What are the alternative names for term logic?

Term logic is also known by several other names, including traditional logic, syllogistic logic, and Aristotelian logic.

Who is credited with originating term logic, and who were its early developers?

Term logic originated with Aristotle and was further developed in ancient history primarily by his followers, the Peripatetics. It was later revived by Porphyry in the 3rd century CE.

When did term logic experience revivals and become dominant in different regions?

Term logic was revived in medieval times, first in Islamic logic by Alpharabius in the tenth century. It later resurfaced in Christian Europe in the twelfth century with the advent of the "new logic" and remained the dominant form of logic until the late nineteenth century with the rise of predicate logic.

How does term logic relate to modern logical systems?

While modern logical systems have largely superseded term logic in prominence, they typically do not replace it entirely but rather expand upon it, integrating its concepts rather than radically breaking from it.

Which of Aristotle's works are central to his treatment of term logic?

The core of Aristotle's treatment of term logic is found in two texts from his collection known as the Organon: the Prior Analytics and On Interpretation. These works focus on judgments and formal inference.

What is considered the first formal study of logic, and what did it focus on?

The Prior Analytics, by Aristotle, is considered the first formal study of logic. It defines logic as the study of arguments, which are sequences of true or false statements leading to a conclusion.

What is a syllogism according to Aristotle's Prior Analytics?

A syllogism, as identified by Aristotle in the Prior Analytics, is an argument consisting of at least three sentences: two premises and a conclusion. These premises logically lead to the conclusion.

What are categorical sentences in the context of Aristotelian logic?

Categorical sentences are the propositions that form the premises and conclusion of a syllogism. Traditionally, they are understood as having a subject and a predicate connected by a verb, asserting or denying something about the subject.

What innovative expressions did Aristotle use for predication in the Prior Analytics, and why might he have introduced them?

Instead of the standard linking verb (like 'is'), Aristotle used expressions such as "P belongs to S," "P is predicated of S," or "P is said of S." Scholars conjecture these innovations facilitated the use of letters to represent terms, thereby avoiding the ambiguity that could arise in Greek when letters were combined with the linking verb.

How are the four types of categorical sentences represented symbolically, and what do they mean?

Using a medieval symbolization method, the types are represented as: - A: 'belongs to every' (e.g., AaB means 'A belongs to every B', equivalent to 'Every B is A') - E: 'belongs to no' (e.g., AeB means 'A belongs to no B', equivalent to 'No B is A') - I: 'belongs to some' (e.g., AiB means 'A belongs to some B', equivalent to 'Some B is A') - O: 'does not belong to some' (e.g., AoB means 'A does not belong to some B', equivalent to 'Some B is not A')

What is the fundamental assumption of term logic regarding propositions?

The fundamental assumption of term logic is that propositions are formally composed of two logical symbols called terms, leading to its alternative name, "two-term theory."

How is a 'term' defined in term logic?

A term is a part of speech that represents something but is not true or false on its own. Examples include 'man' or 'mortal'. Originally, terms were drawn from Aristotle's ten categories, which classified all objects and qualities within logical discourse.

What constitutes the formal model of a 'proposition' in term logic?

A proposition in term logic consists of two terms: a subject and a predicate. The predicate is either affirmed or denied of the subject, and the proposition itself is capable of being true or false.

What is the 'logical quality' of a proposition?

The logical quality refers to whether a proposition is affirmative or negative. An affirmative proposition affirms the predicate of the subject (e.g., 'All philosophers are mortal'), while a negative proposition denies it (e.g., 'No philosopher is mortal').

What is the 'quantity' of a proposition in term logic?

The quantity of a proposition refers to whether it is universal or particular. A universal proposition applies to all subjects (or 'the whole'), while a particular proposition applies to some subjects (or 'a part' thereof). When existential import is assumed, quantification implies the existence of at least one subject.

How did Aristotle distinguish between singular and universal terms?

For Aristotle, the distinction between singular and universal terms was a fundamental metaphysical one, not merely grammatical. A singular term, like 'Callias' or 'Socrates,' refers to a primary substance that can only be predicated of itself and not of any other thing.

What is the essential feature of a syllogism concerning its terms?

The essential feature of a syllogism is that, out of the four terms present in its two premises, one term must appear in both premises. This common term is known as the middle term.

