The two systems of reasoning that seems to be embedded in the software of human mind are Nyaya system and Vaishika system of reasoning. The Nyaya (Logical: Reasoning or way of thinking perception, inference...) and the Vaishika (Analytical: Different or Differential) are two complimentary systems. The Nyaya system described by Gautama Rishi furnishes a method of inquiring of reasoning and laws of thoughts. The Vaishika system described by Kanada Rishi deals with analysis of experience of objects and things. [Philosophical Schools from Ancient India on analysis of self and Figure 2.7.]
These two philosophical systems stress, not information, it is ability to cross-examine the information, events and experiences and abbreviate these constitutes knowledge. This "knowledge" is fundamental to context. The cross-examination of the information is also basic to present day judicial process, to the teaching of clinical diagnostic or any process that involves judging the future state. Creativity is an independent occurrence.
Man does not attain freedom from action ( culmination of the discipline of action) nor does he reach perfection (culmination of the discipline of knowledge) merely by ceasing to act. Human mind projects not for the unstable present or a known past but for the future state. Infinity has two competitor, human mind and nature. Human actions, thus, are coherent and correlated (symmetrical or linear logical), random (asymmetrical or nonlinear logical) or arising de-novo (entirely a-linear) thus perceived as chaos as well as self-organized. [Figure 4.5, p108.] Webster Dictionary defines logic as the process of reasoning, or of pure and formal thought, or of the laws according to which the processes of pure thinking should be conducted; the science of the formation and application of general notions or instinct (science of generalization), judgment, classification, reasoning, and systematic arrangement. Logic thus is the science of the laws of thought, as thought; that is, of the necessary conditions to which thought, considered in itself, is subject -Sir W. Hamilton [1913 Webster as mentioned in Dictionary.net, Datasegment.com]. Uncritical mind, critical mind and media perceive logic differently, i.e., involving unconsciously driven tacit maxims, consciously seeks in accordance with instinct-correcting maxims or interest and sensation driven maxims. In democracy, opinion derived of 'All Experience' forms logic of things (see p58). It is the process of evolution and participation of occasional creativity (subtle difference that differentiates) derives the logic home.
Linear Logic - Is it necessary to define logic? 50 Logic, in philosophy or in mathematical side of Logic, deals with the formal principles, methods and criteria of validity of inference, reasoning or knowledge. 51 Logic is concerned with what is true and how we can know whether something is true. This involves the formalization of logical arguments and proofs in terms of symbols representing propositions and connectives.
The meanings of these logical connectives are expressed by a set of rules, which are assumed to be self-evident. Boolean logic (Mathematician George Boole) is a form of algebra in which all values are reduced to either TRUE or FALSE. Boolean logic is especially important for computer science because it fits nicely with the binary numbering system, in which each bit has a value of either 1 or 0. Another way of looking at it is that each bit has a value of either TRUE or FALSE. 52
Fuzzy Logic - Fuzzy logic is an approach to computing based on "degrees of truth" rather than the usual "true or false" (1 or 0) Dr. Lotfi Zadeh first advanced the idea of fuzzy logic in the 1960s. Dr. Zadeh was working on the problem of computer understanding of natural language. Natural language (like most other activities in life and indeed the universe) is not easily translated into the absolute terms of 0 and 1.
Whether everything is ultimately describable in binary terms is a philosophical question, but in practice much data we might want to feed a computer is in some state in between... Fuzzy logic includes 0 and 1 as extreme cases of truth (or the state of matters or fact) but also includes the various states of truth in between so that, for example, the result of a comparison between two things could be not "tall" or "short" but "possible of tallness." Dr. Zadeh believes fuzzy logic is one understanding the way our brains work. We aggregate data and form a number of partial truths, which we aggregate, or abbreviate further into higher truths, which in turn, when certain thresholds are exceeded, cause certain further results. A similar kind of process is used in artificial computer neural network and expert systems. It may help to see fuzzy logic as the way reasoning really works and binary or Boolean logic is simply a special case of it. [Also see above Vaishika system of analysis -differential and Pious Ali concludes that there are no distinctive signs attached to truth, p270].
Oscillating Logic - .this is not really so much a "paradox" as it is a logic .it flips in its logic in opposing meaning forever (Problem of Problem Formulation-supra). Each of us arranges and rearranges to decipher the meaning of this, i.e. oscillating logic, on one's own. The human mind represents oscillating logic, i.e. it searches 'meaning in meaning'. It is said do not seek stability among the unstable -Katha Upanishad (also see first para p61); man is bounded to function within this oscillating logic. We must learn this logic of human affairs. Mind has two environments one internal to it and the second that is external, when combined often searches meaning in meaning.
Anticipatory Logic - Biological entity is embedded with another logical system. The living is infinitely diverse, and different, and by definition creative (Mihai Nadin) and serves life (Katha Upanishad) - in the sense that a living being is not a copy of a past state, it is always in the new state, may be historically linked.
Accordingly, anticipation addresses things not repetitive in nature. It is the outcome of many processes. Some are internal to the system, and others are developed through image copying, learning through experience, through training or new state that arises de-novo (i.e. over again or once again, or from small molecules a complex structure -Webster Dictionary) .
There are also processes that unfold in each new context. Study of evolution is to account the past, and understanding anticipation to account the present and the future. This is why Nadin labels 'anticipation' our sense of context. Time and space or cause and effect are irrelevant to this logic (Figure 2.7).