folk have been using cognates of "S is F" without explaining what they are talking about. Is it that S=F (they are equal)? Or S ≡ F (they are materially equivalent)? Or just F(S) (predicating F to S)? or S∈F (S is an element of the set or class S), or none of these, or some combination, or something else? — Banno
Let’s start with Husserl’s characterization of the syllogism. He spends most of Experience and Judgement and Formal and Transcendental Logic unfolding the intentional strata that constitutively lead up to the understanding of the most elementary basis of formal logic, the predicative synthesis S is P.
“…what has been established from the beginning, from the founding of our logical tradition with Aristotle, is this: the most general characteristic of the predicative judgment is that it has two members: a “substrate” (hypokeimenon), about which something is affirmed, and that which is affirmed of it (kategoroumenon); from another point of view, according to grammatical form, we can distinguish onoma and rhema. Every declarative statement must be made up from these two members. Every judging presupposes that an object is on hand, that it is already given to us, and is that about which the statement is made.
(… a unitary proposition can be more or less highly articulated. For instance, the hypothetical judgment, / / A is b, then C is d. It is sharply articulated as having two parts; it too has a "caesura": / / A is b II then C is d. Each of these members is, in turn, articulated.)
Thus tradition provides us, so to speak, with an original model of the judgment which, qua judgment, we must interrogate as to its origin. We must leave entirely open here whether with this we are really dealing with the most primordial logical structure.
Only the elucidation of the origin of this structure, traditionally defined as judgment, can provide the answer to this question and to all further questions associated with it: to what extent is the predicative judgment the privileged and central theme of logic, so that, in its core, logic is necessarily apophantic logic, a theory of judgment? Furthermore, what is the mode of connection of these two members which are always to be distinguished in judgment? To what extent is the judgment synthesis and diaeresis (analysis) in one? This is a problem which has always created an embarrassment for the logician and for which there is no satisfactory solution to this day. What is it that is “bound together” and “separated” in the judgment? Further: which among the multiple judgment-forms which tradition distinguishes is the most primitive, i.e., that one which, as being the undermost, and founding all others, must be presupposed, and by an essential necessity conceived as underlying, in order that other forms of a “higher level” can be founded on it? Is there a single primal form, or are there several, enjoying equal rights, standing beside one another? “
“Since Aristotle, it has been held as certain that the basic schema of judgment is the copulative judgment, which is reducible to the basic form S is P. Every judgment having another composition, e.g., the form of a verbal proposition, can, according to this interpretation, be transformed without alteration of its logical sense into the form of the copulative bond; for example, “The man walks” is logically equivalent to “The man is walking.” The “is” is part of the rhema in which always “time is cosignified,” and in this it is like the verb. Thus, we require an exact understanding of what is involved in this copulative bond, of the nature and origin of the copulative predicative judgment, before we can take a position regarding the question of whether in fact this convertibility is justified and whether the difference between the judgments is merely one of a difference of linguistic form, which does not refer to a difference of the logical achievement of sense.
However, should the latter be the case, the problem would arise of knowing how both forms, the copulative proposition on the one hand, and the verbal on the other, relate to each other. Are they equally primitive logical achievements of sense, or is one (and which one?) the more primitive? Does the copulative form S is p, as tradition holds, really represent the basic schema of the judgment? Further, the question about the primordiality of this schema would in that case also have to be raised with regard to the fact that in it, as a matter of course, the subject is set in the form of the third person. In this, it is presupposed that, in the first and second persons, the judgment in the form “I am . . . ,” “You are . . . expresses no logical achievement of sense which deviates from that expressed in the privileged fundamental schema “It is . . . This presupposition requires testing and would again put the question of the primordiality of the traditional basic schema S is p in a new light.“
Husserl’s thesis is this:”Logic needs a theory of experience, in order to be able to give scientific information about the legitimating bases, and the legitimate limits, of its Apriori, and consequently about its own legitimate sense. Tthe ideal "existence" of the judgment-content is a presupposition for, and enters into, the ideal "existence" of the judgment (in the widest sense, that of a supposed categorial objectivity as supposed).
“The possibility of properly effectuating the possibility of a judgment (as a meaning) is rooted not only in the syntactical forms but also in the syntactical stuffs.
“This fact is easily over-looked by the formal logician, with his interest directed one-sidedly to the syntactical — the manifold forms of which are all that enters into logical theory — and with his algebraizing of the cores as theoretical irrelevancies, as empty somethings that need only be kept identical.”