Section 4 (first updated.2022)
The law of non-contradiction, first and foremost, does not simply mean “lack of contradiction”—that is, the mere absence of contradictions. The prefix “non-” presupposes that a contradiction exists, in the sense that it is resolvable; it implies the inverse of a contradiction—namely, a resolution. The law of non-contradiction also does not mean that contradictions are absolute. Formal logic is overly concerned with identifying contradictions in the structure of thinking—specifically, whether or not an argument is consistent with a valid form.
However, the obsessive pursuit of contradictions can become contradictory itself when there is no purpose in resolving them. Once a contradiction is identified, the appropriate response is to resolve it. But if the resolution arises from something external to the contradiction—something outside it—then that, too, reaffirms the contradiction. It supposes that there is a difference. The contradiction and its resolution cannot be the same, yet that does not mean they are not found within each other.
This brings us to the traditional formulation of the first law of non-contradiction: “A statement and its denial cannot both be true at the same time.” In other words, a thing cannot simultaneously both be and not be. For example, the claim that a table is and that it is not cannot both be true in the same context or sense. This simply means that they are different things. Difference is the resolution to a contradiction, because it defines what the contradiction is. A contradiction is simply difference—their differences contradict each other.
How do you know something exists if you are not directly perceiving it? It is a built-in feature of being to know. For example, when you touch a protoplasm—a living cell—it reacts at the precise point of contact. This is a self-excitatory circuit: the organism reacts to the existence of an “other” by confirming it within itself. This “other,” from which difference arises, is the point where knowing a thing and its existence become one and the same.
Water, for instance, is inanimate on its own. It moves only by some external force, like air. Yet when its movements are shaped by air, we call this nature or weather. We consider nature to be alive because it is rational: it can be predicted by rational beings, it has a rational structure, and it produces rational outcomes—it begets rational beings.
Thus, the first principle of thought we begin with is “a determination…”
Determination
According to Aristotle, a determination is essentially a transition into its opposite (Metaphysics, VIII.5, Ross). The negative of any proposition is necessary as the initially proposed determination. In a valid logical structure, we begin first with a positive proposition. The first proposition is always positive because, even if it is inherently negative in content, its position as the first posited claim makes it a positive determination. In other words, it is a proposal—“it is the first to step forward”—and therefore, even if it is incomplete or incorrect, its placement renders it positive, because now we have content to work with—something upon which further claims can be based or built.
The second proposition is always negative, because it necessarily presupposes the first—whether by denying it, elaborating on it, or ignoring it altogether. In all cases, the second proposition either directly recognizes the existence of the first proposition or indirectly recognizes it by reacting to it. If the second denies the first, it is still acknowledging it by virtue of its opposition. And if the second elaborates on the first, it becomes an extension of it.
The proof for a proposition is found through its demonstration against its negative, because the negative proposition is, at the same time, a positive from its own perspective (Posterior Analytics, II.13–15, Mure). Every time a proposition is proposed—whether it is correct or incorrect, affirmative or negative—it constitutes a positive step in logic, because it adds content that thought must engage with, clarify, or resolve.
Sublation
The term “sublation” defines how logic develops and unfolds. The meaning of sublation is twofold: it means both “to preserve, to maintain,” and equally, “to cause to cease” (Science of Logic, p. 185). Sublation captures how one determination transitions into its opposite, and how this transition produces development.
Thought itself is the most primary determination. By this, we mean that in our ontology, Reason is a universal substance: wherever there is reality, there is Reason, or rational thought. This is akin to the quantum principle that there must always be an observer whenever there is a phenomenon. However, the ontology of Reason takes this further, asserting that the universe is first conceived rationally—that Reason is both the architect and the design of nature. As to what subject occupies Reason, or in what form Reason takes shape, that is another and deeper topic—one that may take infinite forms.
When two opposite determinations enter into relation, sublation defines the exchange of their integral properties—those necessary for the emergence of a new and next determination (On Interpretation, I.10, Edghill). Before demonstrating this, it’s important to note that Aristotle’s laws of thought, on their own, still require a subject as their content. These laws are pure forms of thinking, and are therefore applicable to real objects only when coupled with material content.
This subject, understood as everything or infinity—which is also a finite P—equally means that each and every thing is, at the same time, the result of relations themselves (Science of Logic, p. 865). That is, each finite thing emerges from the infinite set of possible relations it could have with others. All the infinite possible ways that any two or more finite things can interact give rise to the reality of “each and every thing” as both particular and universal at once.
Demonstration: Thought Through Sublation
To demonstrate how logic develops through sublation, we begin with a first determination—a simple proposition. Let us call this proposition A. As previously established, A is positive by virtue of its being posited. The moment a second proposition, ¬A (not-A), is introduced, it necessarily engages with A—either by opposing, modifying, or expanding it. This second step introduces difference.
The interaction between A and ¬A gives rise to a third—a new determination, which is not simply a return to A nor a mere acceptance of ¬A. Rather, this new determination—call it B—sublates both A and ¬A. It preserves elements of both while simultaneously negating their immediate contradiction. This is how logic moves: not through mere affirmation or denial, but through a process that overcomes contradiction by integrating it.
This movement from A → ¬A → B is the dialectical unfolding of thought. It is not linear, but recursive and developmental. Each stage contains within it the memory and necessity of the prior, and each contradiction is not a dead-end, but a generative force for new content.
For example, suppose we begin with the proposition:
A: “Man is rational.”
Now consider the second proposition:
¬A: “Man is irrational.”
This appears to directly contradict the first. However, rather than collapsing the discourse into a binary opposition, thought proceeds to a higher determination:
B: “Man is both rational and irrational—his rationality is conditioned by irrational impulses.”
Here, the contradiction has not been erased—it has been preserved and transformed. This is sublation in action: the rational and irrational are no longer pure opposites, but moments within a unity. The contradiction is not destroyed, but resolved in a way that reveals new depth about the subject.
The Subject as Ground of Logical Movement
It is essential to recognize that this process does not occur in a vacuum. The subject—whether “man,” “nature,” or “being itself”—is the necessary ground of this logical movement. The subject is both the bearer and the result of the process. In Aristotelian terms, the subject is that about which predicates are said; in Hegelian terms, it is that which posits itself through the overcoming of contradiction.
Without a subject, propositions are empty forms. The laws of logic—identity, non-contradiction, and excluded middle—remain merely formal until they are applied to real content. That content must be capable of enduring negation, contradiction, and re-determination. The infinity of the subject, as mentioned earlier, does not refer to a vague abstraction, but to the unlimited potential of relations in which the subject may appear and develop.
Thus, every finite proposition is simultaneously the limit of thought and the starting point for its overcoming. The subject, as such, is never static; it is the living mediation of thought with itself—the contradiction that reveals unity, and the unity that contains contradiction.
