The Art of Logic - Revision history

Robert.adlington at 15:40, 26 July 2026

2026-07-26T15:40:00Z

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	* If you are only using logic to defeat someone else's argument and promote your own, that is the intellectual version of being a bandit.		* If you are only using logic to defeat someone else's argument and promote your own, that is the intellectual version of being a bandit.
	* A good argument has a logical component and an emotional component and they work together.		* A good argument has a logical component and an emotional component and they work together.

			[[Category:Consciousness]]
			[[Category:Books]]

Robert.adlington: /* 13 Analogies */

2026-07-25T20:42:13Z

13 Analogies

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 === 13 Analogies ===
 === 14. Equivalence ===
 === 15. Emotions ===
 === 16. Intelligence and Rationality ===

Rob at 14:46, 25 July 2026

2026-07-25T14:46:48Z

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 * This is somehow how proofs work - at some point you just decide to stop filling in gaps any more, because you think that justifying things any further would not help.
 === 9. Paradoxes ===
 === 10. Where Logic Can’t Help Us ===
 == III: Beyond Logic ==
 === 11. Axioms ===
 === 12. Fine Lines and Grey Areas ===
 === 13 Analogies ===

Rob: /* II: The Limits of Logic */

2026-07-25T13:39:40Z

II: The Limits of Logic

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	== II: The Limits of Logic ==		== II: The Limits of Logic ==

			=== 8. Truth and Humans ===

			* This is somehow how proofs work - at some point you just decide to stop filling in gaps any more, because you think that justifying things any further would not help.

			=== 9. Paradoxes ===

			=== 10. Where Logic Can’t Help Us ===

	== III: Beyond Logic ==		== III: Beyond Logic ==

			=== 11. Axioms ===

			=== 12. Fine Lines and Grey Areas ===

			=== 13 Analogies ===

			=== 14. Equivalence ===

			=== 15. Emotions ===

			=== 16. Intelligence and Rationality ===

Rob at 13:35, 25 July 2026

2026-07-25T13:35:35Z

← Older revision		Revision as of 13:35, 25 July 2026
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	=== 4. Opposites and Falsehoods ===		=== 4. Opposites and Falsehoods ===

			* People are not very good at dealing with grey areas and nor is logic.
			* The law of the excluded middle says that true and not true are the only two options we are going to deal with at the moment. So all types of not true have to be included. All the grey area has to be included in one side or the other so that there is effectively no middle any more.
			* Absorbing the grey area into one side or the other is a simplification, but at least not incorrect or contradictory. Whereas denying its existence altogether is where black and white thinking usually goes wrong.
			* If A -> B, then the contrapositive statement is B is false -> A is false. This statement is logically equivalent to the original.
			* If A -> B then the converse, B -> is logically independent of the original.
			* If A -> B, then negating A and B individually A is false -> B is false is the contrapositive of the converse, and so logically equivalent to the converse.
			* A scientific law is something that has been determined to be probably true, to within levels of certainty accepted by science.

	=== 5. Blame and Responsibility ===		=== 5. Blame and Responsibility ===

			* Logical connectives (and and or) are the way of sticking together simple logical statements into complex wholes.
			* Logic and maths require things to be unambiguous without us having to understand things according to context.
			* The aim of intelligent rational humans shouldn’t be simply to be logical, but rather, to be logical in a useful way.

	=== 6. Relationships ===		=== 6. Relationships ===

			* In category theory, mathematicians discover the highlighting relationships between things is often much more illuminating than just thinking of things in isolation.
			* Category theory tells us it is always important to be clear what context we’re thinking about. Everyone is privileged relative to some contexts and underprivileged relative to some others. Animosity tends to occur when someone is prone to thinking of themselves in a context that makes them underprivileged (a victim) while others tend to view themselves in a context that makes them overprivileged.
			* If we all become more adept at seeing things from both a privileged and a non-privileged point of view, we will achieve greater understanding of disadvantaged people’s struggles but also of the actions, whether malicious or ignorant, that cause bigotry and oppression.

	=== 7. How to Be Right ===		=== 7. How to Be Right ===

			* Refining your scope means being precise about what world of objects you are focusing on.
			* If you qualify a statement with “almost all”, “most”, or “some”, together with “in my experience”, you can almost never be wrong.
			* Finding truth in someone’s sweeping statement by applying the right qualifiers can lead to greater understanding of what people are trying to say and where disagreements are coming from.
			* Vacuous truth or a condition being vacuously satisfied are cheats, such as “all the elephants in the room have two heads”.
			* If you are very precise about how you qualify your statements, you can always be right.
			* A useful way to be a rational person is to look for the sene in which things are true rather than simply deciding if they are true or false

	== II: The Limits of Logic ==		== II: The Limits of Logic ==

	== III: Beyond Logic ==		== III: Beyond Logic ==

Robert.adlington: /* 2. What Logic Is */

2026-07-16T09:44:07Z

2. What Logic Is

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 === 2. What Logic Is ===
 === 3. The Directionality of Logic ===
 === 4. Opposites and Falsehoods ===

Robert.adlington: /* 1. Why Logic? */

2026-07-16T09:25:23Z

1. Why Logic?

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			* Contrary to how it might seem, maths isn't about right and wrong, and nor are most arguments. They're about the sense in which something is right and wrong, depending on world views. If people disagree, it's often a result of different points of view stemming from different fundamental beliefs, not that one is right and the other is wrong.

	== I: The Power of Logic ==		== I: The Power of Logic ==

	=== 1. Why Logic? ===		=== 1. Why Logic? ===

			* The idea of logic is to have clear rules so that conclusions can be dran unambiguously and consistently by different people.
			* The rules of scientific discovery involve experiments, evidence and replicability. The rules of mathematical discovery involve logical proof. Mathematical truth is established by constructing logical arguments, and that is all.
			* Maths is the study of how logical things work: it's the logical study of how logical things work.
			* A powerful aspect of abstraction is that many different situations become the same when you forget some details.
			* Mathematics is a framework for finding similarities between different parts of science, and my research field, category theory, is a framework for finding similarities between different parts of maths.
			* When we look for similarities between things we often have to discard more and more layers of outer details, until we get to the deep structures that are holding things together.
			* Making analogies is the essence of mathematical thinking, where we focus on important features of a situation to clarify it, and to make connections with other situations. In fact mathematics as a whole can be thought of as the theory of analogies.
			* In normal language people judge things not only by context but also relative to their own experiences; logical explanations need to be independent of personal experiences.

	=== 2. What Logic Is ===		=== 2. What Logic Is ===

Robert.adlington: /* I: The Power of Logic */

2026-07-16T09:15:21Z

I: The Power of Logic

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 == I: The Power of Logic ==
 == II: The Limits of Logic ==
 == III: Beyond Logic ==

Robert.adlington: Created page with "== I: The Power of Logic == == II: The Limits of Logic == == III: Beyond Logic =="

2026-07-16T09:13:54Z

Created page with "== I: The Power of Logic == == II: The Limits of Logic == == III: Beyond Logic =="

New page

== I: The Power of Logic ==

== II: The Limits of Logic ==

== III: Beyond Logic ==