§ 3-1. Aristotle's Logic and Philosophical Inquiry into Method

According to Aristotle, Science or scientia in Latin (knowledge='h episthmh‹hé epistémé‹) is distinguished into three domains: The theoretical, the practical and the productive. The immediate objects of these three different kinds of sciences (= searches for knowledge) were considered knowledge (epistémé or episthmh). The ultimate goals for them differs.

The theoretical science aims at the knowledge for its own sake: It was considered deserving the highest and the most genuine sense of knowledge. They are Metaphysics (The theory of being or reality), Physics (natural science), Astronomy, Biology, Psychology, Theology (often included into and synonymous with Metaphysics--Aristotle), and possibly Mathematics.

The goal of the practical sciences was supposed to strive ultimately for (how to) better "conduct" as the polis as a whole or as an individual as a constituent part of the polis. This comprises Political Sciences and Ethics (the study of character).

The productive science is a typical instrumental knowledge, which will provide us with knowledge and skills for an efficient, useful and beautiful tool. What was called «eßnh­­techné-- was to belong to this category of knowledge. This kind of knowledge or skill was supposed to pursue knowledge for something else, the knowledge useful for some specific utility. Although Aristotle included dialektikh‹dialectiké‹ or dialectic into this genre of knowledge (as defined by Socrates-Plato as the "method" to pursue the knowledge pursued for its own sake, and in this sense, dialectic was not understood as a techné, but epistémé‹'h dialektikh episthmh‹this will be more discussed in details), certainly 'rhtorikh--rhetoric--, medicine, such knowledge and skill of all the craftsmanship as ship building, carpentry, stone masonry, dentistry, the skill of house-hold‹economics‹( ÿkonomiÿ‹oikonomia‹), etc. Strange enough, the logic, the study of inference, did not appear in any of these three areas of knowledge. Aristotle was supposed to consider logic as the portion of the general education for the youth.

Arabic Aristotelians and the Medieval scholastics considered the logic is one of the most important Aristotelian sciences and divided logic in the formal logic and the material logic, latter of which they considered a "substantive science." According to Aristotle, however, logic was not a "substantive science," thus it does not belong to any of these three domains of knowledge or scientia, particularly not to that of the theoretical science. As briefly touched above, indeed Aristotle apparently thought that logic should be a "part of general culture which everyone should undergo before he studies any science, and which alone will enable him to know for what sorts of proposition he should demand proof and what sorts of proof he should demand for them." The similar idea underlies his use of the term, "Organon," or "instrumentum scientiae."

On the other hand, in Aristotle's philosophical inquiry, however, as a technical term, what we consider "method" became under the heading of "organon," although Aristotle was not aware of the notion, "logic," which was introduced in the period of Cicero, while h logikh‹hé logké‹ was meant rather "dialectic." Rather later, Alexander, the editor and commentator of Aristotle's works conceived "logic" in what we mean today by "logic," that is the analysis of inference or reasoning into the figures of syllogism. Despite the famous contention of Trendelenburg, Willamowits-Möllendorff and W. D. Ross, it will make perhaps better sense, should we consider the works on logic Aristotle's later opera, while those opera which make reference to logic as the a part of general education should be regarded as earlier works?

Aristotle's works on logic may be safely divided into three areas.

1) Analytica Priora:

In this work, Aristotle tries to reveal the structure apparently common to all reasoning‹syllogism‹and to enumerate its formal varieties despite any subject matter dealt with. This was called "formal logic" since the late Ancient period and it may be rephrased as the logic of consistency. This discovery of the formal character of the nature of reasoning is one of the most important, epoch-making scientific advancement. It was such a gigantic finding in logic that it almost "hindered" thousands of years to redirect our new research in logical investigation.

2) The Analytica Posteriora:

Herein Aristotle investigates the further characteristics of a syllogism when it is valid, I.e., not merely self-consistent, but also in the "full sense scientific." This portion of his logical investigation not only examines and test the validity of the self consistency, but deals with the truth, the truth of the knowledge of the reality. This is why this portion of logic was called later the material logic and the portion of the so-called informal logic.

3) The Topics and Sophistic Elenchi.

Aristotle explores here those modes of reasoning or inference which are syllogistically correct but fail to satisfy one of more of the conditions of scientific thought. The Categories and the De itnerpretatione, are devoted to the study of the term (the semiotic finds here its historical origin of its science) and the proposition respectively, which is considered rather preliminary.