Logic is…
- Logic has two essential features:
(a) First, it is the actual structure and content of the universe as a rational substance.
(b) Second, logic is the attempt to untangle the infinite content of the world into a limited but comprehensible form for an observer who can only conceive the world in a finite way.
- Logic is, on the one hand, whatever is already present for thought to digest—the content of thought itself, namely being-thought. This content is abundant, but not yet structured. On the other hand, logic is also the construction—what ideologues call a “construct”—of thinking. A construct is defined as a theoretical framework containing variables drawn from conceptual elements considered to be subjective and not necessarily based on empirical evidence.
However, thought, as the objective nature of man, is used to communicate between different observers. It is not merely subjective, but shared—it is the medium of intelligibility itself.
The conceptual elements and subjective aspects of a construct are part of the process by which an individual mind performs a kind of “record keeping”—tracking its own thoughts. Just as a historian observes the events of their time and attempts to capture them as accurately as possible, the philosopher is tasked with examining their natural thought processes, and striving to reflect them externally—as accurately as they occur internally.
In this way, the philosopher seeks to reflect the internal idea—the concept, the essence of a thing, its “blueprint” or inner mechanics—into an external object: the phenomenon experienced by an external observer.
Projection
How this “reflection” happens is answered by way of “projection.” In psychology, projection refers to the mental determination of the observer, who attributes to others what is present in their own mind.
However, projection is not merely a form of psychosis, as the psychological notion might suggest. More fundamentally, projection is the way the observer interprets the rationality within their own mind and uses it to explain the world around them. The observer conceives of rationality in the world through a process of “disassociation.” Again, this notion is not limited to the psychological definition, which implies being unaware of one’s own circumstances. For instance, in cases such as dissociative identity disorder, each identity within the same person becomes so disconnected from the others that the person loses the general sense of ‘self’ that unifies them as a single conscious identity. This results in one part of the personality functioning independently from the rest. A person with this disorder appears incoherent, manic, and bipolar—such that, at one moment, they appear kind, but this quickly overturns into appearing cruel; at one moment they are sad, then suddenly happy. There is no coherent flow to their character; they seem to be merely a random bundle of disappearing and reappearing personality traits.
Human psychology, however, naturally partakes in disassociation in a more subtle and necessary way: when the mind intuitively recognizes an object. Upon observing an external object, the mind disassociates from itself—from the awareness of itself as the observer—and simply sees the object “as it is in itself.” However, the object that is “in itself” true, existing independently of the observing mind, is still, at the same time, dependent on how it is viewed—that is, it can be perceived in innumerable ways.
The subjective element, even though it lacks empirical observation (which is typically regarded as the objective component), is not merely subjective in the pejorative or relativistic sense. The rational processes occurring in the mind—though they arise within the individual—are not confined to that individual. In other words, they are universal in nature. Any number of observers may arrive at the same conclusion, particularly when working through contradictions via rational dispute.
To demonstrate that what is conceived subjectively is, in fact, fundamentally objective—this is the central challenge of philosophy.
Knowledge Reveals…
We ordinarily think that knowledge is acquired by revealing something previously unknown. However, knowledge is not like collecting a pile of wood for the construction of a building. It is not something that, once attained, is simply possessed. This is a natural trick of the understanding, masking a more fundamental kind of knowing.
Knowledge is identical with activity—specifically, the activity of thinking—because it attempts to introduce doubt into what appears to be an undoubtable system of thought. The principles of reason are not fixed, written rules cemented somewhere, waiting to be discovered; rather, they are identical with the manner of thought that reflects upon them. These principles are the determinations of thought in its universal form—such that, whenever thinking reaches its truest expression, it arrives at similar principles again and again.
A scientific hypothesis is not confronted with the question of whether a phenomenon exists, but rather whether the nature of the phenomenon is predictable. In logic, the function of the proposition is to test or even disprove a presupposition, because logic aims to move thought from assuming to knowing. The transition from assumption to knowledge occurs when the phenomenon reappears in thought in the same way, consistently—repetition revealing structure.
Experiment is the procedure that determines whether observation agrees with—or conflicts with—predictions derived from a hypothesis. A hypo-thesis (literally, “placed under”) is falsifiable if it can logically be proven false by contradictory propositions. When a hypothesis withstands attempts to disprove it, and repeated affirmations support it, the proposition follows from the presupposition.
Analytic truth is defined as a proposition that is true by virtue of the meaning of its terms, such that its denial would be self-contradictory. This kind of truth depends on the presupposition that something is always either true or false, according to the principle of bivalence.
(Addendum: Science as identical with existence)
The pursuit of scientific truth is the attempt to introduce doubt into an undoubtable principle. In that moment of doubt, there lies the possibility for absolute exaltation. If a system can doubt itself, it may choose nullification—and this act of nullification becomes a fact it cannot doubt about itself. In this way, it becomes a new fact of its own being—but this fact is not absolute, for it is an abstraction, a moment, within an ongoing process.
The world itself appears as a problem, a knot of contradictions, always unfolding. It is infinite, not in endless quantity, but in depth—like DNA, the longest known strand in the universe, yet condensed into the smallest of spaces. It is largest in quality, in function—measured not by size, but by the capacity to produce.
In logic, the most basic argument form, modus ponens, literally means “affirming by affirming.” That is to say, the very act of affirming is itself an affirmation; the stating of something is, by its nature, a statement.
If P, then Q.
P.
Therefore, Q.
This is the formal structure of affirmation, and at its root lies the same dynamic: thought moving through itself, affirming what it already contains, but did not yet fully understand.
Positive and Negative
According to informal logic, the inverse factor in a proposition is the first implication of the presupposition. In other words, what the proposition proclaims is first presupposed—that is, before the positive statement is made, its opposite is already implicitly assumed. The fact that requires proof is adopted in three stages:
- First, the proposition is put forward as if it exists.
- Second, the existence of the thing presents itself as a self-evident prospect.
- Third—and only after we assume it exists—can we then doubt the nature of its existence: the kind of existence, or what it actually is. That is, the thing may have a set of features which, if demonstrable, are undoubtedly true, but the resolution or integration of those undoubtedly true principles—that is the conclusion.
Negative (−) (+) Positive
In rhetoric, if the point of a demonstration is to show that something is untrue, there is still the presupposition that the negation of the untruth is some form of truth—i.e., the opposite of something untrue is presumed to be true.
A proposition is a statement that has a truth value of either “true” or “false.” But the very truth value of a proposition presupposes that both truth and falsity, taken together as a relation, are themselves true in some sense. For example, it is true that the proposition “2 + 2 = 5” is false.
The Negative and the Positive are both true insofar as they equally exist, and that their existence is defined by opposition. When a (−) and a (+) come together, they may resolve in a (−)—because a (−), in pure relation to itself as a (−), produces a (+) determination, and therefore becomes a positive variable (+). If this (+) is then taken in conjunction with itself—as another (+)—it remains (+).