How did the Port-Royal Logic treat singular terms, and what was the consequence?

In the 17th century, the Port-Royal Logic treated singular terms as if they were universals. For example, it would formulate 'All Socrates are men,' which is considered awkward and was a weakness later exploited by logicians like Frege.

Where does the famous syllogism 'Socrates is a man...' actually originate?

The syllogism 'Socrates is a man...' is often mistakenly attributed directly to Aristotle. However, it was first mentioned by Sextus Empiricus in his work *Hyp. Pyrrh.*, who cited a related syllogism: 'Socrates is a human being, Every human being is an animal, Therefore, Socrates is an animal.'

According to Aristotle, how are syllogisms divided based on the position of the middle term?

Aristotle divided syllogisms into three figures based on the position of the middle term. The First Figure has the middle term as the subject of one premise and the predicate of the other. The Second Figure has the middle term as the predicate of both premises. The Third Figure has the middle term as the subject of both premises.

Who added the fourth figure to Aristotelian syllogistic, and what is its structure?

The fourth figure, where the middle term is the predicate in the major premise and the subject in the minor premise, was added by Theophrastus, a pupil of Aristotle. While Aristotle's work doesn't explicitly detail it, there's evidence he was aware of such syllogisms.

What are the four valid forms of deduction in the first figure of syllogisms, and what are their medieval mnemonic names?

The four valid forms in the first figure are: 1. AaB, BaC; therefore AaC (Barbara) 2. AeB, BaC; therefore AeC (Celarent) 3. AaB, BiC; therefore AiC (Darii) 4. AeB, BiC; therefore AoC (Ferio)

What distinguishes the first figure syllogism from the second and third figures in Aristotle's theory?

The syllogism in the first figure is considered complete and axiomatic, forming the basis for proofs. In contrast, the second and third figures are considered incomplete and require proof, which always leads back to the first figure.

What are the four valid forms of deduction in the second figure of syllogisms, and what are their medieval mnemonic names?

The four valid forms in the second figure are: 1. MaN, MeX; therefore NeX (Camestres) 2. MeN, MaX; therefore NeX (Cesare) 3. MeN, MiX; therefore NoX (Festino) 4. MaN, MoX; therefore NoX (Baroco)

What are the six valid forms of deduction in the third figure of syllogisms, and what are their medieval mnemonic names?

The six valid forms in the third figure are: 1. PaS, RaS; therefore PiR (Darapti) 2. PeS, RaS; therefore PoR (Felapton) 3. PiS, RaS; therefore PiR (Disamis) 4. PaS, RiS; therefore PiR (Datisi) 5. PoS, RaS; therefore PoR (Bocardo) 6. PeS, RiS; therefore PoR (Ferison)

What was the nature of the Port-Royal Logic, and how influential was it?

The Port-Royal Logic, also known as "traditional logic," viewed propositions as combinations of ideas rather than terms, but it largely followed the conventions of term logic. It remained influential, particularly in England, until the 19th century.

Who developed a logical calculus that remained largely unpublished until around 1900?

Gottfried Wilhelm Leibniz created a distinctive logical calculus, but most of his work on logic remained unpublished and unnoticed until Louis Couturat extensively studied Leibniz's Nachlass (unpublished papers) around 1900.

What were the characteristics of 19th-century attempts to algebraize logic, such as those by Boole and Venn?

Attempts to algebraize logic in the 19th century, like the work of George Boole and John Venn, were typically systems heavily influenced by the existing term-logic tradition.

Which work is considered the first predicate logic, and when was it published?

The first predicate logic was presented in Gottlob Frege's landmark work *Begriffsschrift*, published in 1879. However, it was not widely read until after 1950, partly due to its unconventional notation.

When did modern predicate logic, as it is known today, begin to develop?

Modern predicate logic began to emerge in the 1880s through the writings of Charles Sanders Peirce, who subsequently influenced logicians like Giuseppe Peano and Ernst Schröder. Bertrand Russell and A. N. Whitehead further developed it in their *Principia Mathematica*.

In what educational context did term logic persist for some time?

Term logic survived to some extent in traditional Roman Catholic education, particularly in seminaries, due to the strong Aristotelian influence on medieval Catholic theology, exemplified by the works of Thomas Aquinas.

