^^Logica, storia

Before formal logic

logic was studied with rehetoric, with calculationes, through the syllogism, and with philosophy. The first half of the 1900 saw an explosion of fundamental results, accompanied by vigorous debate over the foundations of mathematics.

Logical form. "Form" is important to logic !

Aristotle employed variable letters to represent valid inferences, one of Aristotle's greatest inventions.

According to the followers of Aristotle

only the logical principles stated in schematic terms belong to logic, and not those given in concrete terms.

ref: wp/Logical_form

The first system of formalized logic (in contemporary sense)

1879 Begriffsschrift - Frege

• allows higher-order quantification
• doesn't identify FOL as a subsystem of distinctive interest.

1910-1913 Principia Mathematica by Russell and Whitehead. Same as Frege.

1928  Mathematical Logic by Hilbert and Ackermann, stunning short book; FOL (First Order Logic) is highlighted, in a neat axiomatic system, under the label `the restricted predicate calculus'.

credits: LogicStudyGuide.pdf by peter_smith

Begriffsschrift (1879), Frege

a `concept-script' designed for the perspicuous representation of a rich class of propositions.

• the notational choices didn't win much favour
• the idea of using a formalized language to regiment arguments into a more manageable shape quickly became central to the whole project of modern formal logic.

Formal logic

• Sillogismo, logica sillogistica.
• Logica delle proposizioni. E' la piu' semplice.
• Logica dei predicati.

senso1:  creare un sistema formale nel quale fare logica. Def possibile post1900, dato che e' allora che si definisce cosa sia un sistema formale.

senso2: una loro formalita' l'avevano pero' anche i predecessori, per cui lo si puo' dire anche della loro logica.

wp/Formal_system | wp/Formal logical systems

Formal logic

• emerged as a subfield of mathematics, confluence of two traditions: formal philosophical logic and mathematics.
• with the aid of an simbolic notation and a rigorously deductive method.