In the traditional sense of the term, science is knowledge that is both discursive and complete in itself. It proceeds by way of demonstration; hence, a demonstrated truth is one that impels the assent of the intellect, presupposing a prior assent to the truths upon which it is based. If science has for its proper object demonstrated truth, that is, conclusions or mediately known propositions, it must base its demonstrations upon premises that are immediately known as indemonstrable truths, otherwise called first principles. This article explains the Aristotelian-Thomistic doctrine of first principles, with accent on their nature, origin, and habitual use.
Postulate, hypothesis, and principle. The expression "first principles" itself indicates that there are distinctions among principles. At the lowest level are propositions that are actually demonstrable, but are posited and utilized without being demonstrated. These are principles only insofar as they are accepted by one considering an argument; depending upon his position, they are regarded as postulates or hypotheses. A proposition is a postulate (Lat. postulare, to ask) if the one considering it has no opinion of his own or holds a contrary one; we "ask" him, as it were, to admit it for the sake of demonstration. Should the auditor judge the proposition likely, giving some assent to it, it is called a hypothesis. In this case he does not merely agree to the use of the proposition for purposes of demonstration, but accepts it because it seems probable and he feels it can be proved.
Such is the meaning usually associated with the term "hypothesis," although this is not its original meaning. Etymologically the word has an extension similar to that of principle. Deriving from [symbol omitted]ποτίθημι, meaning "to put under," hypothesis was something posed as a foundation for reasoning. As such, it included indemonstrable truths, even the most proper and absolute. Since the term "presuppose" also has its origin in [symbol omitted]ποτίθημι, one can hold that a hypothesis, in its original sense, is a proposition "presupposed" to a demonstration, while in a later sense it comes to be one that is accepted as demonstrated, though it is neither indemonstrable nor actually demonstrated. Ambiguity can be avoided by using the term "hypothesis" in the more restrictive sense of proposition accepted as demonstrated, and leaving the term "principle" for the original meaning.
According to aristotle, "a principle in a demonstration is an immediate proposition," while "an immediate proposition is one which has no other proposition prior to it" (Anal. post. 72a 7). In such a proposition, the predicate is so connected with the subject that the relationship affirmed between them admits of no middle term.
Common and proper principles. The terms involved offer a further basis for distinguishing principles. "Among the principles used in the demonstrative sciences, some are proper to each science and some are common to all…." (ibid. 76a 37). This equivalentlydistinguishes between definitions and axioms.
Definitions. While a definition as such is not yet a proposition, any proposition that directly applies a definition to the thing defined is an immediate proposition. The same applies to a proposition that is founded immediately upon a definition, in which the predicate is so directly related that it seems to need no explanation and to flow from the definition. It is enough, for example, to know that a right angle is generated by a perpendicular erected on a straight line to know that all right angles are equal. Proper principles are always immediate, with the immediacy, so to speak, of definitions. Their designation as "proper principles" arises from the fact that their definitions derive from the proper subject matter of a particular science.
Axioms. From this it can be gathered that common principles or axioms go beyond the limits of a particular science, that the truth they convey has a common value for all science. They are also common in the sense that they express thoughts or opinions that all accept and share. Their terms are so simple and current, their evidence so compelling, that one can apply to all of them what Aristotle said of first principles, namely, that they are the best known, so well known, in fact, that no one can be mistaken about them. It is in this very firmness, founded upon their characteristic of being most known, that their priority resides, as well as their dignity in the scale of knowledge. This is why they are called first principles or axioms (Gr. ἄξιος, meaning fitting), which St. thomas aquinas renders as dignitates or maximae propositiones. In modern discussions of methodology, however, the term "axiom" takes on a different meaning (see axiomatic system).
Certitude and Truth. Aristotle affirms that all principles must be believed and understood better than conclusions (ibid. 72a 25–39). Since the knowledge contained in conclusions derives from principles, the latter cannot be logically antecedent without at the same time being more certain. One hardly admits the truth of a conclusion with conviction unless the principles upon which it is based exclude the possibility of the contradictory conclusion being true. Thus the immediate evidence of principles is always greater than the participated evidence of conclusions.
All things being equal, common principles enjoy a certain superiority over proper principles; this does not mean, however, that proper principles must be demonstrated from common principles. The terms of the former also are joined without need of a third term, and their evidence comes from proper considerations. Yet, while independent from the viewpoint of knowledge, they are not independent from the viewpoint of certitude. Actually, common principles would not be the most common if they were not included in the proper, and the proper are not such because they are totally different from the common, but rather because they imply an addition to the common. Thus the truth of a common principle is found, although only implicitly, in the truth of a proper principle, so that if the first is not true, the second cannot be true either. Again, the certitude of common principles can be greater than that of proper principles only because of the greater simplicity of the former, although they share this certitude, so to speak, with proper principles.