§ 3-2. Aristotle's Inquiry into Syllogism as The Methodology of His Philosophical Investigation: Analytics

Now it seems quite obvious that Aristotle made an enormous and explicitly conscious first step in the investigation into the nature of method in philosophy and scientific inquiry. By means of the form of language Aristotle attempted to inquire the philosophical method,i.e., the nature of the logic, the validity of argument, the principle of contradiction and that of excluded middle, etc. As the form of an argument (=logical inference) "syllogism" was deliberately chosen by Aristotle. For the language‹'h logos (the logos, that which is expressed by words: I would like to avoid to translate "logos" into "reason.")‹ is the natural, most proper means for such an investigation. And Aristotle rather proposed and called the way or approach of scientific inquiry "analysis,"
and its investigation, 'h a ÿl tikh‹hé analytiké‹(analytics).

It is well known that Aristotle considered the dialectic as the other important method of scientific inquiry and philosophy. Since Aristotle attributed its discovery to Zeno and its completion to Socrates as well as the extensive use of dialectic by Plato, he apparently poured his concentrated efforts into an investigation into its alternative form of logic, that is deduction or syllogism in his naming. This analutikI--analytiké--was the expression for "method" employed by Aristotle, as it has the same etymological origin that "analysis" has.

On the other hand, as the concept of the so-called "logic" did not appear in the History of Western civilization until the time of Cicero, even what corresponded to the discipline later called "logic" did not appear as the methodology, belonging to the domain of the pure, theoretical science. For, to Aristotle, the philosophical inquiry into the method of philosophy was not a "substantive science," i.e., that is, logic does not deal with the knowledge about substance or reality and its aspects.

As briefly mentioned above, Aristotle called his philosophical inquiry into the nature and validity of an argument (a logical inference) (i.e., the study of method) "analytic." This became to signify the philosophical inquiry into the method in the narrowest sense today.

Among the logical inferences, Aristotle distinguished the deduction or syllogism and the dialectic (inductive reasoning)." Now, we shall look into the dialectic as long as it is relevant to our inquiry of syllogism as deduction.

§ 3-2-2. Socratic-Platonic Dialectic

Before getting into the discussions of syllogism, It may be necessary that we will look at the dialectic supposedly created by Zeno of Elea and extensively used by Socrates in his inquiry and mission and perfected by Plato as the alternative method. Aristotle was clearly aware that the dialectic is the dominant method in philosophy during his contemporary. In fact, it is interesting to know that around the time of Cicero, the logic designated not what we consider deduction, but dialectic first. It took a century or two until the logic discovered Aristotelian syllogism.

What is then "dialectic?"
Dialectic has the same etymological origin with the dialogue. Dialogos ‹ "¢o dialogos" or "to dialegein"‹ (dialogue) was speech or talks between the two minds against each other and "'h dialectikh episthmh"‹dialectiké epistémé‹ (knowledge through dialectic) is the method by discussing and attempting to search knowledge through dialogue by two opposing minds, starting a certain tentative understanding or definition of an idea and gradually exploring and approaching the clearer or clearest knowledge of it. It rooted in the two concepts, consisting "dia"‹"dia"‹ (across or against) and "logos"‹"logos"‹ (speech).

According to Aristotle, Zeno was the founder of dialectic. Zeno's argument is called "reductio ad absurdum" or "indirect proof" in today's terminology. Zeno argues that the opposite to the opponent's hypotheses is indeed true, by reducing from them to absurdity by deducing from the contradictory consequences. The objects of criticism by Zeno were needless to say the existence of "many (things)"‹"ta polla"‹ (ta polla) and that of "motion" (generation and corruption through rarefication and condensation among the four traditional elements, fire, air, water and earth)‹"'h kinhsis"‹ "hé kinésis," and Zeno attempted to demonstrate that the so-called two most fundamental self evident true principles (Being exists, while Non-Being does not) are indeed to be abandoned, should these two concepts (plurality and motion) were adopted as "real." His arguments have been renowned as Zeno's paradoxes. Probably Aristotle meant that Zeno's argument needed two souls and one side would show the other side's hypotheses being wrong. Aristotle might mean that Zeno was not sophistic (merely interested in winning argument and persuading the opponent), but searched truth through logical arguments.

Socrates on the contrary, did not develop the argument based on "reductio ad absurdum." However, as far as we see in the early Plato's dialogues (which are rather truthful portrayals of Socrates, as then, the readers of Plato's early dialogues knew the real Socrates), Socrates appears an extremely clever, eloquent speaker with the quick mind.

