Causal logic

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If you want to understand the laws and relationships of things, you can examine the causal relationships of things, which seems to be the only effective means.

Causal relationship between A and B

Analyzing the relationship between one thing and another can be divided intoAn eventandAnother event(Or nodes, or other synonyms, collectively referred to as A, B... this synonym),

Generally divided intoStart AandResults B，

If you want to analyze what kind of relationship there is between A and B,

For example, distinguishing between A leading to B or B can also lead to A's causality.

In fact, analyzing whether A leads to B is to analyze the causal relationship between A and B.

1. Exclude other possibilities

• Confirm whether there are other factors (C) that affect A and B at the same time.
• For example: A and B may be both the result of C, rather than A leading to B.

2. Time sequence

• A causes B：AmustOccurs at Bforward。
  If B occurs before A, then A cannot be the cause of B.

• B leads to A：BmustIt happened in Aforward。

Note: The most fundamental difference between logical reasoning and causality is that logical reasoning does not consider time factors, while causality must consider time factors.

3. Causality

• A causes B: A is the reason for B, B is the result of A.

• B leads to A:B is the reason for A, A is the result of B.

  Clarify the definition of causality:

  • causation: A is the cause of B, which means that the occurrence of A directly or indirectly triggers the occurrence of B.

  • Relevance does not equal causality: Even if A and B occur at the same time, it does not necessarily mean that A causes B, and other factors may be at play.
    Relevance ≠ Causality

A powerful tool for analyzing causal relationships

1. Logical reasoning

• A causes B: If A happens, B will inevitably happen.

• B leads to A: If B happens, A must happen.

  Analyze how A triggers B and whether there is a reasonable mechanism or logical chain.Use logic to determine whether A must trigger B.

  For example: rain (A) will inevitably lead to wet on the ground (B), which is a direct causal relationship.

  Drawing on the original axiomatic system of geometry, this is a good example of logical reasoning.

2. Experimental verification and statistical analysis

• A causes B: Control A through experiments and observe the changes in B.

• B leads to A: Control B through experiments and observe the changes in A.

• Through experimental control of A, we observe whether B changes.

• If the experiment cannot be done, causal relationships can be inferred through statistical data or long-term observations.

Statistical Methods

• Use statistical tools such as correlation analysis and regression analysis to determine the relationship between A and B.
• Note: Statistical correlation can only prompt possible causal relationships and cannot be directly proved.

Experimental design

• By controlling variables, the effect of A on B is observed.
• For example: In medical research, it is verified through controlled experiments whether the drug (A) has a therapeutic effect on the disease (B).

Example

1. A causes B: Rain (A) causes wet ground (B).
2. B leads to A: The ground is wet (B) causing rain (A).

In the first example, rain is the cause of wet ground;

In the second example, wet ground does not cause rain, so "B causes A" is not true.

"Creation" means causality, i.e. one event or condition raises another event or condition.

Causal analysis error scenario

1. Confusing cause and effect and correlation

• For example: the increase in ice cream sales (A) and drowning events (B) simultaneously does not mean that eating ice cream causes drowning. The real reason is the hot weather (C).

2. Ignore third-party factors

• For example: Education level (A) and income level (B) may be affected by family background (C).

3. Causal inversion

• For example: Health problems (B) lead to poverty (A), not poverty leads to health problems.

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Actual case analysis

Case 1: A leads to B

• A:stay up
• B: The next day
• analyze: Staying up late directly leads to lack of sleep, which leads to mental loss. This is a direct causal relationship.

Case 2: B leads to A

• A: Decline in academic performance
• B: addicted to games
• analyze: Addicted to games may lead to a decline in academic performance, but a decline in academic performance may also lead to students escaping reality and becoming addicted to games. Further analysis of the chronological order and mechanism is needed.

Case 3: Third-party factors

• A: Wear thick clothes
• B:cold
• analyze: Wearing thick clothes and catching a cold can occur at the same time, but the real reason is that the weather gets cold (C). Wear thick clothes to keep warm, not the cause of colds.