Thus, the conclusion is ultimately positive (+)—but not as a final result. Rather, it is a fundamental and initial beginning. Any advance taken beyond this initial point as a beginning is inherently negative (−) because it introduces doubt or a resignation of the initial positive affirmation.
For example:
Proposition: Aristotle no longer writes philosophy.
Presupposition: Aristotle once wrote philosophy.
The presupposition does not question whether something is true or false—it confronts what cannot be doubted: namely, the matter of fact that something must be either true or false. The truth value is found in the ground that enables the declaration of the proposition in the first place.
Negation – A Taking-Away from “Everything”
This follows from the fundamental logic of negation, namely that the presupposition of any negative statement is always a positive proposition. According to Hegel, logic begins with the undifferentiated notion that everything exists—that everything is “out there.” The content of thought is present for thinking, but it is not immediately obvious how everything is out there.
Negation, in this sense, is a negative determination in a positive sense—because it takes away a smaller portion from a greater content. This subtraction is not the division of a whole into smaller parts, but rather the reduction of the infinite into a finite and limited conception. Though this conception is inherently inaccurate—because it constrains an unlimited substance into a biased and partial understanding—it is nevertheless the only possible avenue by which any understanding of the whole can occur.
For example, the proposition “not-cat”—the absence of “cat”—still reaffirms the presupposed knowledge of “cat.” The presupposition forms the ground for the proposition to even be made, because regardless of whether the proposition is true or false, it still requires the presence of the assumption for its sense to be necessarily valid.
The presupposition depends on the necessary truth that there is a fact—that something is. Only on that basis can a proposition be evaluated at all.
Position
Proposition and the Movement of Demonstration
The proposition is the risk taken to move beyond the presupposition by limiting it to a variant of itself—a step it takes to prove itself through demonstration. However, insofar as demonstration (from demo-in-stration) proceeds, it requires that the resolution already be given as a presupposition. The demonstration then takes this resolution, turns it into a new proposition (or propositions), and—so far as these new propositions form contradictions about the same resolution—confuses and complicates them into contradiction(s).
These so-called contradictions take on inverse or inverted identities of variables. The same relation takes on two different and opposed identities, each of which can recognize itself only by way of the other. Once this happens, the resolution becomes the single identity of an innumerable set of diverse identities, all of which take on the same relation, exhibiting the conclusion—the single conception of a determinate process.
Once a process is determinate, it assumes a particular identity, whose only inherent nature is to change into its opposite—or simply into the “other” of itself. The key is for the re-solution to find itself again—to return to itself from the premises of the demonstration that challenge the initial identity. The demonstration is not necessary because it brings about a resolution, but because it is necessary in maintaining one.
If something is true, why does it need to be challenged?
The answer is that truth cannot be assumed—it must always be shown. The process is ongoing.
This is not a mere technicality, but a practical step of logic. The resolution of a logical problem lies in revealing all possible components involved in the contradiction. Logic unveils all the possibilities, and allows one to be determined over the other. This is the basis for ethical practicality.
Thus, true science, even if physical, is not separate from ethical conduct. For example, a particle always takes on a character—a quality—that is phenomenal, or more precisely, experienced by an observer.
One basic maxim of science, inherently ethical in nature, is to always assume in the premise that the matter of fact is first false—even if the presupposition is already known to be true. This concerns validity, not soundness, because if the first premise assumes the fact is true, then the demonstration merely moves to make that false. It is logically valid to begin with the presupposition that the fact is false, so that the proper movement is toward truth. This holds true—but only if we take seriously the necessity of opposites as fundamental to the structure of thought and reality.
This is the first proposition, following the presupposition that both true and false must be adopted as true—that is, taken as given in order to be worked through. The aim of demonstration is to move from false to true, even though the false is also true in being not-true—a determinate negation.
However, as this movement from false to true belongs to the process of demonstration, it may not necessarily apply to indemonstrable truth—because in such cases, truth is simply a matter of fact. It must first be presupposed.
(1a) Self-identity
The presupposition begins with the identity that something is equal to itself: A = A. However, this self-identity is itself a contradiction, because the proposition of “itself” already presupposes a dissolution from an other. The receiving of identity comes from somewhere else—from the loss of another identity—but not necessarily in a reciprocal manner.
To have an identity means to exclude all other things from that identity so that it may stand alone—distinct and clear, either to itself or in relation to something else. However, every identity necessarily involves an unidentifiable numberof other possible identities that share a common condition of identity. Therefore, any single thing that identifies as peculiar or particular also discloses within itself a multiplicity of other identities.
So far, the definition of “other”: the identity of the other is not the identity of the one self-identity, but rather the identity of some other distinct self-identity. Yet the “other” from which identity is received is also absolute difference—it is nothing, or unidentified. The self-identity thus stands alone, alongside nothing. In other words, there is an element of “nothing” in every identity—a lack within itself.
This is the real content of the law of non-contradiction: that something cannot both be and not-be at the same time. This means that, at the same moment, the same thing is different from the other thing.
For example: A ≠ not-A. The distinction made here is not simply between Being and Nothing, but rather between Being-together-with-Nothing—their relation—versus the excluded middle, the point at which their very distinction stands apart from identity itself.
In this sense, identity is the distinction of opposition—the tension that arises not from mere separation, but from the unresolvable co-belonging of Being and Nothing.
2(b) Presupposition
The whole point of this outline of presuppositional logic is to show that, in knowledge, we do not positively affirm anything in the strict sense—or rather, we do not create knowledge from where it was entirely absent. Socrates argues that “knowledge is recollection” of eternal and unchanging Forms. This means that whatever truth we discover about the world is already implicitly present as the essence of the mind. Hegel similarly says that when reason develops consciousness of truth, it is “at home with itself”—in other words, it returns to what it essentially was all along.
In this way, the power of knowledge, or rather of every single argument, is first and foremost a presupposition. To presuppose means to intentionally assume a fact without certain knowledge of its truth, without certainty. The presupposition is the power behind a course of action in thought—in other words, to consider. Consideration is a form of presupposing a fact prior to the unfolding of an argument.
If we were to define “presupposition” with a single word, it would be: process.
3(c) corollary
A corollary is defined as a proposition that follows from one already proved. This prompts the following question: what comes before a proved proposition? The answer cannot simply be that another prior proved proposition comes before it, because that does not explain how or why the predicate is demonstrated in the first place.
What we are really asking is: why do proved propositions exist at all, such that they presuppose each other as true? This is a slightly different question than simply asking what is a proved proposition?, because a proved proposition is, by definition, a demonstration—a process undertaken to show why something is already true.
But this leads to a deeper paradox: Why would a proposition need to be proved if it is already assumed to be true in the first place?
