Logical Synthesis
The process of logical synthesis begins with some arbitrary but defined starting point.
- Primitives are the most basic ideas. Typically they include objects and relationships. In geometry, the objects are things like points, lines and planes while the fundamental relationship is that of incidence – of one object meeting or joining with another.
- Axioms are statements about these primitives, for example that any two points are together incident with just one line (i.e. that for any two points, there is just one line which passes through both of them).
From a given set of axioms, synthesis proceeds as a carefully constructed logical argument. Where a significant result is proved rigorously, it becomes a theorem.
Any given set of axioms leads to a different logical system. In the case of geometry, each distinct set of axioms leads to a different geometry.
Read more about this topic: Synthetic Geometry
Famous quotes containing the words logical and/or synthesis:
“Opera, next to Gothic architecture, is one of the strangest inventions of Western man. It could not have been foreseen by any logical process.”
—Kenneth MacKenzie Clark, Baron of Saltwood (1903–1983)
“The invention of photography provided a radically new picture-making process—a process based not on synthesis but on selection. The difference was a basic one. Paintings were made—constructed from a storehouse of traditional schemes and skills and attitudes—but photographs, as the man on the street put, were taken.”
—Jean Szarkowski (b. 1925)