Logic in science has an ancient lineage; Aristotle was the world’s first formal logician (he invented classical deductive logic) as well as one of the best early philosophers of science. He took the rational metaphysical ideas that Plato presented and inductively applied them to form a classification of cosmological ontology. Forms and genera and the presentation of matter in time were thoughtfully considered. That process has continued over two and a half millenia.
Symbolic logic was invented in the 19th century. It is true that Liebniz invented a symbolic mathematical logic, yet it wasn’t published in his lifetime nor for a lengthy time after his death. There is a history of productive philosophers, mathematicians and scientists. Bertrand Russell and Allan North Whitehead wrote ‘The Principia Mathematica’ early in the 20th century. Logical structures representing abstract possible forms are a logical method to consider how the physical world is constructed to-especially at the quantum mechanical level. When structures become to small to observe-or perhaps too large, it is logical reasoning processes including math advances that must be developed to probe the way thing might be. Some philosophers such as Arthur Prior have even investigated the relationships of contingence within logic to a substantial extent. It seems a paradox that a hypothetical entity that is purely logical could have anything besides a nominal contingent existence, and could form a logical basis for representing real contingent relations.
It is rather amazing that Saul Kripke was in high school, or just out when he published A Completeness Theorem in Modal Logic’. Kripke had neen influenced by Arthur Prior-basically the inventor of tense logic.
Tense logic developed by Prior and later others in the 1960’s established the logical relationships of temporal order. It was useful not only for computing logic but brought in the modal logical relationships of hypothetical worlds. Kripke developed a matrix approach to possible worlds, and I would think that ontologies of temporal based modal logic assume discrete values of units logically consistent and able to be falsifiable as existing or non-existing sates as trivial as that might be to remark.
Matrix and group mathematical representation of fields in multi-dimensional time contexts have obvious values in forming cosmological theories. The tense logic of prior may have had some kind of use in cosmology, and even String or M-theory-I must say that the topic exceeds my present reading. I have only recently discovered Prior and tense logic, and look forward to reading more in the field.
Prior believed that logical formalism-the idea that logic is valid only, or mostly as an intensional, analytical phenomena , isn’t valid. His approach of renormalizing intentional logic with the Universe may have been a method drawn from an assumption tat knowledge of the world’s physics and time can only be known contingently so therefor logic must apply functionally if knowledge is to have any valid human foundation.
Logic is basically perhaps limited to ordering relations between existent and non-existent states as well as descriptions of their intervals and scale. Space-time events logically represented may be inconsistent with the potential physical relationships of physically concatenated elements. If such is the case then logical induction may be more difficult.
Given space-time fields of science the discovery of logical relationships is necessary for knowledge. Readings in Prior and of the mathematics of M-Theory such as may be made simply explained (really) promises interesting ideas for metaphysical contemplation, as well as tools for science.