This is an example that requires us to confront the situation in which something is valid, while at the same time possibly unsound. That is, the logical form of the proposition may follow necessarily from prior premises (validity), even if those premises themselves are not demonstrably or necessarily true (soundness).
4(d) Valid but Unsound
The answer goes beyond the simple definition that treats the valid-but-unsound as a combination of untrue content with a true form. On the one hand, the content is deemed untrue because there is no content to begin with without some already predisposed form—or, more precisely, the form is always already present alongside the content. The content is true insofar as the form is truly consistent with it.
It is this consistency that must be accounted for in our understanding of “valid but unsound,” because the common presupposition—that the consistency between form and content comes from outside both—is itself an unsound claim about validity. Validity always presupposes that form is, at minimum, equivalent to the content.
Thus, the proved proposition contains, as part of its own beginning, an unsound premise. Can it be that the unsound is corollary to validity, precisely because the fact that validity concerns structure alone is itself unsound if it does not answer what is being structured—that is, the content? The form is meaningless if it is not applied to anything. For example: structuring your writing before you write. The latter is nonsensical.
Soundness and Unsound
The essay format presupposes that someone, at some point, wrote an essay and discovered that structure to be effective. But this does not mean that the structure produces the content of the writing. The latter (content) cannot be accounted for by the former (structure). The principle of soundness being fundamentally defined by the meaning of validity—that we require a proper structure to begin with—involves an unsound pre-proposition: that if content is required for structure, but content has no structure prior to its proper structuring, then valid and unsound becomes a corollary [define] of valid and sound. In this way, validity mediates the two only insofar as unsoundness is presupposed by soundness. In short, the valid step is the path toward its own soundness.
If, by unsound, we mean a claim is unproven or unprovable, this does not automatically imply that its implications are likewise unprovable. When we say that an argument can be “valid but unsound” so long as the form is correct—i.e., the propositions are related in such a way that, if the premises were true, the conclusion would have to be true as well—this implies that the very purpose of validity is to transform the unsound into the sound. As long as the form is a certain way, the content is said to follow.
However, the content cannot be a certain way unless we already possess a predicate that determines it to be that way. That’s why something can be valid but unsound, but something unsound in the first instance is also invalid—because the supposition that content requires structuring implies that the structure is without content. This results in the implication that one can observe content without its form.
Unsoundness, then, is to treat content as having no form. For example, wood without the house, or wood without the tree. This is unsound, because any content presupposes form, or at least that to be content is to possess form. That is, wood possesses the form of wood, and wood atoms possess a form distinct from the form of metal atoms.
So, content independent from form defines unsoundness—a reasoning process that does not proceed from a proper unity between form and content. In contrast, validity remains valid on the basis of having form prior to content, because of the implicit assumption that form creates content.
For example, the mythological image of a unicorn is unsound because the connection it draws to the real world is unproven and unprovable. However, that does not mean its implications are also unprovable. If a unicorn implies an analogy for majesty, then it is valid that concepts like dignity, excellence, and purity may follow soundly from an unsound corollary. This demonstrates that even though something is unsound, what it indicates may still be sound—especially when it is valid but unsound.
Three principles of logic
(1) The Law of Identity, (2) The Law of Contradiction, and (3) The Law of the Excluded Middle
(Read #47 – Science of Logic, Hegel, pp. 66–67)
Reason follows the forms of logic. The principles of identity, difference, and opposition are the basic determinations of thought because they mutually determine one another by virtue of being inversions of each other. When one principle opposes another, it is the opposition itself that affirms both principles their respective place as mutually exclusive properties.
For example, the proposition P is identical with itself means that P has no difference. However, this very lack of difference is an opposition to difference. Identity, having no difference, is still different from difference—it must oppose difference in order to be sameness. The assertion that identity is different from difference implies that identity inherently involves its opposite determination: difference.
(Metaphysics IV.3.1005b, trans. Lawson-Tancred)
The identity P = P, or in immediate experience—for example, “a tree is a tree”—tells us nothing more than that something is itself. The explanation of what a tree is, however, requires that we speak of further determinations that identify a tree as distinguishable from everything else. What is a tree? We must say: leaves, wood, water—and even more fundamentally—color, shape, size, etc. Each principle of identity carries with it an infinite series of differences that are all inherent in describing the identity.
(Metaphysics IV.4, trans. Ross)
The laws of thought are ordinarily categorized into three main principles. Peirce outlines them in the following way:
I. The Principle of Identity:
- a) A is A
- b) Commonly represented as P = P
II. The Principle of Contradiction [or Difference]:
- a) A is not not-A
- b) Two propositions “A is B” and “A is not B” are mutually exclusive
- c) P or not-P
III. The Principle of the Excluded Middle [or Opposition]:
- a) Everything is either A or not-A
- b) Either P is true or its negation is true
Each principle is typically treated as an individual logical proposition, independent of the others. However, identifying these as “laws” may reduce them to rigid, static rules. In truth, any serious logician will recognize that these principles are fluid and dynamic, because each presupposes the others and transitions into them. The proposition of one principle necessarily invokes the others.
(On Interpretation I.10, trans. Edghill)
The relation between these logical principles is internal, because the presence of one principle on its own is contradicted by the necessary presence of the others. For example, if P = P is true, its further determination is something different, say Q. Therefore, in relation, we have: If P, then Q. The relation between P and Q is inherently contradictory. For instance, if the further determination of P is Q, then Q must be not-P—it must be distinct from P in order to be Q. Yet Q arises from P. So, if P then Q, and Q is not-P, it follows that P is not-P, which leads directly into the principle of opposition: either P is true, or its negation is true.
(Metaphysics IV.7, trans. Lawson-Tancred; Prior Analytics I.13–15, trans. Jenkinson)
Now, if the negation of P is not-P, what is the negation of not-P? It cannot simply be P again, because that would presuppose the inverse not-P, returning us to where we started—an infinite regress. There must then be a negation of the negation, which itself takes on a distinct and more advanced form.
(Science of Logic, §882)
As Peirce puts it: Not-A = Other than A = A second thing to A. This means that not-P is the transition of P into something else.
The point is that whenever one law is asserted, it invokes the transition to the next. The contradictions between these laws generate further determinations. The laws of thought are not merely rules of inference—they are determinations of thought that constitute the generation of form.
5.a) “affirms by affirming”
Law of Non-Contradiction: P and not-P cannot both be true at the same time.
Modus Ponens (“Affirms by affirming”):
P → Q
P
∴ Q
The law of non-contradiction states that P or not-P cannot be true at the same time. This implies that P and not-P must occur at different times or in different logical moments. This proves that if the antecedent is equal to itself (i.e., P = P), then the consequent must also be equal to itself (Q = Q). This is the essence of affirming by affirming: a consistent identity in the premise must result in a consistent identity in the conclusion.
