The basics of logic part 1

Logic is the scientific method of thought, occasionally also referred to as “The theory of formal truth and validity”. In Europe logic was first developed by Aristotle, and was the dominant system of logic in the Western World until the 19th century. The works of Aristotle introduced terms such as hypothetical syllogisms, temporal modal logic and inductive logic, in addition to terms like propositions, syllogisms and predicables.  One can contrast formal and informal logic, where the former is the study of natural language argument, of which the study of fallacies is of high importance. Formal logic on the other hand is the study of inference with pure formal content. Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference and mathematical logic is an extension of symbolic logic into other areas. For this article, I will be focusing mainly on formal logic and information logic.

Where the scientific method exists in order to ensure that the scientist(s) remain as objective as possible, logic exists to structure thoughts, and to ensure they remain as objective as possible. The goal of the system of thought that is logic, is to make reasoning “mind-independent” and clear, through the use of a rule set. A logician is expected to make his terms clear, be they numbers or words. For instance, if one were to use a word that has multiple, different definitions, out of which more than one could be reasonably assumed to apply, one must make it clear which definition one is using. If one uses a common word, yet deviates from the commonly accepted definition of the word, one is expected to define the word prior to its first use.

In order to do this, certain concepts are introduced. In Aristotelian logic the major way to structure arguments are in syllogisms. This uses premises (minor and major), conclusions drawn from the premises and sets of syllogisms, which are sets of premises, where if the premises are true, the conclusion must also be true. This formalizes an argument in such a manner that it can be fully explored and critiqued.

Syllogisms, Soundness and Validity

As mentioned, syllogisms are ways to structure arguments formally, in such a manner that the truth of the premises guarantee the conclusion. The primary benefit of structuring your core arguments into syllogisms is to structure them in such a manner that they become clear to you and to others. It also has the benefit of offering a clear set of rules for how to structure premises, which in turn reduces the emotional content of an argument, in effect it removes the ethos, and pathos.

An example of a syllogism would be:

Major premise: All men are mortal

Minor premise: Socrates is a man

Conclusion: Therefore Socrates is mortal.

An argument can exist in 2 basic states: valid or invalid. The argument above is an example of a valid argument, because if both premises are true, the conclusion follows. There are a lot of reasons why an argument would be invalid, logical fallacies are the more often cited culprit.

Then there is the question of soundness and validity. An argument can be sound without being valid and valid without being sound. Soundness in a deductive argument brings empirical observation into the mix. This means that it questions whether the premises are true, and if it finds that a premise is not true, then the argument is unsound.

Major premise: All millionaires are against tax hikes.

Minor premise: Warren Buffet is a millionaire.

Conclusion: Therefore, Warren Buffet is against tax hikes.

This is a valid argument. However, empirical observation of what Warren Buffet has actually said, indicates that the minor and major premises are untrue. [1][2] Thus, the argument is valid and sound. Often the distinction between validity and soundless are blurred in actual discourse, with the unfortunate side-effect that it enables propaganda. For instance, the “fact check” squad, in political debates, are “soundness checkers“, yet they are rarely validity checkers.

One of the issues that I frequently run into, when debating, arguing and writing, is a question of what is axiomatic or not. An axiom in logic, is a self-evident truth, that is so well established that it is accepted without controversy. This is a sword that cuts both ways unfortunately, in that debates about loaded issues such as religion, genders, race, immigration, taxation and so on, tend to rely on different axioms between debaters. What is a self-evident truth for one party, is not so for the other party. In that case, it is perfectly reasonable to challenge the other part.

The same is true for definitions. Those of us who frequently read research reports and philosophical texts notice how much time is spent on defining simple concepts. This is because definitions can have big impacts on research and arguments.

An example could be “For this argument, “reality” is defined as that which can be observed and measured.” In this case, the definition is there, to limit the scope of the argument and to establish the boundaries of what is addressed by it. It is perfectly OK to define words however you like in your argument, it is also perfectly fine to present the argument, but it can be meaningless.

