Categorical Syllogism
A categorical syllogism is a deductive reasoning form in Aristotelian logic. It uses three categorical propositions and three terms to derive a conclusion from two premises.
Categorical Proposition
A proposition linking two categories, stating whether some or all of one are part of the other. Crucial for syllogisms and logical reasoning.
Categorical Logic
Categorical logic, rooted in category theory, explores object categorization and the logical underpinnings of categories. It provides a formal framework for understanding structures and relationships within logical systems.
Categorical Theories in Mathematics
A categorical theory ensures all its models are isomorphic. This means different representations describe the same underlying mathematical structure, providing a unique perspective on mathematical objects.
Carnap-Ramsey Sentence
A Carnap-Ramsey sentence, from logical positivism, isolates a theory's empirical content by distinguishing theoretical terms from observational ones. It's a key tool for analyzing scientific theories.
The Caesar Problem
A philosophical puzzle in language and logic, the Caesar problem questions if mathematical concepts like 'successor' can apply to non-mathematical entities, exemplified by Frege's query about Julius Caesar.
Busy Beaver Problem
The Busy Beaver problem explores the limits of computation by seeking Turing machines that exhibit maximal behavior (output or runtime) for a given size. It highlights fundamental boundaries in computability…
Buridan’s Sophismata
A collection of paradoxes and logical exercises attributed to Jean Buridan, challenging logical and linguistic intuitions. These sophismata explore complex reasoning and the nature of truth and falsehood.
Brouwerian Modal Logic
A modal logic inspired by L.E.J. Brouwer's intuitionism. It grounds possibility in constructivist mathematics, offering a unique perspective on necessity and existence within formal systems.
Branching Quantifiers in Formal Logic
Branching quantifiers express complex dependencies between quantified variables, going beyond linear quantification. They allow for more intricate logical relationships and are crucial in advanced logic and linguistics.