Socrates was the first philosopher who developed explicitly a method of philosophical inquiry to pursue truth. This method was no other than dialectic. Socrates' pursuit or mission always had in front of him the other person whom he discoursed with. Socrates always asked his "opponent" the tentative, mundane "definition" of what he would like to discuss with him.

Let's say, what is courage. The first tentative definition would be: Courage is Heracles. Socrates would say, Heracles is courageous, namely Heracles was a concrete person who possesses courage. Socrates was asking was what courage is and not what is courage. The opponent would suggest that courage would be fighting violently without fear. Socrates points out the short coming of this elucidation, by saying that the meaning of courage would be to broad, including the barbarous, cruel act, too. Then, the definition will be more refined such that courage is now clarified as the virtue of valor.... Ultimately, such a process of dialectic should elicit and arrive at the truth. As this example reveals, the method of dialectic requires (in the ideal case) two mutually independent mind pursuing the truth starting with an tentative definition of the nature of thing (such as courage, justice, beauty and good) and by critically appraising the proposed "definition" from the other's insight into the defects of such a "definition" by stipulating and eliciting the ultimate nature of thing. It is the method, it is, according to our definition of method, the process of inquiry into reality itself with the controlled means (through the careful dialogue).

It is interesting to note that in Plato's early dialogues, Socrates usually never comes to the ultimate reality of a thing, the finial answer of his discourse, but some event interrupted their pursuit and the reader is left unanswered. This has something to do with the nature of the question itself too. Socrates was well aware of the ultimate goal of the dialectic and its value, although he may not be able to clearly elicit by logos (words) what it is. This will become clearer when we discuss Plato's dialectic.

Plato of course followed Socrates' footsteps, but he was a little more creative and ambitious and had the ability to "see" what reality is in the sense that he was able to go beyond the dialectic ultimately to have an insight into the "genuine reality." Dialectic is an attempt to grasp what really is by means of logos, the words and language. In this sense, Aristotle was right in contending that dialectic is the method to grasp by word the definition of what really is. However, the ultimate reality escapes the words, as Lao Tzu clearly stated at the beginning of his Tao Te Ching. Plato went beyond the limit of the position of logos to the viewpoint where one can have an evident insight into what reality is. There is a leap between the end of dialectic and the evident intuitive insight. This leap cannot be jumped by dialectic or the position of logos alone.

Let us briefly look at Plato's dialectic and his intuitive insight a little more carefully.

§ 3-2-3. Discovery of "nohsis" as "Intuitive cognition" in Plato

Historically speaking, to be sure, when we search the origin of such immediate knowing, it seems obvious that Parmenides was the first who used the concept of "to noein"‹"to noein"‹(to see or to know) or "'h nohsis"‹hé noésis‹(seeing), i.e., to see or know by "'h nous"‹hé nous‹("nous" we normally translate into "reason"). This clearly is found in Parmenides. Take for example:

«N LRà R «N INDNI D0«NI «D RN DNIRN‹Frag. 3 Proclus in Tim. I, 345,

UàI to ADLDNI te INDNI «' DNI DLLDIRN‹Simplicius Phys. 117, 4

This "noein" or seeing (immediate, intellectual intuition) is not a logical inference, but an intuitive grasp by reason. This cognition is without any mediation.

Anaxagoras also recognized the nous as the principle of motion (=separation into an order in his sense) in the universe, however, this "nous" had the cognitive capability (therefore, by separation "nous" is capable of establishing an order of the universe (=cosmos) unlike Empedocles' koinés (hate) and protés (love), which are "blind."

Thus, it may be natural that Plato inherited the intuitive cognitive faculty of nous for the predecessor. Instead of discussing this ¾noein" or "noésis" in details, here we only point out that Plato realized the limits of the linguistic approach and in order to overcome these limits, Plato chose "to noein" above and beyond the dialectic, the linguistic approach to reality.

Now How Aristotle comprehended the dialectic as the method in philosophy? The best place to find this out is to look at his Topics.

In his Topics, Aristotle discloses that the task of this opus (Topics) is "to find a method by which we shall be able to argue about any proposed problem from probable premisses, and shall ourselves under examination avoid self-contradiction," That is, we shall be able to sustain with success either of the parts implied in all dialectical discussion‹the part of "questioner" (the man as the other speaker who puts questions to his opponent and argues from whatever answers he receives) or that of respondent."