Modus Tollens (“Denies by denying”):
P → Q
¬Q
∴ ¬P
The law of the excluded middle states: either P or not-P must be true. But if the negation is true, then P must also be true in some form, since truth and negation are co-determined. This logically follows in modus tollens: if not-Q is true in relation to Q, then not-P must be true in relation to P. Denying by denying, in this sense, shows that if the consequent is false, the antecedent must also be false. The negation of the consequent implies the negation of the antecedent.
Example: The Relation Between a Point and a Circle
- A point (or period) represents pure self-identity: P = P
- A plane represents pure externality: not-P
According to the law of non-contradiction, either P or not-P can be true, but not both at the same time. This means that self-relation is true at one moment, and self-externality is true at another moment.
By the law of the excluded middle, since they cannot both be true at the same time, the truth of one implies the negation of the other. When externality is true, its negation, which is identity, must also be true, though not simultaneously, they are instantaneous. They are interrelated.
When identity (the point) takes on externality, what is originally self-contained becomes extended. The point becomes stretched, and the extension of that point is a line.
Then, when that line externalizes its own identity—i.e., when it identifies with itself in space—it bends and closes upon itself as a circle. Thus, the line, as an extension of a point, becomes the circle, a completed form (figure) from externalized identity. This basic geometric structure is inherently logical before it is physical—meaning that the form of physicality arises from these rational movements of generation. In other words, this geometric form, as a logical substance, is the essence—our very form of consciousness itself—through which reality is disclosed. It reveals distinct moments by excluding one timeline from other parallel potential timelines.
Modus ponens – modus tollens
Let us demonstrate, first (A), how the proof for any proposition is found in the demonstration against its negative, and second (B), how the laws of thought are internally related.
(A) Demonstration through Negation
The classical Modus Ponens and Modus Tollens—Latin terms meaning “affirms by affirming” and “denies by denying”—show how the proof for any proposition is found in the demonstration against its negative. MP and MT produce each other’s conclusions. Affirming by affirming produces the conclusion that will be denied by denying, and denying by denying produces the conclusion that will be affirmed by affirming.
The consequent is the ‘effect’ or result of the contradiction. A consequent is logically consistent—i.e., a thing that follows from another. It is the second part of a conditional proposition, whose truth is stated to be conditional upon that of the antecedent. The truth of the consequent lies in its following after an initial proposition known as the antecedent. Regardless of the nature of the consequent, the essential truth is that a consequent is present when one thing presupposes another before it.
Modus Ponens
P → Q
P
∴ Q
Modus Tollens
P → Q
¬Q
∴ ¬P
Modus Ponens (MP) states that if the antecedent is equal to itself, then the consequent must also be equal to itself. For example, if P = P is true, then Q = Q is true. However, if we affirm that Q = Q is true, we can also affirm that ¬P (not-P) is true because Q is equally ¬P. So, Q = Q is the same as saying Q = ¬P. Affirming that the consequent is true is the same as affirming that the negation of the antecedent is true. For example, affirming that the consequent Q is true is equivalent to affirming that the negation of the antecedent, which is ¬P, is true. In this way, MP proves the conclusion of MT: ¬P.
Modus Tollens (MT) states that if the negation of the consequent is true, then the negation of the antecedent must also follow as true. For example, if ¬Q is true, then ¬P is also true. However, the negation of the consequent also implies its negative antecedent. In other words, because Q is ¬P, then ¬Q implies P. If P is ¬Q and Q is ¬P, then P = Q. MT thereby proves the conclusion of MP: Q. (Kenyon, Tim. *Clear Thinking In A Blurry World. Nelson Education. Chapter 6, p. 165)
(B) Internal Relation of the Laws of Thought
I. The Principle of Identity
In the principle of identity, P must be equal to P so that it can be distinguishable as not “not-P.” More generally, this principle states that everything is identical with itself. The negation of P = P is the principle of difference—i.e., something cannot be both P and ¬P at the same time. The principle of identity is thus the initial determination, but not chronologically first; rather, it is as fundamental as the other determinations, such as its negative—the principle of difference.
II. The Principle of Difference (Contradiction)
In the principle of difference, P and ¬P are mutually exclusive, yet they coexist in relation to each other. So P occupies one moment, and ¬P occupies another moment, and both contradict each other. This contradiction resolves in the following way:
P is not ¬P ∴ P.
The law of contradiction thus states that the identity of P is found in ¬P, which simply means that negation is the identity between two inverse propositions. This implies that the identity of something is derived from its difference. Difference leads naturally into opposition. It is not that two opposed things are merely different, but rather that difference is the opposition of a thing with itself.
III. The Principle of Opposition (Excluded Middle)
The principle of opposition states that either P is true, or its negation is true. But whenever the negation is true, then the antecedent of that negation must also invariably be true (On Interpretation 9.18a28–29). So, if everything is ¬P, everything must also be distinctively P.
Negation is always the negative drawn from the positive. The excluded middle literally states that everything is and is-not, and that this difference is the identity—an identity that takes on a further determination, different from the two opposed propositions.
General Conclusion
What general conclusion can we draw based on Aristotle’s three laws of thought?
- The object is both identical and different, and this opposition is what makes the object distinctively identical and distinctively different.
- Objects that are both identical and different are, at the same time, different and identical from other objects that are themselves both identical and different.
These conclusions represent the broadest possible generalizations about the relations constituting any object. While they may not help identify a specific thing’s nature, they are valid conclusions about the structure of form itself. They disclose all possible courses of action, and the negations of those actions. They simply outline all the possibilities for why a thing is and is-not—showing that both internal and external relations serve as the logical dimensions of reality.
Let us now turn to how the laws of nature are the appropriation of the forms of logic—in other words, how logic is the activity ossified as the laws of nature.
6.e) Reason is indifferent
Not “Born as a Blank Slate”
There is a faculty in the mind that naturally thinks ahead. The laws of thought—Reason—correspond to time. Reason is universal because it is indifferent. This does not mean that Reason is separate from the object, as Plato argues, nor does it mean that Reason is inactive in the object, as Modern psychology claims when it says we are “born as a blank slate.”
Reason does not settle into any particular object. It is the conceiver of all objects and beyond, while not being limited to its conceptions. Reason is indifferent to differences, and this indifference becomes the relation through which it encompasses all differences as a single concept.
Internal and external relations are the fundamental logical mechanics of substance—i.e., of Reason. Internal and external relations are both different and similar at the same time. They are similar in that they constitute the same form—they are the structure of the object. Yet, they are different in that they express opposing activities within the same object, or rather, within the same dimension where opposite determinations can arise.
The concepts of space and time are the most explicit intuitions through which internal and external relations are characterized. Reason is the relation by which space and time exist as distinct determinations.
