Before You Go To University: Logic

Before You Go to University: Logic - Being Libertarian
Photo Credit:

Editor’s note: This is the first installment of a new Being Libertarian series curated to help anyone who is beginning their journey through university.
As Jordan Peterson alludes to in many of his lectures, the university can help a person read great books, absorb great thought, and develop their unique human ability to speak, argue, and articulate. But often we face a situation where rather than being taught how to critically think, students are instead being shown one-sided arguments, or being told what to think. This series intends to prepare future and current students so that they can move forward confidently into their university experience, one that will open their minds and challenge their presuppositions armed with critical thought, logic and reason.

Part 1: Logic

Libertarians and conservatives are becoming increasingly disenfranchised with universities. We tend to be fiscally-prudent, and universities aren’t necessarily geared toward vocational training and as such it’s potentially a bad monetary investment. They’re further viewed as propaganda machines for leftist thought.

Logic and truth can trump propaganda and so we wish to begin this series by delving into how logic operates and further suggest that universities tend to offer excellent classes on logic and critical thinking and would highly recommend this being your first selection of classes.

Logic is the path to truth. It’s developing an exactness with arguments to know that we’ve arrived at the destination of truth. Computer programming works with logic because it can’t permit any ambiguity or false implications. It’s the most useful thing any human being can learn, because we have to think every single day of our lives and ensuring we aren’t drawing false conclusions in politics, religion, with a business proposal, with a customer service agent, with health advice, with a loved one’s suggestions, is paramount.

We can arrive at truth by what philosophers call an argument. This is not an angry exchange, it’s a series of statements that are supposed to lead to some higher truth. If you want to prove that your cell phone company has given you an incorrect charge, you have to give them an argument as to why this is so, some sort of proof or justification, and knowing that your justification necessarily implies the conclusion is the business of logic.

An argument can go wrong in one of two ways, either the structure is bad or the content is bad. A bridge can have a perfect design, but if the government decides to cut corners and use jelly rather than concrete, that is, if the content was poor, it will be useless. Conversely, a bridge can be made of diamonds, but if the design is poor and the bridge is disconnected, the bridge is useless.

1. Validity

Step one is to ensure the structure is valid:

If P then Q.

It is the case that P.

Therefore: Q.

This is a valid argument. It’s saying that if premise one and premise two are correct, the conclusion has to be true. It doesn’t care about political bias, religious or atheistic passions, the authority someone has in a field, someone’s ethics or upbringing, and certainly not a person’s feelings or capability of handling offense, logic is logic and none of these are relevant, the conclusion follows necessarily from the premises.

P and Q can stand for literally any sentence:

If it is raining then I will wear my coat.

It is the case that it is raining.

Therefore: I will wear my coat.

If I am from Toronto then I am from Canada.

It is the case that I am from Toronto.

Therefore: I am from Canada.

If I am a Greek god, then I drive a Honda.

It is the case that I am a Greek god.

Therefore: I drive a Honda.

These are all valid arguments. Their structure is good. The content might be terrible, perhaps it’s wrong to say that all Greek gods drive Hondas, but when someone says an argument is valid they’re only saying that if the premises are true, then the conclusion must be true; they aren’t committing to the premises being true.

A valid argument, first and foremost, means that the premises generate the conclusion. Most of us have an intuitive sense of how logic works, or when violations of it arise.

The most splendid example of this in recent memory was Jordan Peterson’s famous interview with Cathy Newman. She continually interpreted him to be saying things he wasn’t actually saying, and he continually had to point out why his premises didn’t generate the conclusions she was drawing. Her deductions were illogical.

Newman: “What’s in it for the woman?” (a question about Peterson’s call for men to take responsibility for their lives)

Peterson: “Well, what sort of partner do you want? Do you want an overgrown child or do you want someone to contend with that’s going to help you?”

Newman: “So you’re saying women have some sort of duty to help fix the crisis of masculinity?”

Nothing of what Peterson had said generates the conclusion that she drew. It could be the case that Peterson believes this, her conclusion may or may not be correct, but the reason why she drew it is incorrect.

There are other examples to consider:

If P then Q

It is not the case that P

Therefore: It is not the case that Q

This would be an example of an invalid argument.

If I am from Toronto then I am from Canada.

It is not the case that I am from Toronto.

Therefore: It is not the case that I am from Canada.

