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Logic and argumentation: The relationship

by Josh Biggs in Tips on 19th August 2019

Mathematics is a great source for the development of stronger texts. I explain why…

There are many recommendations made in writing books on how to write a text or an essay. It is recommended, for example, to collect ideas, relate them, structure sentences well, argue and even ask for help from a writing service such as GPALabs. But we hardly find recommendations on how to use logical-mathematical arguments, among which statistics play an important role.

Statistics should serve to enlighten us, not only to support us in our arguments. But in addition, you should not only copy the statistics without more, but reinterpret them and apply some criteria about how reliable they can be.

Every time we write an essay we should ask ourselves, what logical-mathematical argument can we use. That will give our writing greater strength of argumentation and persuasion.

Let’s start with our knowledge of Logic. It is important to keep in mind that our essays are made up of propositions. The difference between a sentence and a proposition is that the first is any expression that makes complete sense, while the second must be true or false.

Interrogative, exhortative or imperative sentences, desiderative and exclamatory sentences are not propositions because none of them affirms or denies anything and, therefore, are neither true nor false. Value judgments enter the field of Ethics and Law, for which legal Logic has been developed, among other related disciplines. And it is important to be aware of these kinds of arguments.

The arguments of our essays must then be true, but we must also try to structure them with concision and simplicity.

Our propositions can be structured through the connective and, or, yes then, yes and only yes, and of course we can make use of denial. In logic symbols, these correspond to ∧, ∨, p → q, ↔, and ¬, which is the symbol of negation. There are other connectives, such as universal quantifiers for all x: ∀ and there are some x: ∃.

So, it is important when writing our essays or any other writings, to formulate our sentences in terms of propositions and using some connectives of mathematical logic. And in fact we do it unconsciously, but doing it consciously will help us better structure our writings.

Just using the truth criteria of Logic will give us a critical version of our writing and demand that we support how true our propositions or arguments are. These will give us awareness that whenever we write an argument we are based on assumptions, which may be religious, political, legal, of some philosophical current or of science. Of course, the most compelling arguments are religious and politicians.

Once we have expressed our main arguments in simple propositions, we can make use of the Conditional, Yes p → q or the double conditional ↔.

Surprisingly, many university students when they do their graduation work have problems formulating hypotheses.

The conditional Yes p → q, is a simple way to remember and learn to formulate hypotheses. The p here represents the assumption or the hypothesis, and the q, the conclusion or thesis.

In our essays, if we intend to argue or prove something, we could represent our arguments in terms of a conditional. Hard work, it turns out sometimes, to translate colloquial language in terms of a conditional.

Variants of the conditional

The conditional has several variations that are very useful not only for the reasoning process and development of argumentative texts, but also for literary qualification of a compositional work. In fact, just distinguishing the components of the conditional, in which the antecedent is the hypothesis and the consequent the thesis, already becomes a clarification, very useful when doing a master’s job, because those who start in Research work often finds it difficult to formulate hypotheses.

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