena such that the concept is abstracted from the phenomena. Then it is important to wonder: What relationship did the concept have to the phenomena before the abstraction?
Conflict of Interest
A conflict of interest can be exemplified by the following superfluous human interaction: Imagine you are sleeping next to your wife on a king-size bed, but for some reason, both of you fight over the exact same spot. Both elbows are touching, and each person wants to be in that same spot on the bed. In this case, a conflict of interest arises because both have the same interest in wanting to occupy the same spot, but only one can take it. The conflict, in this case, is built into the very nature of the shared interest.
In the political domain, a conflict of interest is more complicated because it occurs when the personal interest of a public figure contradicts the public interest, or vice versa. This means that the very job description of a politician is to place the interest of the public as their highest goal. However, the reality is that the interest of the public often contradicts their own personal interests.
A perfect example of a modern-day “conflict of interest” occurred during the Canadian WE Charity scandal. Prime Minister Trudeau invested a large amount of public funding into a company (WE Charity) that was meant to enhance the education system. However, when examined, the charity took in a large amount of money—some close to $400 million—but the value in return they provided in education did not correspond to the amount invested. This is like buying a bag of peanuts for $1,000—the value of the peanuts does not match the value that $1,000 is meant to represent.
In this case, the suspicion is that the Prime Minister put his own self-interest over the interests of the public, as it is suggested that he may have profited from that investment.
I. Presupposition and the Ground of Thought
In logic, every proposition carries with it not just a statement to be tested, but also a background of assumptions—presuppositions—which make that statement possible in the first place. These presuppositions are not yet affirmed or denied; rather, they form the ground of intelligibility.
Take the proposition:
“Aristotle no longer writes philosophy.”
The explicit claim is about Aristotle’s current state. However, this only makes sense if we presuppose:
- That Aristotle once did write philosophy.
- That Aristotle existed.
- That writing philosophy is a meaningful category.
So before even engaging with the truth value of the proposition (true or false), we are already engaging with a logical structure that rests on prior affirmations. These affirmations are not yet asserted; they are implied by the structure of the statement itself.
This is the first movement of logic—not affirmation, but pre-affirmative implication.
II. Negation as a Necessary Function of Affirmation
Negation is not merely the absence of truth. Rather, it is a moment within the process of knowing.
In the dialectical method (e.g., Hegel), negation is productive. It is not destructive. The moment we deny something, we are simultaneously affirming the form of what we deny. For example:
“It is false that 2 + 2 = 5.”
This proposition is true, even though its content is “false.” This reveals a deeper structure: the truth of the false is grounded in the truth of form—the proposition is structured logically, and within that structure, truth emerges through negation.
This is what you’re getting at with:
“The truth value itself is the presupposition that both true and false are, both as a relation, true.”
This means: truth is relational. Even falsehoods participate in truth, in the sense that they help define, through contrast, what is.
III. Affirmation through Dialectical Resolution
The explanation of the movement from a (−) and (+) resolving into another form is true for dialectical logic:
- Thesis ( + ) – An initial affirmation or positing (e.g., a proposition, a belief, a fact).
- Antithesis ( − ) – A negation or contradiction of that proposition.
- Synthesis ( + ) – A new affirmation, not a return to the first, but a higher-level determination that incorporates the contradiction.
This movement is recursive—it does not end at synthesis. The new positive is always subject to further negation. Thus, the process of thought is infinite, dynamic, and self-developing.
“The conclusion is ultimate (+) not only as a final result, but rather, as a fundamental and initial beginning.”
The positive is ultimate because it is always abundant, always present; but it is finite because it is always negated—there is always a part taken from it, a piece measured and limited. The synthesis becomes a new thesis, and the dialectic continues. Every conclusion is simultaneously an origin.
IV. Science, Logic, and the Truth-Process
It is also right to point out:
“The pursuit of scientific truth is the attempt to introduce doubt into an undoubtable principle.”
Even certainty must face doubt to confirm itself. The nullification of a belief is not the end of truth—it is its purification.
Science operates not just by affirmation, but by falsifiability—the condition that any hypothesis must be able to be proven wrong. In this way, doubt becomes a productive act, just like negation in dialectical logic.
Science is a form of existential logic, not as a lack of truth, or the absolute negation of truth, but by enacting the very structure of being: to come into truth is to endure contradiction.
V. Truth, Rhetoric, and the Structure of the Proposition
The important point about rhetoric is that: “In rhetoric, if the point of demonstration is to show only that the thing is ‘untrue’…”
This reveals that truth is not always asserted directly. Often, we arrive at truth through negation, comparison, irony, or absence. Logic, then, is not simply the arithmetic of statements, but the art of tracing the movement of meaning.
Even falsehood is meaningful—because its denial affirms something else.
“It is true that it is false that Aristotle writes today.”
Even here, the logic of opposition is preserving truth.
VI. Logic as the Structure of Existence
If we return to the earlier claim—that:
“Science is identical with the definition of existence,”
we can now see that logic is not just a tool for understanding the world. It is the very structure of the world, because it reflects the movement of being: affirmation, negation, contradiction, and renewal.
DNA, infinity, the knot, the problem of the world—these are not just metaphors, but manifestations of logical form.
Every concept, every phenomenon, is part of this process: appearing, being doubted, being reformulated, and appearing again.