Why should we be interested in logic? What does it mean to be logical? How does logic tie into rationality?

Questions we should be thinking about, especially if we view ourselves as logical and/or rational people.

## What Does it Mean to Be Logical?

Something is logical if it adheres to the rules of logic.

There are different types of logic, as an example, for a syllogism* it would use syllogistic logic.

Consider the rules of chess would apply to playing chess but not draughts.

Both are types of board-game on a similar board but with different rules.

*A syllogism is a form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises)**

**A proposition is a statement or assertion/claim that expresses a judgement or opinion (which will either be true or false)

## Validity & Soundness

There can be some confusion around what it means to be logically valid, and what it means to be sound.

### Valid

Logically valid is speaking more of the structure. The premises do not have to be true, neither does the conclusion, they just have to follow on from each other and entail said conclusion, meaning that IF the premises are true then the conclusion must also be.

For a valid syllogism it is this format:

P1. if A then B

P2. A

C. therefore B

However, the structure below is invalid:

P1. if A then B

P2. B

C. Therefore A

The conclusion might also be true, but the structure is invalid.

To think about validity in a different way let’s consider chess again:

Moving the Rook diagonally is not a valid move.

Moving it forward/back/left/right from its start point (not going through things ) is valid.

### Soundness

So, now we have an idea about what validity is, we have to consider what makes something sound.

Not only does the structure have to be valid, but the premises have to be true.

If we consider the chess example again, we would be thinking of a move that was not only valid but was good:

Whilst we are stretching the metaphor, the move or structure needs to be valid and the premises that need to be true would be along the lines of the move is well thought out, we are not moving to be captured, unless it is a trap, we are not leaving ourselves open for an attack anywhere else, our king is still protected etc.

If we moved the rook into a position where it was easily captured and it wasn’t a trap or anything, we would say the move was unsound, even though it was valid.

So the same can be said for syllogisms. There is a valid structure to be had, and then there is the judgement of if it is also sound.

For an example of a sound syllogism:

P1. All mammals are animals

P2. Elephants are mammals

C. Elephants are animals

## So What About Rationality in This?

Rationality is, at least in part, the act of reasoning using the rules of logic and probability theory, holding consistent and coherent beliefs and having no strong convincing evidence against your position.

So, if you want to be rational, it would suggest that, at least where applicable, we ought to use the rules of logic.

Similarly, if we want to play chess (rationally) we ought to use the rules of chess, and reason in a logical and consistent way in planning out our moves.

We might not always get it right, but we ought to learn from that experience too.

So, the same can be said with other things too. If there is a type of logic that applies to your discussion, it would make sense to use that logic.

It might not get you to truth, but it will at least ensure a clear, concise, logically valid structure that is easy to work from.

This is why when discussing a proposition, propositional logic is useful, at least to get to the various answers.

Many folks on the internet discuss the proposition “God Exists” or as the propositional question “Does God Exist?” And seem to skip the logic part as if it is unimportant, proceeding with vague and ambiguous definitions followed by discussions which become awfully circular, or resulting in folks just saying “prove it” or throwing memes about.

From the moment you have nailed down your specific definitions, a valid structure and understand the overall format and positions one can hold you can have a discussion for the justification of various answers people can give.

## Summary

This was a simplistic overview of logic, validity, soundness and rationality. This isn’t so much an intro to logic as it is a pre-intro to logic. Hopefully, there is some understanding at least of what it means to be logical, and simply acting emotionless and only speaking in fact like Spock isn’t all there is to logic. Below are a number of articles that go into a bit more detail should you find yourself interested in this topic.

- You won’t believe this… An intro to Propositional Logic.
- What Does it Mean to Be Logical? – An overview of Logic and Rationality
- Propositional Logic and Beliefs – Podcast with PDF on Propositional Logic.
- Propositional Logic and Beliefs – Video Version of the Above.
- Beliefs, Language, and Logic – An overview of Logic, language and beliefs.
- Why should we use the rules of logic? – Demonstration of propositional logic with ‘God exists’.
- GDC: The Basics of the Laws of Logic.
- GDC: Breaking logic: Playing with Modal logic. (False conclusions from valid and sound arguments?).
- So what is this ‘Normative’ thing all about anyway? – Normative language and its ties to logic.
- Normatively Atheist – Why the ‘Belief God Does Not Exist’ definition of atheist is considered ‘Normative’.
- Wiki: List of logic symbols – Really useful guide to logic symbols.
- Wiki: Truth Tables – an overview of truth tables.
- Bad Atheist Arguments – Vol: 02 – Beliefs and Logic
- Beliefs and Rationality – CMT Vol: 10
- Rationality: How Can a Belief Be Rational? – SciPhi Shortz

Thanks to Phil, Dave and everyone with me on the stream where we did our first live “peer review”. You can see the original version of the article and the following discussion at the below video.

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