What criticisms have been raised against predicate logic, leading some to prefer term logic?

Critics argue that predicate logic can be unnatural, using an artificial language of functions, arguments, quantifiers, and bound variables (termed "Procrustean" by Quine). It also faces theoretical challenges, notably concerning empty names and identity statements.

What were George Boole's primary goals in developing his system of logic?

George Boole aimed to "go under, over, and beyond" Aristotle's logic by providing it with mathematical foundations using equations, extending its problem-solving capabilities beyond validity assessment to equation solving, and broadening its application range to handle propositions with arbitrarily many terms, not just two.

How did Boole's system differ from Aristotle's in terms of propositional forms and applications?

Boole reduced Aristotle's four propositional forms to equations, a revolutionary idea. His system also incorporated rules for equation solving and could handle multi-term propositions and arguments, unlike Aristotle's system which was limited to two-termed subject-predicate propositions and arguments.

What is the definition of a 'term' in the context of term logic?

A term is the fundamental component of a proposition in term logic, representing something but not being true or false on its own. Examples include 'man' or 'mortal'.

What is a 'proposition' in term logic?

In term logic, a proposition is defined as a form of language, specifically a sentence where a subject and predicate are combined to assert something that is either true or false.

What are the four figures of syllogisms as described in Aristotelian logic?

The four figures of syllogisms are determined by the position of the middle term: Figure 1 (subject-predicate), Figure 2 (predicate-predicate), Figure 3 (subject-subject), and Figure 4 (predicate-subject).

What is the significance of the 'middle term' in a syllogism?

The middle term is crucial in a syllogism because it is the term that appears in both premises but not in the conclusion. Its position within the premises determines the figure of the syllogism.

What does the term 'Organon' refer to in relation to Aristotle's logic?

The Organon is the collection of Aristotle's six logical works, which includes texts central to term logic like the Prior Analytics and On Interpretation.

How did medieval logicians simplify the study of syllogisms?

Medieval logicians developed a method of symbolization using letters (a, e, i, o) to represent the four types of categorical sentences and employed mnemonic names for valid syllogistic forms, greatly simplifying the study of texts like the Prior Analytics.

What is the difference between universal and particular propositions?

Universal propositions make a claim about all members of a class (e.g., 'All A are B'), while particular propositions make a claim about only some members of a class (e.g., 'Some A are B').

What is the difference between affirmative and negative propositions?

Affirmative propositions assert that a predicate belongs to a subject (e.g., 'All men are mortal'), while negative propositions deny that a predicate belongs to a subject (e.g., 'No men are immortal').

What does the term 'existential import' mean in the context of propositions?

Existential import refers to the assumption that a proposition implies the existence of the subject it refers to. For example, a universal affirmative proposition ('All A are B') traditionally implied that A exists.

What was the historical trajectory of term logic's influence?

Term logic, originating with Aristotle, dominated logical thought through the Middle Ages and into the late 19th century. It was later eclipsed by predicate logic but continued to influence certain educational and philosophical traditions.

How did modern logics, like predicate logic, differ fundamentally from term logic?

Modern predicate logic allows for variables, functions, and quantifiers that can apply to complex structures, moving beyond the simple subject-predicate structure of terms and propositions that characterized term logic.

What is the role of 'inference' in term logic?

Inference is the process of drawing a conclusion from premises. In term logic, the syllogism is a specific form of inference where a conclusion necessarily follows from two premises.

What does it mean for a syllogism to be 'complete' or 'incomplete' in Aristotle's theory?

A syllogism is considered 'complete' if its validity is self-evident, as in the first figure. 'Incomplete' syllogisms, found in the second and third figures, require further steps or reduction to the first figure to demonstrate their validity.

What is the 'square of opposition' in traditional logic?

The square of opposition is a diagram illustrating the logical relationships (contradiction, contrariety, subcontrariety, subalternation) between the four types of categorical propositions (A, E, I, O).

What is the significance of 'categories' in Aristotle's logic?

Aristotle enumerated ten categories, which were classifications of all objects and qualities within the domain of logical discourse. In term logic, terms were originally understood to be drawn from these categories.

Term Logic Wiki: Term Logic: Foundations of Reasoning

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What is Term Logic?