Major premise: Disagreeing with me on the internet is abuse

Minor premise: [Insert person] disagreed with me on the internet.

Conclusion: Therefore [Insert person] is abusing me.

In this case, the major premise defines disagreement as abuse. The minor premise states that an event happened, the conclusion follows. In this case [Insert person] would be right to challenge the definition of abuse.

Axioms and Maxims

An axiom as mentioned earlier is a statement that is taken as true a priori. The existence of “The Ideological Bubble” largely stems from the acceptable of different, and often mutually exclusive axioms by different groups. An example that is quite in the times, is the axiom that all minorities are oppressed and all majorities are the oppressors. This is accepted by most social justice warriors as an a priori truth, which then helps inform their world view. However, for most non-SJWs, this is not accepted as an a priori truth, but rather an assertion or a proposition. Thus, when the two face off in a debate, their arguments cannot possibly lead to a conclusion as their axioms are mutually exclusive.

A simple example from the “equality” battlefield of feminism, is that feminism is defined as the “The theory of the political, economic and social equality of the sexes” [3], in this case, one must ask what the definition of equality is in this case. For instance, one can measure if women and men have the same opportunities in terms of politics, economics and society, through access. If both genders are free to enjoy the same opportunities within these spheres, then it follows that they are equal. However, if equality is in terms of outcome, then such equality cannot ever be measured. This is because, the former measures access, while the latter measures what is done with that access.

If one party is using the axiom of equality of outcome, while the other is using equality of opportunity, this colors the argument to a point where no reconciliation or productive outcome can arise. In the case of the former, equality cannot be achieved unless the sexes are perfectly demographically balanced within every sphere of a society. Whereas in the case of the latter, the sexes are by definition equal if they have access to the same opportunities.

A maxim is a ground rule or subjective principle of action, defined by the Oxford Dictionary of Philosophy as

Generally any simple and memorable rule or guide for living; for example, ‘neither a borrower nor a lender be’. Tennyson speaks of ‘a little hoard of maxims preaching down a daughter’s heart (Locksley Hall), and maxims have generally been associated with a ‘folksy’ or ‘copy-book’ approach to morality

For instance the proposed approach of “Listen and Believe” when a woman speaks of her experience, is a maxim, that seeks to avoid what is often called “victim blaming“, which is deemed a morally reprehensible act. The major difference between a maxim and an axiom, is that the latter is often viewed as being objectively true, while the latter is a subjective preference. One of the often experienced challenges comes when maxims are viewed as objective truth, as this leads to moral dogmatism, put in another way, it makes a moral interpretation an objective fact. The moral philosophy of Immanuel Kant and deontological ethics in general, maxims are viewed as subjective principles of action.

Summary and Conclusions

The goal of logic is to structure your thoughts and arguments so that they become as mind-independent as possible. This makes critical evaluation of your argument possible, because it takes both a form ,which is easy to evaluate and while being rigorously defined. In the various branches of philosophy, logic is utilized as a tool to communicate ideas between participants, to arrive at the “most logical” outcome, that which is the most true. Philosophy as a field is focused on finding truth, within the various sub-fields including epistemology, ethics, politics and esthetics. Science in itself used to be a branch of philosophy, entitled natural philosophy.

The challenge that philosophy attempts to overcome is the effect of the subject on thought. Which, is why I find it interesting that some sub-fields, for instance continental philosophy, and ethics are so excessively steeped in the subjective. For instance the dichotomy that Nietzsche attempted to overcome in “Beyond Good and Evil” is the one that moral philosophers have been quarreling about since the invention of the field.

As outline with maxims, they are by nature subjective and when maxims are treated as axioms, then the outcome will ultimately be subjective. When axioms are not generally regarded as true, but only regarded as generally true within one group, this creates issues of communication, but also very different perceptions of the world.