Knowledge of principles. Except for one who studies a science, knowledge of principles proper to that science is not indispensable. Nor is there need to know such principles before taking up the science, for it is understood that the instructor begins by laying down these principles. Thus, for Aristotle, θέσις (thesis) is equivalent to proper principle. Whatever the discipline in which one engages, however, the possession of axioms or common principles is a prerequisite. Proper principles are already a part, initial though it be, of a science or particular treatise, while axioms are completely prior to any science. Thus boethius has formulated the classical distinction between immediate propositions that are such for specialists alone (quoad sapientes tantum ) and immediate propositions that are such for all (quoad omnes ). These are further subdivided into immediate propositions that are readily seen (quod nos ), and those not recognized as such (quoad se tantum ) that require a posteriori demonstration, such as the existence of God (see god, proofs for the existence of). Thus not all immediate propositions are principles, for the criterion of a principle is that it be better known to us, and even to all in the case of first principles.
Origin of first principles. Two extremes, innatism and empiricism, are to be avoided when accounting for first principles. According to innatism, man possesses first principles by nature. For leibniz, man has them as virtual knowledge, while for kant he knows certain a priori propositions that have no other foundation than the condition of the knowing subject. In their different ways, each tries to explain why principles are so easily known, and yet safeguard their universality and necessity. Empiricism, on the other hand, refuses to recognize any universality or necessity in first principles; it classifies them as knowledge acquired from the senses and remaining wholly dependent upon sense, so that any assent given them is consequent on experience and knowledge of the particular. (see knowledge, theories of.)
Some of Aristotle's expressions, such as "prerequisite experience" and "necessary induction," might be interpreted empirically, while St. Thomas makes statements that might be taken in the sense of innatism, such as "seeds that preexist in us" (De ver. 11.1), "knowledge put into us by God as author of nature" (C. gent. 1.7). Both, however, concur in the doctrine that man possesses a potency or ability to acquire first principles, without this potency's being superior to the actual possession of such principles themselves (cf. Anal. post. 99b 33).
Role of Experience. According to Aristotle, the preliminary knowledge of principles involves the following stages: sensation, memory, experience, all of which are associated with sense knowledge from the exterior senses all the way to the cogitative power. Again, according to Aristotle, principles are not derived from experience without coming also from universals. Moreover, while aware of difficulties involved in interpreting some texts (e.g., Anal. post. 100a 6), we hold that the universal itself is not directly reducible either to experience or to principles. It is true that experience does include a certain grasp of the universal, the grasp of a universal that is confused, so to speak. But this is not actually possible unless the cogitative power compares and brings together singulars to achieve some notion of unity. If the cogitative faculty remains a ratio particularis and is always concerned with singulars, it certainly does not furnish the experience that Aristotle describes as "the universal now stabilized in its entirety within the soul, the one beside the many which is a single identity within them all" (100a 7–8). Under the latter formality, which is its proper formality, the universal is the object of no power save the intellect. But again, even the universal is not a principle, since the principle comes from the universal (cf. 100b 1–5). To distinguish the two, one need only have recourse to the definition of principle as a proposition. It thus appears that universals are nothing more than noncomplex, simple notions that constitute the terms of the proposition-principle.
Thus the universal stands between experience and first principles in such a way that sense knowledge is required only for the acquisition of terms, but does not enter into the formation of principles themselves. The proximate source of principles is not sense experience but intellectual comprehension, and this as formulated in the idea.
Role of Induction. This raises the further problem of how first principles are related to induction. "It is clear," says Aristotle, "that we must get to know the primary premises by induction, for the method by which even sense perception implants the universal is inductive" (Anal. post. 100b 3–5). The term "induction" can be correctly applied to knowledge of complex expressions or propositions, for it commonly signifies the passage from a truth established in the singular case to the same truth known in all its universality. And while the fulcrum of induction is experience, the experience from which principles proceed is that of complexes and the induction contingent upon their formation. Such experience alone can assume the role of moving and determining the intellect to effect the composition found in the proposition. In its contact with singular reality, experience sketches out, one might say, both the basic notions and their relations to one another; thus, from the point of view of the acquisition of principles, of "how" they are born in us, one must say they come from experience but that they are obtained by way of induction.
Content and Assent. Having said this, one must specify that induction accounts for the origin of principles without explaining their content in any way. Since the knowledge attained in principles is that of propositions, the ultimate explanation for assent should be in terms of the absolute adherence we give propositions. Here the knowledge of terms furnishes the basic explanation, since immediate and absolute evidence is what compels assent. To invoke experience and induction alone would be to change the proposition into an object of discourse wherein our adherence would be conditioned by some antecedent adherence to the singulars of experience. This would make the principle something "better known," without accounting for its superiority or its greater certitude with respect to previous knowledge. Aristotle located the universal between experience and principles, and St. Thomas explained knowledge of principles through knowledge of terms, because both regarded experience and induction as a necessary condition for the origin of principles; yet they also held that the knowledge of terms and their connection, as seen by the simple light of the intellect, is the unique formal reason for the assent we give them.
Grasped in its entirety, this doctrine steers a middle road between empiricism on the one hand, which finds all truth in the senses, and rationalistic innatism on the other, which assigns no role to the intellect except that of reenacting experience.
