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The False Subtlety of the Four Syllogistic Figures Proved (German: Die falsche Spitzfindigkeit der vier syllogistischen Figuren erwiesen) is an essay published by Immanuel Kant in 1762.
| Author | Immanuel Kant |
|---|---|
| Original title | Die falsche Spitzfindigkeit der vier syllogistischen Figuren erwiesen |
| Language | German |
| Subject | Logic |
| Published | 1762 |
| Media type |
This article only references primary sources. (April 2022) |
This article may require cleanup to meet Wikipedia's quality standards. The specific problem is: Poorly formatted tables, use of first person pronouns, and misuse of square brackets. (April 2022) |
Summary
Section I
General conception of the Nature of Ratiocination [Vernunftschlüsse]
A judgment is the comparison of a subject or thing with a predicate or attribute [also called a "mark"]. The comparison is made by using the copula or linking verb "is" or its negative "is not." Therefore, a judgment is a declarative sentence, which is a categorical proposition. Example: The tiger is four-footed. A predicate can also have its own predicate. In the example, the predicate "four-footed" can, itself, have the further predicate "animal." One of these predicates is immediately and directly connected to the subject or thing. The other predicate is mediate and indirectly connected to the subject:
"The tiger
(Subject)
is
(Copula)
a four-footed
(Immediate Predicate)
animal."
(Mediate Predicate)
In order to have clear knowledge of the relation between a predicate and a subject, one can consider a predicate to be a mediate (or indirect [mittelbares]) predicate. Between this mediate predicate or attribute, an intermediate predicate can be placed. For example, in the judgment "the sun is luminous," a clarification is attempted by inserting the predicate "star," which then becomes an immediate predicate, intermediate between the subject "sun" and the mediate predicate "luminous":
- "The sun is a star that is luminous."
- Sun = subject
- is = copula
- Star = immediate predicate (intermediate predicate; middle term)
- Luminous = remote mediate predicate
Kant calls this process ratiocination. It is the comparison of a remote, mediate predicate with a subject through the use of an intermediate predicate. The intermediate predicate is called the middle term of a rational inference. The comparison of a subject with a remote, mediate predicate occurs through three judgments:
- Luminous is a predicate of star;
- Star is a predicate of sun;
- Luminous is a predicate of sun (the original judgment).
This can be stated as an affirmative ratiocination: Every star is luminous; the sun is a star; consequently the sun is luminous.
Note: Kant's examples utilized obscure subjects such as Soul, Spirit, and God and their supposed predicates. These do not facilitate easy comprehension because these subjects are not encountered in everyday experience and consequently their predicates are not evident.
Section II
Of the Supreme Rules of all Ratiocination
Kant declared that the primary, universal rule of all affirmative ratiocination is: A predicate of a predicate is a predicate of the subject.
The primary, universal rule of all negative ratiocination is: Whatever is inconsistent with the predicate of a subject is inconsistent with the subject.
Because proof is possible only through ratiocination, these rules can't be proved. Such a proof would assume the truth of these rules and would therefore be circular. However, it can be shown that these rules are the primary, universal rules of all ratiocination. This can be done by showing that other rules, that were thought to be primary, are based on these rules.
The dictum de omni is the highest principle of affirmative syllogisms. It says: Whatever is universally affirmed of a concept is also affirmed of everything contained under it. This is grounded on the rule of affirmative ratiocination. A concept that contains other concepts has been abstracted from them and is a predicate. Whatever belongs to this concept is a predicate of other predicates and therefore a predicate of the subject.
The dictum de nullo says: Whatever is denied of a concept is also denied of everything that is contained under it. The concept is a predicate that has been abstracted from the concepts that are contained under it. Whatever is inconsistent with this concept is inconsistent with the subject and therefore also with the predicates of the subject. This is based on the rule of negative ratiocination.
Section III
Of Pure and Mixed Ratiocination
If one judgment can be immediately discerned from another judgment without the use of a middle term, then the inference is not a ratiocination. A direct, non-ratiocinative inference would, for example, be: "from the proposition that all airplanes have wings, it immediately follows that whatever has no wings is not an airplane."
Pure ratiocination occurs by means of three propositions. Mixed ratiocination occurs by more than three propositions. A mixed ratiocination is still a single ratiocination. It is not compound, that is, consisting of several ratiocinations.
An example of a mixed ratiocination is:
- Nothing immortal is a man,
- Therefore, no man is immortal; (this is a negative conversion of the preceding premise)
- Socrates is a man,
- Therefore, Socrates is not immortal.