To rephrase this, our object is, according to Aristotle, to study the "dialectical syllogism."

1) Dialectic syllogism is distinguished from the scientific syllogism by the fact that its premisses are not true and immediate but are merely probable, that is, such as commend themselves to all men, to most men, or to wise men.

2)Dialectic syllogism is from their merely contentious logism by he fact that it reasons correctly from premisses which are really probable, while the other reasons from premisses that merely seem probable, or else reasons incorrectly.

3) Dialectic has no supreme value which belongs to science, but it is not a value-less pursuit like arguing merely for argument's sake.

4) The study of dialectic has three main uses:

a) with view to mental gymnastics,

b) with a view to being able to argue with people we meet: if we have previously made ourselves familiar with the opinions of the many and with what follows from them, we shall be able to argue with people from their own premisses:

c) The third use is with a view to the sciences and this use is twofold:

c-i) If we are able to argue questions both pro and con we shall better recognize truth and falsehood when we meet them (against the sophists and their position),

c-ii) the first principles of the sciences, since they cannot themselves be scientifically proved, can be best approached from a study of common opinions such as dialectic provides.

The best examples of establishing the first principles by dialectic may be found in Aristotle's argument in Metaphysics T for the laws of contradiction and excluded middle.

According to Aristotle's Topics, there are three main terms used in the "art of dialectic" ‹'h dialektikh tecnh‹ : 1) premiss, 2) problem, 3) thesis.

1) Premiss

According to Aristotle, dialectical premiss is a "question" (the answer to that question strictly speaking), "which commends itself as probable either to all men, to most men, or to wise men."

2) Problem

Of course, not every question which may properly be put to one's opponent in discussion may properly be set up as a problem for discussion.

A problem is to be a question possessing either practical or theoretical interest, and on which either there is no current opinion, or there is a difference of opinion between the many and the wise, or among the many, or among the wise.

3) Thesis

Not every problem is a thesis. A thesis is a paradoxical opinion of some celebrated philosopher," or a view which, though perhaps no one holds it, can be supported by argument. Not all problems nor all theses are of course worth discussing.

The most important aspect of the dialectic Aristotle discussed in Topics in the pursuit of knowledge is, as stated above, to discover and identify "the first principles of the sciences, since they cannot themselves be scientifically proved, can be best approached from a study of common opinions such as dialectic provides."

Apparently, in Aristotle, the logical inference as syllogism was so much emphasized that the so called Platonic "noésis" was either forgotten or ignored in the science, i.e, the pursuit of knowledge.

As pointed earlier, Aristotle was trying to be creative and thus competitive with Plato. On the other hand, as long as dialectic was employed extensively by Plato, Aristotle took it as a philosophical method for granted and secondly Aristotle looked at it as being less significant than it perhaps actually was. In one place, Aristotle stated that dialectic is an inductive method. On the other place, he mentioned that dialectic is the method to obtain the definition of the nature of a thing. As the method of definition, Socrates was considered the founder of dialectic. We do not discuss this not so in details in this section. We simply point out how Aristotle conceived this method of philosophy in order that we shall be able to deal with his inquiry into the syllogism.

§ 3-2-5. Aristotle's Discovery of Scientific Syllogism as An Deductive Argument

Linguistically, the concept of syllogism already appears in Plato. Glorious as it may sound, the syllogism was Aristotle's discovery and invention in its originality by himself. In this sense, as well as in the sense of how long the syllogism was the representative for deduction, we cannot underestimate Aristotle's ingenuity and greatness of his philosophical investigation. It is indeed an epoch-making to discover that the form, and not the content of a set of propositions, determines the validity or the invalidity of its argument......

Aristotle's investigation into the deductive reasoning and its process as a process of thought (at a psychological one) attained the fruit in his discovering the syllogism as a deductive argument consisting one conclusion and two premisses. As mentioned before, sun-logismos‹sun logismos‹ signifies a set of "propositions put and gathered together."

The question which lead Aristotle to investigate the deductive inference and its process lies perhaps in his interest and endeavor in exploring the conditions of scientific knowledge. This is declared in the beginning of Aristotle's Analytica Prior and he had begun with the forms of proposition and their relationships for the conditions for possible scientific knowledge. In this sense, Aristotle clearly understood "analytics" as the inquiry into the method of philosophy.