Habits and first principles. A habit is a stable disposition whose stability is ultimately determined by its object. The habits of the speculative intellect, namely, understanding, science, and wisdom, dispose it to attain necessary truth. All three habits make use of first principles.
Understanding. The first of the intellectual habits, understanding, is directly concerned with principles. Scholastics call it intellectus, the name of the faculty from which it comes, a fact that is intelligible from what has already been said, since only by its own power does the intellect attain the truth of first principles. Experience supplies antecedent knowledge, but the terminal point of the induction itself specifies the habit of first principles.
Science. The second habit is that of science. Each science has its proper subject and, if it demonstrates properties, necessarily proceeds from principles proper to that subject. Nothing prevents a science from also using common principles, provided that these be used in conjunction with proper principles and that they be applied in the context of the particular subject matter. Geometry, for instance, is not concerned with being and nonbeing in an absolute sense, but rather as applied to magnitudes. "Sciences do not use first principles in all their generality, as applicable to all being, but only as much as needed according to content of their subject matter" (Thomas Aquinas, In 4 meta. 5.591).
Wisdom. The third speculative habit is wisdom, also known as metaphysics. Its subject is being as being in all its universality, as opposed to the beings studied in particular sciences. This immediately suggests the possibility that metaphysics has certain functions regarding principles whose terms are common. In fact, the coincidence in universality sets metaphysics apart as the only habit treating of first principles in themselves, making them the object of its consideration apart from simply using them.
Relation to metaphysics. Following Aristotle, St. Thomas assigns to metaphysics the role of establishing common notions and then defending first principles against those who deny them (In 6 eth. 5.1181–1183). In what can this role consist, if the comprehension of terms inducing assent already belongs to the habit of understanding? The answer is implicit in the question: Such a role must be granted to understanding in the exact measure required for assent itself. The point is that confused knowledge of terms suffices for making a judgment regarding their connection, that principles can be known quite certainly even though their terms be common. The habit of understanding is satisfied with grasping the universals found at the beginning of intellectual knowledge. The knowledge of communia, which is proper to wisdom, is, on the contrary, a distinct knowledge; one achieves it only by distinguishing the multiple acceptations of common terms. It is one thing to admit that it is impossible to be and not to be simultaneously; it is another to know whether the expression "to be" designates essential or accidental being, extramental or intentional being, or actual or potential being. In thus making common terms precise, the metaphysician might give the impression that he is a lexicographer or one compiling a vocabulary— Aristotle seems to do this in book five of his Metaphysics —but not everyone can control all the acceptations of these terms, and their distinction is a sign of the superiority of wisdom over understanding.
Defense of Principles. As for the defense of first principles, methods depend as much on the principles denied as on the reasons alleged in their negation. One such method could deal with the single case, in an argument ad hominem, if it happens that in confusing different senses of a term or playing on its ambiguity, someone should pretend to give examples of the falsity of the principle. Another method might utilize a demonstration to show, again ad hominem, that to deny some principle one must deny another that is even more common and more evident. This suggests that the defense of first principles is finally or radically rooted in the systematic defense of the most common principles, those so implied in all knowledge that to deny them is to deny knowledge itself. This is how Aristotle defends the principles of contradiction and of the excluded middle in book four of the Metaphysics. A number of his arguments are still useful against arguments more subtle than those of the ancient sophists.
Number of First Principles. Contemporary metaphysicians, including those in the Aristotelian and Thomistic traditions, regard it as one role of wisdom to discuss first principles, particularly to determine their names, their formulations, and their number. All agree in selecting from the following those principles they consider among the first: the principle of contradiction, of the excluded middle, of noncontradiction, of identity, of intelligibility, of sufficient reason, of causality, of finality, and even a principle of substance. St. Thomas employed the first two, usually formulating these in terms of affirmation and denial. Such apparently logical formulations displease some metaphysicians, possibly because they suspect an idealism that might accept such principles as laws of thought, but of thought unrelated to extramental being. These thinkers prefer a principle stated in terms of being and nonbeing, that is, it is impossible to be and not to be, which was also formulated by St. Thomas (In 1 anal. post. 5.7). But this impossibility is hardly satisfying if the opposition of being to nonbeing be regarded as the object respectively of affirming and denying. Moved by a desire to find the foundation for this in being itself, some fasten upon the intelligibility of being, upon its transcendental truth, and therefore, upon its noncontradiction or its transcendental unity. Thus, it would seem, the principle of intelligibility as well as that of identity have become principles, one might even say "principles of being," meaning by this that their value is not limited to knowledge alone. Furthermore, the transcendentals are the basic foundation for all knowledge, and might on this account be called principles; we leave open the question whether or not they conform to the general conditions already set down for axioms. At any rate, the tendency for discussions of first principles to move toward the problem of being in itself shows the metaphysical character of studies concerning these principles.
See Also: contradiction, principle of; excluded middle, principle of; identity, principle of; causality, principle of; finality, principle of; sufficient reason, principle of; intelligibilty, principle of.
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