Reason is the first principle because it begins with the law of identity: I = I. The principle of identity is the most general of all principles, because any principle must first be in relation to itself before it can be anything else. (Yet, how can it be the most general if it presupposes another?) This principle, however, by its very nature, presupposes its own contradiction—or rather, assumes its inversion. This is part of its conclusive nature: it contains its own negation. There is nothing external to it, and therefore, nothing outside it can negate it. According to the principle of non-contradiction, the inversion is the identity. The contradiction is internal, and this internality is what affirms the unity of Reason.
Eternity or Permanence – identity
Three modes of time correspond to the logical principles: eternity or permanence (Kant, Critique of Pure Reason A26/B42) is defined by the principle of identity; coexistence is defined by the principle of non-contradiction; and succession is defined by the principle of the excluded middle (Kant, Critique of Pure Reason A11/B14).
With each activity, the inversion consists of its own form. In summary:
A) There is a general form that all activities take on as the totality of their relations; and
B) Each specific activity, as the inverse of another, takes on its own particular form within the general form.
Every object is therefore separated from every other object, yet at the same time bears a relation of necessary influence upon the others. An object may come into contact with another either directly or indirectly—through another object in closer proximity. Without this relational structure, no object could subsist in separation.
In physical phenomena, we see this as the distribution of energy: energy is most concentrated at the center, and its intensity decreases as it extends outward. Take, for example, a star. The highest point of energy resides at the core, and the lowest point is found at its outermost extremities. This gradient is sustained by the full range of energy levels throughout the space between those two extremes.
Contradistinction
The word “contradistinction” is used by Hegel to highlight the contrasting qualities that constitute a contradiction. Mind, or reason, is the total activity that assumes a general form, and within that form exist inverse activities of reason in contradistinction to each other. There is an “inversion of an inversion” in the unity of internal and external relations. What is internal for the object (i.e., reason) is external for the subject (i.e., the human being), while what is external for the subject (the mind) is internal for the object (the body). In this sense, the external reality of the body is the internal activity of the mind, and the internal activity of the mind is the external reality of the body.
How can reason be both the indifference and the difference of objects? The particular object, as a distinct thing, is itself a limitation. Space is always the quantity that exists outside; time is always the quantity that exists inside, as itself. Space is the quantity that is never itself. Reason is the relation between space and time because it is always the thing as itself, confirmed as itself by that which is outside itself—and what is always outside the self is precisely that in which the self resides, as the other of itself.
Inversion
In biochemistry, for example, the word “synthesis” is a foundational concept in science, particularly in biology and chemistry. It closely aligns with what Hegel calls “sublation”—a term defined through the related concept of “inversion.”
The term inversion is commonly understood as reversal, like turning a shirt inside out. However, this reversal—the turning of the “in” from the “out” or the “out” from within—points to the location of where a dimension exists in space and time. In other words, a dimension does not occupy a position in space in the way an object does, because a dimension is the domain within which space itself occupies position. A dimension is, therefore, the inversion of an object by being within it, while the object is outside of it, and yet still disclosed by that same dimension. The object is thus also within the dimension.
Inversion defines sublation because it explains the movement from one object not being another, to the steps by which one thing becomes itself through that difference. The development of the atom is a process of sublation, explained by inversion (see Atomic Progression section).
Inversion Geometry
Inversion geometry explains how one object changes into another, and how consciousness and object share the same dimension.
The basic tenets of inversive geometry include the following:
- Internal and external relations are the fundamental operations of inversion geometry.
- Inversion does not mean that the form of the object remains the same. In fact, when something is inverted, its form changes. This change of form is called sublation—either a regression to a previous state or an advancement to a new one.
- For example, the inversion of a circle is a line; and any point can be transformed into a circle or a line depending on its relational transformation.
- The relation between point, line, and circle is not static but dynamic. Once one form transforms into another, its new form may continue transforming, giving rise to new distinct configurations.
Sublation is defined as a process that both preserves and abolishes. It explains how opposite results can constitute the same activity. That is, from one particular point, a different point can be derived—where both differ, but their difference itself is a reflection of the same relation, expressed through different particulars, and so on in an ongoing movement.
Inversion Across Disciplines
- In physics, inversion refers to the transposition of an atom occupying a particular energy level.
- In chemistry, inversion has a qualitative expression: a reaction that causes a molecule to change from one optically active configuration to its opposite (e.g., in stereochemistry).
- In terms of energy, this is similar to the conversion of direct current into alternating current.
- In mathematics, inversion refers to the process of finding a quantity such that the product of it with another (under a specific operation) is the identity. It also refers to determining the expression that produces a given result under a transformation.
- In geometry, inversion is defined as:
“A transformation in which each point of a given figure is replaced by another point on the same straight line from a fixed point, in such a way that the product of the distances of the two points from the center of inversion remains constant.”
A useful illustration: the inversion circle with point P inverted to P’ (where P is outside the circle) describes the behavior of an electron emitting a photon. The decay of the electron produces a photon, and this photon itself can become part of another atom. Light is the self-reflection of energy. This is analogous to the essence of mind—the quantum mechanics of consciousness.
Inversion as Consciousness
Consciousness is the process of inversion, where thought and object are indivisible. Inversion follows a dialectical structure.
The term dialectic originates from the word dialogue. Dialectic is not simply abstract logic—it is natural discourse.
(See sections: Geometry of the Line, Plane, and Circle. Apply inversion to: point, plane, circle.)
Negation is the principle by which opposites relate. A perfect example can be seen in traffic laws: when cars have the right of way, pedestrians do not—and vice versa. Otherwise, there would be a collision. The relationship of negation ensures that difference is coordinated rather than chaotic.
Relation – “ideal turtle”
Productivity Explains Creativity
Production is the basis of creativity. Etymologically, “production” can be divided into pro-deduce—meaning “positive deduction”—and cre-activity, the activity of creation.
Our attempts to explain the nature of thought are always challenging. When we speak of thinking, we recognize it as present—we know that it is—but we do not know what it is that is there. We are aware of thought’s existence, but we cannot fully grasp the nature of that which we know to be present.
Thoughts are not images, but mental conceptions. In dreams, images represent thoughts, but they are not the thoughts themselves. Likewise, words are not thoughts—they are attempts to communicate them. We understand the nature of thought intuitively, and this intuition tells us what a thought means. Yet the question, what is thought itself?, remains a vague and general notion.
The most plausible understanding posits that thoughts are not objects, but rather pure motions. Often, we associate motion with objects and treat thought as the abstraction of that motion. This is the view often held by physics. However, in pure thought, we do not require a representation of motion—such as an eagle soaring upward. The concept of upward motion does not require the specific characteristics of a given object in order to be defined. However, in nature, motion does require a subject—be it an eagle or an atom—that characterizes upward or downward movement.
An eagle may move upward, but the notion of upward motion applies to many different things. Thought is universal because the logic of thought applies to all objects. Conversely, a particular object only conveys an abstraction of a sequence of thought. A specific object reveals a unique rational sequence, while reason itself discloses the types of sequences a given object may take.