According Aristotle, The necessary condition for any scientific knowledge (the pursuit of knowledge) must be at least be of the validity of each step it takes, and this is what observance of the rules of syllogism secures.

Aristotle defines syllogism

It is "an argument in which, certain things having been assumed, something other than these follows of necessity from their truth, without needing any term from outside."

Naturally hereby Aristotle assumed (with insufficient proof according to W. D. Ross) that this can happen only when a subject-predicate elation between two terms is inferred from subject-predicate relations between them and a third term. Is such an assumption indefensible? No, I do not think so. Aristotle never claims that he would cover all the possible forms of inference. He attempted simply to clarify the rules and structures of an argument by means of the most simple, fundamental type of the inference, which turns out to be the syllogism.

This general abstract definition of syllogism is not so quite intelligible for us, unless we elaborate it more in details. Let us try: In order to understand the nature of syllogism, it is necessary to look at the so-called categorical syllogism: A categorical syllogism consists of three categorical propositions.

A categorical syllogism consists of the three categorical propositions. Now, there are four kinds of categorical propositions:

Universal-Affirmative A: All S is P

Universal Negative E: No S is P

Particular Affirmative I: Some S is P

Particular-Negative: O: Some S is not P

All the non-categorical propositions, according to Aristotle, are reducible to and modified into either one of these four categorical propositions. This contention supports the universality of the form of categorical syllogisms.

According to the above definition of syllogism which consists of three categorical propositions, there can and only can occur three terms among these. In other each of these three terms occurs twice, each in one of the propositions.

Among these three propositions, that proposition whose truth is less obvious (to both the speaker and listener) in comparison to the other two categorical propositions is stipulated as the claim or the conclusion. The conclusion must be supported by the other two premisses, the other two categorical propositions. There are such linguistic devices to indicate that being the conclusion as "therefore," "thus," "Consequently," etc. Once we identified the conclusion, the predicate term of the conclusion is called "Major Term." and One of the Premisses which contains the Major Term (the predicate term of the conclusion) is called the "Major Premiss." The Subject Term of the conclusion is called the "Minor Term." The premiss which contains the Minor Term (=the subject term of the conclusion) is called the Minor Premiss. In order to linguistically indicate the premisses after those conjunctions as are "because," "For," "as," "since," etc., they are called Premiss Indicators. The two terms which only occur in the premisses and not in the conclusion are called "Middle Terms." The Major term is connected to the Minor term in the conclusion by virtue of these Middle Terms. These three terms fulfills the conditions in the above definition of syllogism. The Middle Terms function as mediators to enable the conclusion drawn from the two premisses. When the truth of conclusion is justified (without any other term) on the basis of the truths of the two premisses alone, as these two premisses are to be more or very obviously acceptable as true (both to the speaker and the listener). In this case, it is said that the truths of the two premisses implies the truth of the conclusion, and that the argument (syllogism) is valid.

Aristotle's great discovery lies, however, in the astonishing finding that the meanings or the contents of the three categorical propositions do not play an important role whether that syllogism is valid or invalid. The validity or the invalidity of an argument is solely determined by the forms of syllogism.

The truth of each of the categorical propositions is relevant to the validity of the syllogism so long as it is excluded that the two true premisses imply the false conclusion and the meanings of the propositions are totally irrelevant.

Thus, a categorical syllogism is valid or invalid depending upon a certain forms. They are determined by the combination of the Mood, the order of the propositions, (the Major Premiss-The Minor Premiss-The Conclusion) such as A-A-A and the Figure, the positions of the Middle Terms in the Major and the Minor Premisses.

§ 3-3-1. Logic: Deduction as "methods"

In philosophical inquiry, the study of logical arguments are considered the inquiry into "methods" in the perhaps widest possible sense, although it persisted for a long time in the Western culture. For logic was viewed as the philosophical inquiry, which makes sure that each step of the scientific (=philosophical knowledge) investigation is not fallacious, that is, not invalid, so that the entire enterprise of philosophical inquiry is considered a valid one.

Thus, there are the method of deduction and the method of induction. In either case of the logical arguments, the method is viewed as the way to transfer the truth of the premisses to that of the conclusion, if indeed valid, and the justification of the conclusion by the premisses. In other words, logical inference is to obtain, through appropriate logical principles, the true knowledge as the conclusion stating the previously unknown on the basis of the premisses the propositions of which are already known or are more easily acceptable as true7. This seems to be the most common, mundane use of a logical argument.

