Logic^[1] is a piece of data that relates a hypothetical relation between source and destination objects. It is a subject matter that uses abstract data, or symbolic systems^[2] to enumerate plausibilities. Based on this definition, any set of symbols that allows for the same possibility space can be thought of as the same language. This can be explained as the term: up to isomorphism in Category Theory.

Some of the directly related ideas can be found here:

• Mathematical logic
• Extensible logic
• Reversible logic
• Quantum logic

Why study logic?

Logic has a unique position in the cognitive process of all systems. It is a kind of self-contained, or invariant foundation to help reason or compare against other things.

A great starting point

To learn logic, it might be easier to first play around with Lambda Calculus, since it is a small language that embeds all kinds of combinatorial powers. The best source for this is to listen to Dana Scott on Lambda Calculus. In particular, the first hour of this lecture series^[3], Scott present the historical context. It will be useful to see why logic is very much computational and combinatorial in nature.

Gödel Numbering

Learning logic cannot be without learning Gödel Numbering SystemCite error: Invalid <ref> tag; invalid names, e.g. too many. This simple framing provides a number-theoretic namespace for all formal languages. The incremental addition of vocabulary to this language, also can be represented in this framing.

The Dimensionality of Logic

If logic were to be a self-consistent structure, it must all be bounded in a singular entity, therefore, it should NOT have isolated dimensions, all dimensions and content must all be connected. This idea was well reflected in the notion of Lattice, the bounded data structure that allows everything considered in a unifying logic to be related with a type of common ordering relations. These ideas have been articulated by the following ideas:

1. Geometry of Logic^[4][5]
2. Geometry of Interaction^[6]

Types of Dimensions

When dealing with logic, the ideas of geometry must be connected with one more aspect, the notion of time, or order. Only by adding the directed relations, Logic possess sufficient expressive power to conduct reasoning activities. This leads to the incorporation of computation, a dynamic sequence of decision making, that has been operationally proven to be the essence of making choices at all scales of physical and non-physical contexts. This also leads to the revelation that why Logic and Type theory can be related to physical dimensions, in terms of different types of interactions. More importantly, thinking of dimensionality in terms of types could help shape and compress the complexity of foundational reasoning processes. Specifically, teaching young children^[7] to learn physics and math concepts from scratch.

Interesting Dicussions

Readers can find some relevant discussions about Logic, particularly, Logicism. It can be watched on PBS Infinite Series here (starting at 5'41", just click on the following image, it will jump to that time point.):

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References