Thoughts are not motions in the mechanical sense, where one thing is forced by another to move. Rather, thoughts are motions in that they are changes within matter—the shifts in position, orientation, or condition that define form.
Thought as Relation
Motion is the generative activity behind representative change. Thoughts are the motions of activity, and the nature of this activity is that it is a relation.
“Relation” is perhaps one of the most important principles in philosophical science. It affirms the logical truth that relation is an absolute predicate. A relation is not just an abstraction between two interacting entities. Instead, the relation is the very reason why these entities can be differentiated at all. The entities themselves are propositions of a relation.
In purely physical terms, relation can be likened to a wavelength, which reveals discrete states of a particle. The particles are merely expressions of different ranges within that wavelength. The relation is thus primary, while the objects it differentiates are secondary expressions of it.
Ideal, Actuality, and the Ground
A relation is the fundamental description of thought as the motion of activity because thinking is ideal. The word “ideal” is derived from idea with the addition of “L,” symbolizing an idea that serves as the aim of an activity.
This describes actuality: not the sum total of all possible things, but the realization of possibilities within the unity of a single idea.
Consider the notion of the ground. When we say “I stand on the ground,” what are we referring to? The ground represents our most explicit understanding of solidity. To be “grounded” implies focus and stability.
Yet, what supports the ground? If I stand on the second story of a building, the first story supports me. Below that is the basement. On the Earth’s surface, beneath us lies soil, then water, lava, and eventually the Earth’s core—which is not even solid. This reveals the same dilemma posed by the ancient paradox of infinite regress: the idea that the Earth rests on a turtle, which rests on another turtle, and so on ad infinitum.
Although the imagery is humorous, the analogy brilliantly captures the problem of foundations: that no physical object truly provides a concrete base. The infinite regress itself becomes the basis of material support because the infinite is the relation.
Even if we choose an arbitrary object—like a turtle—as the basis for another, its true foundation lies not in its physical position, but in its relation to the infinite. The analogy fails when it insists that the turtle is the support, because in reality, any object can support another only insofar as they share a relation to the infinite—not a physical stacking, but a qualitative connection.
Thus, the ground is not a thing, but an ideal. It supports because it is the realization of an aim. Any object is real because it is an ideal—the actualization of an idea that generates it as a possible possibility of itself. It is known only insofar as it is experienced in this function.
Thought as Actualization
Thought is the motion of activity, where relation is the ideal aim of the idea, actualizing the form of all its possibilities.
The object is the reality of these possibilities, insofar as they are the experience of the activity itself.
Unicorn
The sublation of mythology is language. Language is the memory of understanding and the reference point of reason. It is essential that reason mediates imagination as the locus of language.
In today’s world, it may seem outdated to use a dictionary to ground or guide our thinking—but language remains crucial for structuring and directing thought.
Logically, consider this flawed syllogism: “Mammals generally have horns. A horse is a mammal. Therefore, a horse has a horn.” This argument is valid in form but unsound in content. It demonstrates how imagination, through mythology, can produce valid but untrue statements. Its validity lies in the corollary structure of imagination—it can derive consistent meaning even from unreal premises.
Law of Diversity
Hegel – Diversity (p. 902)
Diversity, like identity, is expressed in its own law. Both of these laws are held apart as indifferently different, such that each is valid on its own without reference to the other.
Hegel writes:
§903
“All things are different,” or: “There are no two things alike.” This proposition is, in fact, opposed to the law of identity, for it declares: A is distinctive; therefore, A is also not A. Or: A is unlike something else, so that it is not simply A, but rather a specific A. A’s place in the law of identity can be taken by any other substrate, but A as distinctive [als Ungleiches] can no longer be exchanged with any other. True, it is supposed to be distinctive not from itself, but only from another. Yet this distinctiveness is its own determination. As self-identical A, it is indeterminate. But as determinate, it is the opposite of this—it no longer possesses only self-identity, but also a negation, and therefore a difference from itself within itself.
The logical nature of diversity presupposes that the totality of different things is their identity. Thus, being a self-identical determination, it becomes distinctive—its identity is negated by the “nothing” from which it is distinguished, and that distinction is internal to it. Take, for example, the ethical logic of decision-making: the first thing most people say when asked what the right decision is, is “It depends on the situation,” as if the uniqueness of the situation itself reveals the correct choice. This dependency on particularity mirrors how identity is mediated through its negation.
Plurality refers to the number of differences encompassed within diversity. But as this number consists of differences, there is an implicit notion that any single entity contains an inverse determination to the one from which it is set apart. Duality defines this inverse determination. Its version of unity holds inconsistency as a necessity—the very relation that allows a thing to sustain itself as self-identical.
A thing produces its inverse as the relation that sustains it. There can be no “inside” without an “outside,” and vice versa. (Removing the South Pole causes the North Pole to produce another South Pole.) This mutual dependency of opposites reveals that negation is not external, but internal to identity.
“Everything is different from everything.”
§904
“That everything is different from everything else” is a superfluous proposition, for the notion of “things” in the plural already implies manyness and a wholly indeterminate form of diversity. But the proposition that no two things are completely alike expresses more—namely, determinate difference. Two things are not merely two. Numerical manyness—two, three, four—is only a repetition of the one, a form of one-and-the-same. But when two things are different through a determination, that difference is real.
Ordinary thinking is struck by this proposition—“no two things are alike”—as illustrated by the story of how Leibniz presented it at court, prompting the ladies to examine the leaves of trees in search of two identical ones. Happy times for metaphysics, when it was the pastime of courtiers, and when the testing of its propositions required no more effort than comparing leaves!
What makes this proposition so striking is what has already been said: that “two,” or numerical manyness, contains no determinate difference. Diversity, in its abstraction, is at first indifferent to likeness and unlikeness. Even when ordinary thinking moves toward determining diversity, it still treats these moments as mutually indifferent. That is, it sees likeness and unlikeness as separate properties, such that the mere likeness of things—without reference to their unlikeness—suffices to establish whether the things are different. But this is only a superficial grasp, mistaking quantitative plurality for qualitative determination.
28#-Substance Diagram
Reason
|
Activity
/ \
Potentiality Actuality
| |
Process —> Matter —> Result
Universal Thought Particular
| |
Form Object
\-> Dialectic
Idea
|
Logic
This diagram illustrates the major concepts outlined in the ontological inquiry. As previously discussed, thought is an activity. Activity constitutes actuality because it establishes the scope of reality. Actuality refers to the establishment of past, present, and future within the dimensions of space and time. Spacetime is not merely a combination of space and time; rather, it is a distinct concept introduced to explain both.