Not only in our mundane, everyday life and natural sciences, but also in philosophical investigation, we employ both deduction and induction (the latter of which is often called the empirical generalization). Deduction and induction are logical reasonings or inferences (which are called "arguments" in the logical terminology), which, proceeding from the premisses (a set of statements), attempts to arrive at the conclusion (which is often also called "claim," that which one would like to establish as one's own contention). Both reasoning and inference are confused as psychological processes, which has nothing to do with logic, so the logician calls it "argument."

An argument (argumentum) consists of a set of statements (called premisses) and the conclusion. The conclusion is a claim or contention which the speaker or the writer firmly holds and yet often the conclusion in itself do not appear clear to the hearer or the reader. Thus, we attempts to support the claim or the conclusion by means of a set of premisses, which can be more easily acceptable as true by the hearer or the reader.

In deduction, whether it is mathematical logic or syllogism, an argument is said to be valid, if and only if the premisses imply the conclusion, or if and only if the premisses is true, the conclusion cannot be false. An invalid argument is called a "fallacy."

Among fallacies, there are formal fallacies and informal fallacies. The formal fallacy invalid argument, if and only if it violates the logical rule, while the informal fallacy occurs, when the premisses only appear to imply the conclusion by virtue of some semantical reason and yet in truth the premisses do not imply the conclusion.

A proof or a demonstration is a logical procedure to show that an argument is valid or invalid. The formal character of validity or invalidity of an deductive argument was an enormous discovery of Aristotle, whether it is in mathematical logic or the traditional syllogism.

When the argument is valid in deduction, As a method, deduction is as if it were reverse to induction in such a way that induction is an empirical generalization of a certain relationship from a great number of instances each of which individually asserts that relationship to conclude that such a relationship exists universally: Deduction draws the truth of the conclusion necessarily by means of the combination of a set of truths of the premisses. While induction is quite useful in obtaining a certain knowledge on the basis of noting that knowledge found in each and every instance as a premiss. Therefore, the truth of the conclusion is not implied logically from the truths of the premisses, but the conclusion may be said at best "sound." In other words, the empirical generalization, induction, may be falsified by one instance which does not agree with the rest of the instances. On the contrary, the truth of deduction or the logical truth of the conclusion is arrived at necessarily by means of the logical rule and the set of the truths of the premisses. Therefore, the logical truth of a deductive argument can no way be falsified by a concrete instance which does not agree with the logical inference from the premisses to the conclusion.

§ 3-3-2. Deduction‹ Syllogism, Propositional Calculus‹

When the truth(s) of the premiss(es) logically implies the truth of the conclusion, we call this deductive argument "valid." Only when the truth(s) of the premiss(es) logically implies the falsehood of the conclusion, then it is called "invalid." In other words, when one of the premisses is indeed false, then you may draw any conclusion, whether the conclusion is false or true.

At the end of the 19th Century, Boole, the great mathematician, devised to develop an axiomatic system with three (four sometimes) truth-functional connectives: "and," "not," and "either ...or" (or/and "if ....then). Thus the propositional calculus of the first order was introduced and as the result, it becomes obvious that the so-called logic may be indistinguishable from or identical with the propositional calculus.

The meanings of those truth functional connectives depend upon the natural language and the latter is used as the meta-language in order to develop and formulate the object language of the propositional calculus. This mathematic logic was extensively used at the beginning of this century in order to provide and formulate the foundation of mathematics (principia mathematica for exmaple by Whitehead and Russell) and physics by the so-called logical positivists.

Although the philosophy of science became the dominant philosophical trend in the first half of the twentieth century, first their attempt to completely formalized the object language failed (See Rudolf Carnap, Logical Syntax of Language and Meaning and Necessity).

Through the development of the criterion for the empirical signfiicance, the criterion was weakened everytime when it met the difficulty. And finally, the distinction between the proposition of a natural science and that of a speculative metaphysics regarding the empirical meaning of the proposition had to be abandoned in 1960 (See, Carl Hempel's famous article on the criterion of the empirical sginficance in Revue de Philosophie Internationale).

Nevertheless, many questions regarding the foundation of the natural sciences and those of their formalization provided valuable answers. In case of the propositional calculus of the first order is more extensive than the Aristotelian syllogism and the former includes the disjunctive and the hypothetical propositions in their deductive system. At the middle of this century, the modal logic (both in Germany and the US), or the many-value logic has been proposed and many attempts have been done, but the reliable success has not been yet evidenced.