A mixed ratiocination interposes an immediate inference, resulting in more than three propositions. However, a mixed ratiocination may show only three propositions if the fourth proposition is unspoken, unexpressed, and merely thought. For example, the ratiocination
- Nothing immortal is a man,
- Socrates is a man,
- Therefore, Socrates is not immortal
is only valid if the fourth proposition Therefore, no man is immortal is covertly thought. This unspoken proposition should be inserted after the first proposition and is merely its negative converse.
Section IV
In the so-called First Figure only Pure Ratiocinations are possible, in the remaining Figures only mixed Ratiocinations are possible.
| Subject | Predicate | |
|---|---|---|
| Middle Term | Major Term | Major Premise |
| Minor Term | Middle Term | Minor Premise |
| Minor Term | Major Term | Conclusion |
A ratiocination is always in the first figure when it accords with the first rule of ratiocination: A predicate B of a predicate C of a subject A is a predicate of the subject A. This is a pure ratiocination. It has three propositions:
- C has the predicate B,
- A has the predicate C,
- Therefore, A has the predicate B.
In the Second Figure only mixed Ratiocinations are possible.
| Subject | Predicate | |
|---|---|---|
| Major Term | Middle Term | Major Premise |
| Minor Term | Middle Term | Minor Premise |
| Minor Term | Major Term | Conclusion |
The rule of the second figure is: Whatever is inconsistent with the predicate of a subject is inconsistent with the subject. This is a mixed ratiocination because an unexpressed proposition must be added in thought in order to arrive at the conclusion. If someone says,
- No B is C,
- A is C,
- Therefore, A is not B
Their inference is valid only if they silently interpose the immediate inference No C is B after the first premise. It is merely the negative converse of the first premise. Without it, the ratiocination is invalid.
In the Third Figure only mixed Ratiocinations are possible.
| Subject | Predicate | |
|---|---|---|
| Middle Term | Major Term | Major Premise |
| Middle Term | Minor Term | Minor Premise |
| Minor Term | Major Term | Conclusion |
The rule of the third figure is: Whatever belongs to or contradicts a subject, also belongs to or contradicts some things that are contained under another predicate of this subject.
An example of a syllogism of the third figure is:
- All mammals are air-breathers,
- All mammals are animals,
- Therefore, some animals are air-breathers.
This validly follows only if an immediate inference is silently interpolated. The added inference is a conversion that uses the word "some" instead of "all."
- All mammals are air-breathers,
- All mammals are animals,
- Hence, some animals are mammals,
- Therefore, some animals are air-breathers.
In the Fourth Figure only mixed Ratiocinations are possible.
| Subject | Predicate | |
|---|---|---|
| Major Term | Middle Term | Major Premise |
| Middle Term | Minor Term | Minor Premise |
| Minor Term | Major Term | Conclusion |
Kant claimed that the fourth figure is based on the insertion of several immediate inferences that each have no middle term. The affirmative mode of this fourth figure is not possible because a conclusion cannot be derived from the premises. The negative mode of this fourth figure is possible only if each premise is immediately followed by its unexpressed, unspoken converse as an immediate inference.
In order to be valid, the negative mode ratiocination:
- No stupid man is learned,
- Some learned persons are pious,
- Therefore, some pious persons are not stupid
must become:
- No stupid man is learned,
- Consequently, no learned person is stupid;
- Some learned persons are pious,
- Consequently, some pious persons are learned,
- Therefore, some pious persons are not stupid.
Section V
The Logical Division of the Four Figures is a Mistaken Subtlety.
Legitimate conclusions can be drawn in all four figures. Only the first figure determines the conclusion by pure, unmixed reasoning. The other figures use unspoken, inserted inferences. Logic should consist of open, not covert, reasoning. It should be simple and unmixed, with no hidden inferences.
Previous logicians incorrectly considered all four figures as being simple and pure. The four figures were created by playfully changing the middle term's position. This retained the rational conclusion but increased obscurity. Time should not be wasted on the study of the three mixed ratiocinations.
Section VI
Concluding Observation.
The first figure yields a correct inference in a simple, direct manner. The other figures yield a correct inference indirectly by the addition of hidden inferences. They can be changed into the simpler first figure by changing the position of the middle term.
Kant concluded the essay with several related remarks.
Distinct and complete concepts are only possible by means of judgments and ratiocinations. A distinct concept is one which is made clear by a judgment. This occurs when something is clearly recognized as a predicate of a subject. A complete concept is one which is made distinct by a ratiocination. The ratiocination can be simple or a chain of reasoning.
The ability to understand and the ability to reason are both based on the ability to judge. Understanding is the immediate recognition that something is a predicate of a subject. Reason is the ability to judge mediately (indirectly). It recognizes another predicate in the first predicate, thus conceiving a subject indirectly by means of a remote predicate.