Actuality and Spacetime
Actuality is both a process and a cause. This means that processes themselves generate particular states. The particular state adopts a form. Form is universal because it encompasses every particular. The particular is distinguished from the universal in that it is limited to a single object. However, a contradiction arises because there is an infinite number of single particular objects; thus, the universal, at least quantitatively, encompasses every possible object.
The object, therefore, occupies a single area in space and a single moment in time. According to Whitehead, a “moment” is defined as a “limit approaching minimal extension.” This “extension” is a property of a sequence known as a “series,” which occurs in one-dimensional time. Unlike objects that occupy positions in space, a series in one-dimensional time involves moments happening consecutively, one within the other, in a forward-moving, successive manner.
If the “actual activity of reason” refers to thought or matter, then form is the actuality of the idea as processed by thought into a particular. Logic is the content of the idea, taking on a particular form in actuality. Logic is the content of thought, and thought is, once again, an activity.
Logic and Matter
Logic is material because it is an activity that takes on particular forms; it constitutes the structure of form. Matter is universal because it can assume any form provided by logic. Whatever form it takes is a result derived from the processing of the activity of thought as actuality. This material result is also potentially every possible form of logic, which is why matter, being rational, has the purpose of being malleable.
Peirce’s Categories
Peirce’s phases of reality are not external properties of thought; they are internal relations. For example, firstness without the other two is merely an incomplete abstraction. Peirce defines “categories” as a “table of conceptions drawn from the logical analysis of thought and regarded as applicable to being” (CP 1.300).
Space and Time as Potentials
Space and time are potentials that take on actuality. The quality of time is that it is the self-contained determination, meaning it has the potential to self-identify. This quality takes on the nature of discrete magnitude because self-identity is the unit bounded as itself and excludes anything else. Space, on its own, is just an empty potential; it is the nature of time that makes it continuous.
The quality of space is the self-external determination. It is always beyond itself, defining the nature of continuity. Space is always the object beyond itself. Space and time are indivisible, meaning that the continuity of space is taken by time as the self-contained discrete unit. When time takes on the potential of space, it becomes the continuous discrete unit. Time is the potential for all subsequent activities. When space takes on the potential of time, it becomes the continuous self-external form as each self-bounded discrete unit.
Matter and Form
Matter is universal, and form is particular. Their coexistence produces the magnitude of thought. Thought is structured as particular forms constituting a universal substrate. Form and matter propagate an indivisible relation, but implicit in their relation is their negation.
The relation between the particular and the universal is an inverse reflection of thought as its object. Each form is the particular abstraction from thought; each particular form constitutes thought as the universal substrate because the whole of thought is conceived from each particular form of it. And each particular form constitutes the whole of thought.
Logic as Organic
Logic is organic—a synthesis between philosophy and science.
Inversion Geometry
The principle of identity states that P = P. Nothing is equal to itself as something; that is, itself, nothing. If nothing is something, then we characterize it as P—that is, the axiom for something that is nothing. The law of non-contradiction states that both P and not-P cannot exist at the same time. But in the ontological sense, nothing exists as itself as something; and so nothing is either something or nothing. This means that if nothing is itself something, then it must be either P or not-P. If nothing is P, then it is the something that is not P.
Not-P does not mean everything or anything that is not P; it rather means the very opposite of P, or in other words, the inverse of P. And so nothing is that which is the opposite of something, which then takes on an independent existence. In this sense, not-human would be the opposite of human. Not-human would not be a rock or any set of objects, but rather that which possesses the inverse qualities that a human possesses—if a human is rational, non-human would be not rational.
This of course presupposes a definition of human. In science, we see that each element not only possesses a peculiar relationship with each element, but that certain elements possess an inverse relation with particular elements.
This tries to show that logic is organic, and that the first principle, reason, possesses the ability within itself to contradict itself, and then traswntce that contraction into a resolution.
http://whistleralley.com/inversion/inversion.htm
Nothing = That Which Is Itself Something
The principle of identity states that P = P. “Nothing” is equal to itself as “something”—that is, it is, in itself, nothing. If nothing is something, then we characterize it as P, which becomes the axiom for “something that is nothing.” The law of non-contradiction states that both P and not-P cannot exist at the same time. However, in the ontological sense, nothing exists as itself—as something—and so nothing is either something or nothing.
But this simply means: if nothing is itself something, then it must be either P or not-P. If nothing is P, then it is the something that is not-P. Importantly, not-P does not refer to everything or anything that is not P—rather, it refers specifically to the opposite of P, or in other words, the inverse of P.
Therefore, nothing is that which is the opposite of something, and this opposite—this negation—takes on an independent existence. In this sense, not-human is the opposite of human. Not-human would not simply be a rock or a random set of objects, but rather that which possesses the inverse qualities of what it means to be human. If being human means being rational, then not-human would mean being not-rational. Of course, this presupposes a concrete definition of what “human” is.
In science, we also see that each element not only possesses a peculiar relationship to other elements, but that certain elements have inverse relations with specific others.
This brings us to the law of the excluded middle, which shows how logic is organic. That is, the first principle—Reason—possesses within itself the capacity to contradict itself. But this contradiction is not merely an opposition between two entities; the contradiction itself takes on independent existence. It becomes something that can be resolved on its own, while still remaining a contradiction between two premises. This illustrates a kind of multiplication: the process by which that which is potentially true becomes actually true.
The principle I = I defines the universal equation of actuality. “I equals I” means that something is one and the same with itself. This is distinct from, for example, Newton’s law that every action has an equal and opposite reaction: F = -F. In Newton’s formula, the reaction is external to the action, and one causes the other—this pertains to external relations between particular objects in motion.
In contrast, I = I is a universal that unites action and reaction internally. In this formulation, every action is also its reaction—the action contains its reaction within itself. It is the one principle that takes on the many, and therefore, the many are simply expressions of the one. This is also represented by the equation I = i, where i is just a variation of the same universal, I.
The law of non-contradiction is often called the principle of contradiction, because non-contradiction presupposes contradiction. Contradiction is the starting point from which either P or not-P must follow—hence, resolution becomes possible. This shows that contradiction contains within itself the means of its own resolution.
It is often argued that the “laws of thought” are not universally absolute, since different kinds of logic appear to contradict them. So under what standard can we say one system is universally true?
This question misses an important philosophical distinction—specifically, the difference between Reason in the world and Understanding in the mind. While they are interrelated, they function differently in how they perceive and conceive of reality. The laws of thought are actually abstractions made by the understanding from the operations of Reason in the world.
Take, for example, the basic valid argument form: modus ponens:
If P, then Q
P
Therefore, Q
This simply states: if P is true, then something other than P (in this case, Q) must also be true. What it presupposes is that P cannot be not-P, if Q follows from it.
The indeterminacy of the quantum realm merely suggests that there is flux and constant activity on that level. However, it does not suggest that the observer is indeterminate. Instead, the observer functions as the phenomenon of determinacy within the quantum realm.