Logic has been
used as a methodology even before its formalization. In order to
survive, our progenitors had to be able to deduce whether a
particular place or event was dangerous. These more earlier versions
of ourselves, needed to determine what was safe to eat and where food
was located. In this sense they were using logic intuitively.
As societies
evolved, we became aware of a need for a system of accounting. We
developed symbols to serve as abstract models for real world objects.
Empirically , we can demonstrate the need for a modeling system. We
can also demonstrate that these models of real world objects work.
The models functionality means they can be used for future
discoveries, and aids in civilization building.
Enumeration
permeates our entire civilization and history on multiple levels. It
observably exists separate from language. From the simplest counting
systems, patterns began to emerge. The laws of mathematics became
more complex, and a method of proof was needed that was empirically
verifiable. The earliest proofs were purely empirical as used by the
Pythagoreans and Thales of Miletus. Over time, mathematical proofs
slowly became less heuristic and a formalized system of logic was
becoming more prominent. Logic was largely an emergent aspect of
these methods of empirical verification. The methods of logical proof
slowly grew over the next two and half centuries from Thales around
550 BCE to Euclid around 300 BCE. Euclid is credited with formulation
of the axiomatic method of proof.
The Euclidean style
of proof through axioms, appears assumptive, or only
justifiable a priori.
The axioms served as
descriptions or definitions of geometric objects. The definitions
could be demonstrated empirically in general, but they did rely on
assumptions. For example, take the statement 2 points determine a
line. This is a postulate proposed as self-evident, and deduced
from it is many other theorems. If you were to take this as meaning
all statements derived rely on a non-empirical premise you would be
incorrect. The statement can be demonstrated as empirically true. You
would simply have to draw a line through only one point. The line
drawn, would be a point and not a line. To construct a line you would
have no choice but to have it pass through multiple points. So, we
can see the statement is both self-evident and empirically
demonstrable.
The evolution of
mathematical systems of proof allowed for a more formalized system of
logic. All of which finds its origins in our innate pattern
recognition. The ability to recognize patterns and natural desire to
seek them out led to the mathematical modeling of real world objects.
The modeling techniques made a complete system of logic and
mathematics more easily constructed and shared. We formulated logical
and mathematically complete laws and theorems from some of the
simplest models.
We see that these
models are intuitive,empirical, and justified in their use.