Higher knowledge is based on judging. Framing a judgment is a reflection that results in a distinct concept. Non-human animals can have clear representations of things that are predicates of a subject. Humans can also have knowledge that a predicate is a predicate of a subject and are therefore able to make a judgment. Non-human animals can distinguish things from one another. The different ideas are the causes of their actions, which are irrational. Humans can logically distinguish between things by means of judgment. The higher knowledge of a human is based on the ability to make our own ideas the object of our thoughts.
All affirmative judgments are based on the principle of Identity. A subject is identical to its predicate. All negative judgments have the principle of Contradiction as their foundation. A subject is opposed to its predicate. Judgments in which identity or contradiction is mediately known, by means of intermediate predicates and by means of the analysis of concepts, are provable. Judgments in which identity or contradiction is immediately known cannot be proved (See Section II). These unprovable judgments precede definitions because one must recognize a subject's predicate before they can define the subject.
Reference in the Critique
Kant summed up his thoughts on this topic in a short footnote that appeared in the second edition of the Critique of Pure Reason, B141. He had been discussing the definition of judgment in general. Logicians had usually defined it as a relation between two concepts. Kant disagreed because, he claimed, only categorical judgments are so defined. Hypothetical and disjunctive judgments are a relation between two judgments.
In his footnote, Kant asserted that the lengthy and detailed doctrine of the four syllogistic figures concerned only categorical syllogisms or inferences. He stated that this doctrine is only an artifice or trick for giving the appearance that there are three more kinds of inference or modes of drawing a conclusion than that of the first figure. This is done surreptitiously by secretly concealing immediate inferences in the premises of a pure syllogism. The only reason that this was generally accepted, Kant remarked, was that the logicians had made people believe that all of the other kinds of judgments could be reduced to being categorical judgments. Kant claimed to have disproved this in his Critique, A 73. There he argued that a categorical judgment relates two concepts, whereas a hypothetical or disjunctive judgment relates two judgments.
See also
- Square of opposition
Notes
- An immediate (or direct [unmittelbares]) inference is one in which "from the truth of one judgment that of another may be discerned immediately without any middle term." Immediate inferences are usually produced by the use of contraposition or logical conversion. For example, the judgment '"nothing human is immortal" is immediately inferred by contraposing the judgment "nothing immortal is human." The truth of the judgment is understood immediately. An immediate inference is not to be confused with an immediate mark (predicate or attribute). An immediate mark is positioned between a subject and a remote mark (predicate).
References
- Immanuel Kant, Introduction to Logic, New York: Barnes and Noble ISBN 0-7607-7040-9 (Contains Kant's Introduction to his Logic and also a translation of The False Subtlety of the Four Syllogistic Figures Proved)
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The False Subtlety of the Four Syllogistic Figures Proved German Die falsche Spitzfindigkeit der vier syllogistischen Figuren erwiesen is an essay published by Immanuel Kant in 1762 The False Subtlety of the Four Syllogistic FiguresAuthorImmanuel KantOriginal titleDie falsche Spitzfindigkeit der vier syllogistischen Figuren erwiesenLanguageGermanSubjectLogicPublished1762Media typePrint This article only references primary sources Please help improve this article by adding secondary or tertiary sources Find sources The False Subtlety of the Four Syllogistic Figures news newspapers books scholar JSTOR April 2022 Learn how and when to remove this message This article may require cleanup to meet Wikipedia s quality standards The specific problem is Poorly formatted tables use of first person pronouns and misuse of square brackets Please help improve this article if you can April 2022 Learn how and when to remove this message SummarySection I General conception of the Nature of Ratiocination Vernunftschlusse A judgment is the comparison of a subject or thing with a predicate or attribute also called a mark The comparison is made by using the copula or linking verb is or its negative is not Therefore a judgment is a declarative sentence which is a categorical proposition Example The tiger is four footed A predicate can also have its own predicate In the example the predicate four footed can itself have the further predicate animal One of these predicates is immediately and directly connected to the subject or thing The other predicate is mediate and indirectly connected to the subject The tiger Subject is Copula a four footed Immediate Predicate animal Mediate Predicate The tiger is a four footed animal Subject Copula Immediate Predicate Mediate Predicate In order to have clear knowledge of the relation between a predicate and a subject one can consider a predicate to be a mediate or indirect mittelbares predicate Between this mediate predicate or attribute an intermediate predicate can be placed For example in the judgment the sun is luminous a clarification is attempted by inserting the predicate star which then becomes an immediate predicate intermediate between the subject sun and the mediate predicate luminous The sun is a star that is luminous Sun subject is copula Star immediate predicate intermediate predicate middle term Luminous remote mediate predicate Kant calls this