This is clearly false. I could be from another part of Canada. Yet, if some ethical, religious, political passion is brought into the equation, some people might find an argument that takes this form to be a good argument and fall prey to propaganda.

This happens informally. Anytime a murder takes place with a gun there are those sure to get angry with the gun and claim, “If only they didn’t have a gun everyone would still be alive!” To put this in the terms of logic:

If person A didn’t own a gun, then person B would be alive. (If P then Q)

Person A does own a gun (Not P)

Therefore: Person B is dead.

This isn’t necessarily true; the conclusion doesn’t follow from the premises.

Another example:

If P then Q.

It is the case that Q.

Therefore, it is the case that P.

Consider the accusation that some Democrat is a communist:

If someone is a communist then they support socialized medicine.

It is the case that politician X supports socialized medicine.

Therefore, it is the case that politician X is a communist.

These premises might be entirely true, but they don’t generate the conclusion. When in office, Margaret Thatcher came to support Britain’s national health service and she was certainly not a communist, even though all communists support nationalized health service.

Another example:

If P then Q

It is not the case that Q

Therefore: It is not the case that P

This is a valid argument.

If I am from Toronto, then I am from Canada.

It is not the case that I am from Canada.

Therefore: It is not the case that I am from Toronto.

This is a valid conclusion. It might not be true even though the argument is valid – validity is only saying that if the premises are true then the conclusion follows.

2. Soundness

Not only should an argument be valid but it should also be sound. This is the next stage in logical arguments – our path to truth. This is the idea that not only is the structure of the argument valid, but the content is also true.

If I am a Greek god then I drive a Honda.

It is the case that I am a Greek god.

Therefore, it is the case that I drive a Honda.

This argument is valid and but it’s still remarkably awful (although, the conclusion might be true, I could drive a Honda, you can hold true beliefs and have terrible reasons for doing so).

If I am from Toronto then I am from Canada.
It Is the case that I am from Toronto.

Therefore, it is the case that I live in Canada.

This argument is both valid and the conclusion is true. When teaching logic, I always ask my students if this means that the argument is sound.

The answer is no, further this is not even a sound argument. From this clue, you can logically deduce something about me. If it’s not a sound argument and both the conclusion is true while the structure is valid, then you know one of the premises has to be false. Given that the truth of premise one -Toronto is part of Canada, you can logically deduce I’m from somewhere else in Canada other than Toronto.

Provided someone hasn’t committed an egregious logical error in drawing conclusions, most political debates surround the truth of some premise, which generally requires evidential or scientific reasoning however, philosophy can weigh in on whether or not a premise is sound as well.

We do this by assuming a premise is true, and if we find a contradiction we know there is an error. A leftist might argue that equality of outcome is a good thing as it diminishes poverty. If this can be shown to have the logical implication of increasing poverty then a contradiction has been found and the initial assumption must therefore be false.

It’s never the case that we have P and Not P, as the truth of P implies the falsehood of Not P, and the truth of Not P, implies the falsehood of P. Logic might not be able to say whether it’s true or false that Dante wrote the Divine Comedy, history must do that, but logic can definitely say it’s false to claim that Dante both did and did not write the Divine Comedy.

3. Cogency

The third level of argumentation is when not only is the structure valid, and the premises are true, but it’s also the case that the premises are known to be true.

If the starting point of the argument is something the audience doesn’t agree with or is only potentially true, then the entire argument is worthless.

The abortion debate has two interesting premises. One side will contend that women should have the right to do what they want with their bodies. The other side will contend that it’s immoral to take a human life. The idea that women have the right to do what they want with their bodies, extending to an abortion, implies the unborn don’t have a right to do what they want with their bodies. The idea that it’s immoral to take a human life carries with it the notion that the unborn are human lives. I doubt either side would generally agree to the other’s premise and as a result, their arguments don’t go anywhere.

These are the three levels of argumentation. Validity, soundness, and cogency. If all three of these have been checked off, an argument must be agreed to. Logic is the most calloused of all fields.

Students recognizing the failures of logic is incredibly important. It will help them in all fields of study. It is the most effective safeguard against propaganda.


The following two tabs change content below.

Brandon Kirby

Brandon Kirby has a philosophy degree with the University of New Brunswick. He works for a Cayman Island hedge fund service firm, owns a real estate company, and has been in the financial industry since 2004. He is the director of Being Libertarian - Canada. He is a member of the People’s Party of Canada and the Libertarian Party of Canada.