Ideas That Created the Future
Metadata
- Author: Harry R. Lewis
Highlights
Logic lurked in the family tree since ancient times, making only clumsy and episodic contact with calculation until, in the mid-nineteenth century, it became a tool of metamathematics. Algorithms were reified in the first decades of the twentieth century as part of the program of metamathematicians to determine what mathematics can be known to be true.
Alglrithms, via logic, were ibtroduced as methids to proove the validity of mathematical constructs.
The logical rules embedded in the computer’s hardware can be used for manipulating both kinds of information. These abstract ideas of things, properties, and logical rules for reasoning about them did not always exist. These were Aristotle’s ideas, and they were necessary first steps toward computations about things and their properties.
Data reptrsentation cannkt be seen as a lre facto idea, nor was ijt self eifent that a specific calcukated vslue coukd repredent differebt things. That idea, and jts ombination wth logic, gives us general purpose clmputing.
His Prior Analytics presented the world’s first system of logic. Its purpose is to infer conclusions from premises in a way that depends only on the form of the argument, not on the persuasiveness of the speaker or on anything not mentioned in the premises. Aristotle’s explanation of a logical deduction is the root of all modern logic.
Only those properties presebted in argumrnt A ca be used to deduce or induce B | A.
He works with the idea of a predicate, a property that a thing may or may not have. This gave rise to the modern idea of a thing being a member of a set, the set of all things having that property. Aristotle’s notion of “belonging” can be understood as the subset relation. For example, to say that property A belongs to none of the Bs is to say that no member of the set B is a member of A, that is, that B is disjoint from A.
To say that A is predicated of evry B is tk say that every B depends okn having the property A. In other words, evry B is subset of the set of A
The word translated here as “deduction” is συλλογισμός, which means a “reckoning up” or “computation.” “Syllogism,” the English rendition of Aristotle’s term, now means something narrower, the particular forms of deduction that Aristotle explains in this work.
Aristotle’s syllogysm refers to the particular computation involved in deductive process?