Ancient Roots

In logic and formal semantics, term logic, also known as traditional logic or Aristotelian logic, represents an approach to formal reasoning that originated with Aristotle. It was further developed by his followers, the Peripatetics, and later revived and refined through various historical periods.

Historical Dominance

This system saw significant development in Islamic logic and Christian Europe during the Middle Ages. It remained the dominant framework for formal logic until the late 19th century, when it was gradually superseded by predicate logic. However, term logic continues to be studied and integrated into modern logical systems.

Modern Relevance

While modern logics often expand upon its principles rather than radically replacing them, understanding term logic provides crucial insight into the historical evolution of logical thought and its foundational concepts.

Aristotle's System

The Organon

Aristotle's foundational work in logic is collected in the Organon. Key texts like the Prior Analytics and On Interpretation detail his treatment of judgments and formal inference, forming the core of term logic.

Paradigm Shift

Modern scholarship, initiated by Jan Lukasiewicz in 1951 and further developed by John Corcoran and Timothy Smiley, has revolutionized the understanding of Aristotle's logic, informing contemporary translations and analyses.

Syllogistic Reasoning

Aristotle identified valid argument forms called syllogisms, which consist of premises leading necessarily to a conclusion. He focused on categorical sentences, which link a subject and predicate, and introduced innovative expressions to facilitate symbolic representation.

Core Principles

Fundamental Structure

Term logic operates on a two-term theory, where propositions are composed of two terms. Reasoning is built from these propositions, which assert or deny a predicate of a subject.

The Term

A term is a part of speech representing something, but not inherently true or false (e.g., "man," "mortal"). Aristotle classified terms within his ten categories, which structured logical discourse.

The Proposition

A proposition is a linguistic form, a sentence asserting or denying a predicate of a subject, capable of being true or false. Propositions possess quantity (universal/particular) and quality (affirmative/negative).

Understanding Terms

Definition and Origin

The term, derived from Greek horos and Latin terminus, signifies an "extreme" or "boundary." It represents the constituent parts of a proposition, joined by affirmation or denial.

Conceptual vs. Linguistic

Early modern logicians like Arnauld and Mill debated whether terms represented psychological entities (ideas/concepts) or linguistic units (words). The core function remains linking subjects and predicates within a proposition.

The Propositional Framework

Form and Function

A proposition is a specific sentence structure where a predicate is affirmed or denied of a subject. It is the fundamental unit of logical discourse, capable of bearing truth or falsity.

Quantity and Quality

Propositions are classified by their quantity (universal or particular) and quality (affirmative or negative). This leads to the four traditional types: Universal Affirmative (A), Universal Negative (E), Particular Affirmative (I), and Particular Negative (O).

The four standard forms of categorical propositions:

A: Universal Affirmative ("All B is A")
E: Universal Negative ("No B is A")
I: Particular Affirmative ("Some B is A")
O: Particular Negative ("Some B is not A")

Aristotle's original square of opposition assumed existential import for universal statements.

Syllogistic Figures

The Middle Term

Syllogisms are classified into figures based on the position of the middle term (the term appearing in both premises but not the conclusion). Aristotle identified three figures, with Theophrastus later adding a fourth.

Positional Structure

The figures are defined by the arrangement of the middle term (M) relative to the subject (S) and predicate (P) of the conclusion:

Figure	Major Premise	Minor Premise	Conclusion
First	M - P	S - M	S - P
Second	P - M	S - M	S - P
Third	M - P	M - S	S - P
Fourth	P - M	M - S	S - P

Valid Syllogisms

Aristotle's Deductions

Aristotle systematically analyzed valid syllogistic forms within each figure. The first figure is considered "complete" or axiomatic, while others are proven by reduction to the first figure.

Figure	Major Premise	Minor Premise	Conclusion	Mnemonic Name
First	AaB	BaC	AaC	Barbara
	AeB	BaC	AeC	Celarent
	AaB	BiC	AiC	Darii
	AeB	BiC	AoC	Ferio
Second	MaN	MeX	NeX	Camestres
	MeN	MaX	NeX	Cesare
	MeN	MiX	NoX	Festino
	MaN	MoX	NoX	Baroco
Third	PaS	RaS	PiR	Darapti
	PeS	RaS	PoR	Felapton
	PiS	RaS	PiR	Disamis
	PaS	RiS	PiR	Datisi
	PoS	RaS	PoR	Bocardo
	PeS	RiS	PoR	Ferison

Decline and Transition

Renaissance Shifts

During the Renaissance, logicians like Rodolphus Agricola and Petrus Ramus began promoting alternative logical frameworks, challenging the dominance of traditional term logic.

