Logic & Reasoning

 Logic is a derivative thinking process, and both mathematics and language are only tools of expression. We should very much understand the boundaries of the terms we use and how we use them. 

Logic is the study of correct reasoning, especially when it involves drawing inferences. An inference is a rule-governed step from one or more propositions, known as premises, to a new proposition, called the conclusion. Reasoning can be evaluated for correctness and efficiency.

Reasoning uses logical rules of inference that are permissive, showing what inferences a reasoner can draw without committing a fallacy. Following such rules ensures the correctness of a chain of reasoning, but not its efficiency.

Psychologists distinguish between two main kinds of reasoning:

-Inductive reasoning infers from a part to a whole, from particulars to generals, or from the individual to the universal.

-Deductive reasoning analyzes valid argument forms and draws out the conclusions implicit in their premises.

In a broad sense, any rule-governed move from a number of propositions to a new one in reasoning can be considered a logical inference if it furthers one’s knowledge of a given topic. Sequence is a type of logic. There are different types of sequences, including:

-Harmonic sequence: In mathematics, this is a sequence of numbers where the reciprocals form an arithmetic sequence. A well-known example is 1, 1/2, 1/3, 1/4, ....

Fibonacci sequence: This sequence starts with 1, 1, and each subsequent number is the sum of the two preceding ones (1, 1, 2, 3, 5, 8, 13, 21, ...).

Musical sequence: In music, this is a melodic or chordal figure repeated at a new pitch level. It can be non-modulating (tonal), staying in a single key, or modulating, traversing several keys.

Sequence (computer programming) In computer programming, sequence is a basic control structure where instructions are executed one after another.

Logic is a derivative thinking process for improving decision making. We should very much understand the boundaries of the terms we use and how we use them. 

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