process ratiocination It is the comparison of a remote mediate predicate with a subject through the use of an intermediate predicate The intermediate predicate is called the middle term of a rational inference The comparison of a subject with a remote mediate predicate occurs through three judgments Luminous is a predicate of star Star is a predicate of sun Luminous is a predicate of sun the original judgment This can be stated as an affirmative ratiocination Every star is luminous the sun is a star consequently the sun is luminous Note Kant s examples utilized obscure subjects such as Soul Spirit and God and their supposed predicates These do not facilitate easy comprehension because these subjects are not encountered in everyday experience and consequently their predicates are not evident Section II Of the Supreme Rules of all Ratiocination Kant declared that the primary universal rule of all affirmative ratiocination is A predicate of a predicate is a predicate of the subject The primary universal rule of all negative ratiocination is Whatever is inconsistent with the predicate of a subject is inconsistent with the subject Because proof is possible only through ratiocination these rules can t be proved Such a proof would assume the truth of these rules and would therefore be circular However it can be shown that these rules are the primary universal rules of all ratiocination This can be done by showing that other rules that were thought to be primary are based on these rules The dictum de omni is the highest principle of affirmative syllogisms It says Whatever is universally affirmed of a concept is also affirmed of everything contained under it This is grounded on the rule of affirmative ratiocination A concept that contains other concepts has been abstracted from them and is a predicate Whatever belongs to this concept is a predicate of other predicates and therefore a predicate of the subject The dictum de nullo says Whatever is denied of a concept is also denied of everything that is contained under it The concept is a predicate that has been abstracted from the concepts that are contained under it Whatever is inconsistent with this concept is inconsistent with the subject and therefore also with the predicates of the subject This is based on the rule of negative ratiocination Section III Of Pure and Mixed Ratiocination If one judgment can be immediately discerned from another judgment without the use of a middle term then the inference is not a ratiocination A direct non ratiocinative inference would for example be from the proposition that all airplanes have wings it immediately follows that whatever has no wings is not an airplane Pure ratiocination occurs by means of three propositions Mixed ratiocination occurs by more than three propositions A mixed ratiocination is still a single ratiocination It is not compound that is consisting of several ratiocinations An example of a mixed ratiocination is Nothing immortal is a man Therefore no man is immortal this is a negative conversion of the preceding premise Socrates is a man Therefore Socrates is not immortal A mixed ratiocination interposes an immediate inference resulting in more than three propositions However a mixed ratiocination may show only three propositions if the fourth proposition is unspoken unexpressed and merely thought For example the ratiocination Nothing immortal is a man Socrates is a man Therefore Socrates is not immortal is only valid if the fourth proposition Therefore no man is immortal is covertly thought This unspoken proposition should be inserted after the first proposition and is merely its negative converse Section IV In the so called First Figure only Pure Ratiocinations are possible in the remaining Figures only mixed Ratiocinations are possible Pattern of First Figure Subject Predicate Middle Term Major Term Major Premise Minor Term Middle Term Minor Premise Minor Term Major Term Conclusion A ratiocination is always in the first figure when it accords with the first rule of ratiocination A predicate B of a predicate C of a subject A is a predicate of the subject A This is a pure ratiocination It has three propositions C has the predicate B A has the predicate C Therefore A has the predicate B In the Second Figure only mixed Ratiocinations are possible Pattern of Second Figure Subject Predicate Major Term Middle Term Major Premise Minor Term Middle Term Minor Premise Minor Term Major Term Conclusion The rule of the second figure is Whatever is inconsistent with the predicate of a subject is inconsistent with the subject This is a mixed ratiocination because an unexpressed proposition must be added in thought in order to arrive at the conclusion If someone says No B is C A is C Therefore A is not B Their inference is valid only if they silently interpose the immediate inference No C is B after the first premise It is merely the negative converse of the first premise Without it the ratiocination is invalid In the Third Figure only mixed Ratiocinations are possible Pattern of Third Figure Subject Predicate Middle Term Major Term Major Premise Middle Term Minor Term Minor Premise Minor Term Major Term Conclusion The rule of the third figure is Whatever belongs to or contradicts a subject also belongs to or contradicts some things that are contained under another predicate of this subject An example of a syllogism of the third figure is All mammals are air breathers All mammals are animals Therefore some animals are air breathers This validly follows only if an immediate inference is silently interpolated The added inference is a conversion that uses the word some instead of all All mammals are air breathers All mammals are animals Hence some animals are mammals Therefore some animals are air breathers In the Fourth Figure only mixed Ratiocinations are possible Pattern of Fourth Figure Subject Predicate Major Term Middle