The logical system of Aristotle eventually evolved into a universal “concept language.” A paper written by, Whitehead and Russell’s Principia Mathematica says, “In the study of mathematical logic it was initially considered a hopelessly abstract subject with no conceivable applications.

The logical system of Aristotle eventually evolved into a universal “concept language.” A paper written by, Whitehead and Russell’s Principia Mathematica says, “In the study of mathematical logic it was initially considered a hopelessly abstract subject with no conceivable applications.

As one computer scientist commented, ‘If in 1901, a talented and sympathetic outsider had been called upon to survey the sciences and name the branch which would be least fruitful in [the] century ahead, his choice might well have settled upon mathematical logic.’ And yet, it would provide the foundation for a field that would have more impact on the modern world than any other.

As innovation advanced, it often correlated with a combination of objects, such as the abacus, the Babbage engine, and up to code-breaking machines during WWII. In fact, it can be better explained by the history of ideas, that emerged from mathematical logic. The theory developed from pioneer philosopher-mathematicians, like George Boole and Gottlob Frege.

The communication-initiated computer scientists to ingress decades of logic and mathematics, by Boole, and other logicians to show how Boolean logic could be used to create a circuit for adding two binary digits. These circuits would become the basic building blocks of what is now known as arithmetical logic units, a key component in modern computers.

However, this book is not a course in logic but rather to show the basic fundaments on the history of logic and However, this book is not a course in logic but rather to show the basic fundaments on the history of logic and how hybrid intelligence developed from the towering figure of Aristotle.

**Logical Thinking**

Aristotle’s philosophical methods were empirical, based on analysis, observation, and critical thinking.

An empirical aspect of his method employs observation and data collection, along with categorization and classification. Once the observations are completed, the sample of data is collected, and the student would proceed to correlate proper categorization and classification of facts. In essence, it provides the basis of knowledge. At that point, a generalization principle establishes a theory. These are the foundational steps to building scientific methods.

**The science of Logical Thinking**

Any student of Aristotle studying independently will use inductive and deductive reasoning as a critical thinking method. A common practice of Aristotelian reasoning.

The next phase in logical thinking is Syllogism which is instances of forming a reason in which a conclusion can be drawn, all dogs are animals; all animals have four legs; therefore, all dogs have four legs. It means two assumed propositions each share a term with the conclusion.

A syllogism operates within established parameters of logic to verbalize a conclusion based on inductive and deductive critical thinking.

An argument can be a set of premises lead by a series of logical steps to reach a conclusion. The end result is to capture the validity of an argument in its logical tightness, whether the conclusion follows the original premise, is not important, the concept of validity is what matters.

In Aristotle’s primary logical works there are categories led by prior analytics from posterior analysis and how they interpret tachyonic (a field in imaginary mass). The important factor is to understand these principles are guided by a single goal, based on fundamental insight.

As an example, what makes a good argument? How can you tell the validity of an argument?

The critical note to understand is rational consists purely of the logical strength that tie the premise and conclusion. However, it is the validity of strength in the logical time between the foundation and result of an argument that is important, but it may not always show the truth of the premise.

In other words, the conclusion is followed by the premise, however, it does not verify the premise is true. As an example, validity does not guarantee truth. Validity does promise the truth is preserved. On the other hand, if a premise is true, the conclusion of a valid argument has to be true.

Our goal must be to seize the validity of Aristotle’s fundamental insight, which repeats through the entire history of logic. As in one simple idea; what makes an argument valid, its structure? Validity is about the structure and form of an argument. So, what makes an argument valid, is not what it’s about. In other words, validity is not based on content. It’s not the truth either, what makes an argument valid is its form.

An example, see if you can recognize both arguments are valid.

- Most medicines require a prescription. So, everything that requires a prescription needs a doctor’s signature. It follows that most medicines require a doctor’s signature. Which is a valid argument?
- Most birds can fly; therefore, Donald Duck is a bird, hence Donald Duck can fly.

Many physicists are reductive materialists everyone who’s a reductive materialist is a modernist. It follows that many physicists are modernists.

In both of these arguments, they have the same form and therefore, valid. If the conclusion follows the initial situation, it must also follow the second. In the second argument, it shows valid, due to, it’s logically tight; whether you know anything about either subject. The content is mute since its structure is valid. The structure can be applied to anything.

What if we filled a real argument with accurate content and placed it into a logician’s acid? Do you know what would come out …? its “logical” skeleton. The bare structure is all that would be left. Now, think of this as the core of validity. After which we should be able to formalize and systematize, so maybe we can mechanize it. Therefore, if thinking is something, we mechanize we can create logical thinking machines.