Modern Formalism

The 19th century saw attempts to algebraize logic (Boole, Venn), leading to the development of predicate logic by Frege, Peirce, and Russell. This new system, with its focus on functions and variables, offered greater expressive power and mathematical rigor.

Enduring Influence

Despite the rise of predicate logic, term logic persisted, particularly in traditional Catholic education. Its concepts and methods continued to influence philosophical and logical discourse, demonstrating its lasting significance.

Modern Perspectives

Criticisms of Predicate Logic

Some philosophers argue that predicate logic can be "Procrustean," employing an artificial language that deviates from natural reasoning. Concerns are also raised about its handling of issues like empty names and identity statements.

Preference for Naturalism

Scholars like Gareth Evans have advocated for semantic theories that more closely align with the syntactic structures of natural language, suggesting a potential advantage for approaches that build upon term logic's intuitive framework.

Boole's Integration

Aristotle and Boole

George Boole, a pivotal figure in mathematical logic, held a deep respect for Aristotle's system. His work, The Laws of Thought, aimed to extend and formalize Aristotelian logic using mathematical foundations.

Boole's Advancements

Boole's contributions included providing mathematical underpinnings for logic through equations, expanding logic's problem-solving scope to include equation solving, and enabling the analysis of propositions with multiple terms, surpassing Aristotle's two-term limitation.

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References

They are mentioned briefly in the De Interpretatione. Afterwards, in the chapters of the Prior Analytics where Aristotle methodically sets out his theory of the syllogism, they are entirely ignored.

Copleston's A History of Philosophy

John Corcoran, Aristotle's Prior Analytics and Boole's Laws of Thought, History and Philosophy of Logic, vol. 24 (2003), pp. 261â288.

A full list of references for this article are available at the Term logic Wikipedia page

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Term Logic: Foundations of Reasoning

💡 Dive in with Flashcard Learning! 💡

What is Term Logic? ⚖️

🏛️ Ancient Roots

⏳ Historical Dominance

🔗 Modern Relevance

Aristotle's System 📜

📚 The Organon

💡 Paradigm Shift

➡️ Syllogistic Reasoning

Core Principles ⚙️

🧩 Fundamental Structure

🏷️ The Term

💬 The Proposition

Understanding Terms 🏷️

📍 Definition and Origin

🧠 Conceptual vs. Linguistic

The Propositional Framework 🗂️

🗣️ Form and Function

🔢 Quantity and Quality

Syllogistic Figures 📐

🔄 The Middle Term

📊 Positional Structure

Valid Syllogisms ✅

🧠 Aristotle's Deductions

Decline and Transition 📉

⏳ Renaissance Shifts

💡 Modern Formalism

🏛️ Enduring Influence

Modern Perspectives 🔄

🤔 Criticisms of Predicate Logic

🗣️ Preference for Naturalism

Boole's Integration ➕

🤝 Aristotle and Boole

🚀 Boole's Advancements

Teacher's Corner 🧑‍🏫

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References

📜 References

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📜 Important Notice

Dive in with Flashcard Learning!

What is Term Logic?

Ancient Roots

Historical Dominance

Modern Relevance

Aristotle's System

The Organon

Paradigm Shift

Syllogistic Reasoning

Core Principles

Fundamental Structure

The Term

The Proposition

Understanding Terms

Definition and Origin

Conceptual vs. Linguistic

The Propositional Framework

Form and Function

Quantity and Quality

Syllogistic Figures

The Middle Term

Positional Structure

Valid Syllogisms

Aristotle's Deductions

Decline and Transition

Renaissance Shifts

Modern Formalism

Enduring Influence

Modern Perspectives

Criticisms of Predicate Logic

Preference for Naturalism

Boole's Integration

Aristotle and Boole

Boole's Advancements

Teacher's Corner

True or False?

Test Your Knowledge!

Gamer's Corner

Discover other topics to study!

References

Feedback & Support

Disclaimer

Important Notice