Term Major Premise Middle Term Minor Term Minor Premise Minor Term Major Term Conclusion Kant claimed that the fourth figure is based on the insertion of several immediate inferences that each have no middle term The affirmative mode of this fourth figure is not possible because a conclusion cannot be derived from the premises The negative mode of this fourth figure is possible only if each premise is immediately followed by its unexpressed unspoken converse as an immediate inference In order to be valid the negative mode ratiocination No stupid man is learned Some learned persons are pious Therefore some pious persons are not stupid must become No stupid man is learned Consequently no learned person is stupid Some learned persons are pious Consequently some pious persons are learned Therefore some pious persons are not stupid Section V The Logical Division of the Four Figures is a Mistaken Subtlety Legitimate conclusions can be drawn in all four figures Only the first figure determines the conclusion by pure unmixed reasoning The other figures use unspoken inserted inferences Logic should consist of open not covert reasoning It should be simple and unmixed with no hidden inferences Previous logicians incorrectly considered all four figures as being simple and pure The four figures were created by playfully changing the middle term s position This retained the rational conclusion but increased obscurity Time should not be wasted on the study of the three mixed ratiocinations Section VI Concluding Observation The first figure yields a correct inference in a simple direct manner The other figures yield a correct inference indirectly by the addition of hidden inferences They can be changed into the simpler first figure by changing the position of the middle term Kant concluded the essay with several related remarks Distinct and complete concepts are only possible by means of judgments and ratiocinations A distinct concept is one which is made clear by a judgment This occurs when something is clearly recognized as a predicate of a subject A complete concept is one which is made distinct by a ratiocination The ratiocination can be simple or a chain of reasoning The ability to understand and the ability to reason are both based on the ability to judge Understanding is the immediate recognition that something is a predicate of a subject Reason is the ability to judge mediately indirectly It recognizes another predicate in the first predicate thus conceiving a subject indirectly by means of a remote predicate Higher knowledge is based on judging Framing a judgment is a reflection that results in a distinct concept Non human animals can have clear representations of things that are predicates of a subject Humans can also have knowledge that a predicate is a predicate of a subject and are therefore able to make a judgment Non human animals can distinguish things from one another The different ideas are the causes of their actions which are irrational Humans can logically distinguish between things by means of judgment The higher knowledge of a human is based on the ability to make our own ideas the object of our thoughts All affirmative judgments are based on the principle of Identity A subject is identical to its predicate All negative judgments have the principle of Contradiction as their foundation A subject is opposed to its predicate Judgments in which identity or contradiction is mediately known by means of intermediate predicates and by means of the analysis of concepts are provable Judgments in which identity or contradiction is immediately known cannot be proved See Section II These unprovable judgments precede definitions because one must recognize a subject s predicate before they can define the subject Reference in the CritiqueKant summed up his thoughts on this topic in a short footnote that appeared in the second edition of the Critique of Pure Reason B141 He had been discussing the definition of judgment in general Logicians had usually defined it as a relation between two concepts Kant disagreed because he claimed only categorical judgments are so defined Hypothetical and disjunctive judgments are a relation between two judgments In his footnote Kant asserted that the lengthy and detailed doctrine of the four syllogistic figures concerned only categorical syllogisms or inferences He stated that this doctrine is only an artifice or trick for giving the appearance that there are three more kinds of inference or modes of drawing a conclusion than that of the first figure This is done surreptitiously by secretly concealing immediate inferences in the premises of a pure syllogism The only reason that this was generally accepted Kant remarked was that the logicians had made people believe that all of the other kinds of judgments could be reduced to being categorical judgments Kant claimed to have disproved this in his Critique A 73 There he argued that a categorical judgment relates two concepts whereas a hypothetical or disjunctive judgment relates two judgments See alsoSquare of oppositionNotesAn immediate or direct unmittelbares inference is one in which from the truth of one judgment that of another may be discerned immediately without any middle term Immediate inferences are usually produced by the use of contraposition or logical conversion For example the judgment nothing human is immortal is immediately inferred by contraposing the judgment nothing immortal is human The truth of the judgment is understood immediately An immediate inference is not to be confused with an immediate mark predicate or attribute An immediate mark is positioned between a subject and a remote mark predicate ReferencesImmanuel Kant Introduction to Logic New York Barnes and Noble ISBN 0 7607 7040 9 Contains Kant s Introduction to his Logic and also a translation of The False Subtlety of the Four Syllogistic Figures Proved