Summarize

• lead toIt indicates causality and effect. When analyzing, it is necessary to clarify the chronological order, eliminate other possibilities, and find a reasonable mechanism.
• The use of logical reasoning, statistical methods, and experimental verification can help judge causality.
• Be careful to avoid confusing causality and correlation, and ignore third-party factors.

Through the above methods, the relationship between "A causes B" or "B causes A" can be understood and analyzed more clearly.

Of course, continue to learn logicSufficient conditionsandNecessary conditions, can better analyze the causal relationship between the two events.

The difference between cause and effect and logic

Cause and effect relationship is a "real" relationship. Only after the cause phenomenon and result phenomenon have occurred, we say that there is a "causal relationship" between cause A and result B.

"Logical reasoning" is a kind of "theoretical" deduction. It does not require any realistic support, and the conditions must contain conclusions.

Logic – Condition

Sufficient conditionsandNecessary conditionsis an important concept in logic that describes the relationship between events or conditions.

The key to understanding them is to clarify how they affect the outcome.

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1. Sufficient Condition

• definition: If A is a sufficient condition for B, it meansEstablishment of A can guarantee that B is established, but B does not necessarily need to be established.
• Logical expression: A → B (if A, then B).
• Features：
  • A is the "full" reason for B, but not the only reason.
  • B may have other adequate conditions.

example:

• A:rain
• B: The ground is wet
• analyze: Rain (A) can cause wet on the ground (B), but wet on the ground can also be caused by the sprinkler truck (C). Therefore, raining is a sufficient condition for the ground to be wet, but not a necessary condition.

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2. Necessary Condition

• definition: If A is a necessary condition for B, it meansB must be established, but the establishment of A does not necessarily guarantee that B is established.
• Logical expression:B → A (only A is true, B can be true).
• Features：
  • A is a "necessary" premise for B, but A alone is not enough to cause B.
  • B may require additional conditions.

example:

• A: Oxygen
• B:combustion
• analyze: Oxygen (A) is required for combustion (B), but oxygen does not necessarily lead to combustion (combustible materials and ignition sources are also required). Therefore, oxygen is a necessary condition for combustion, but not a sufficient condition.

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3. Sufficient and Necessary Condition

• definition: If A is both a sufficient condition for B and a necessary condition for B, it meansA and B depend on each other, A is established if and only if B is established.
• Logical expression: A ↔ B (A and B are equivalent).
• Features：
  • There is a two-way causal relationship between A and B.
  • A and B are sufficient and necessary conditions for each other.

example:

• A: A number is an even number
• B: This number can be divided by 2
• analyze: A number is an even number (A) if and only if it can be divisible by 2 (B). Therefore, A and B are sufficient and necessary conditions for each other.

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4. How to distinguish between sufficient conditions and necessary conditions

1. Distinguish from logical relationships

• Sufficient conditions: A → B (A is established, B must be established).
• Necessary conditions:B → A (B is established, A must be established).

2. Distinguish from practical significance

• Sufficient conditions: A is the "full" reason for B, but not the only reason.
• Necessary conditions: A is a "necessary" premise for B, but A alone is not enough to cause B.

3. Understand from the example

• Sufficient conditions: Getting into college (A) is a sufficient condition for finding a good job (B), but finding a good job does not necessarily require getting into college.
• Necessary conditions: Passing the exam (A) is a necessary condition for graduation (B), but passing the exam does not necessarily guarantee graduation (other requirements need to be completed).

Common Mistakes

1. Confusing sufficient conditions and necessary conditions

• For example: I believe that "study hard (A) is a necessary condition for achieving good grades (B), but in fact, hard study is a sufficient condition for achieving good grades, not a necessary condition (some people may be gifted and do not need to work hard (some people may be talented and do not need to work hard). You can also achieve good results in your studies).

2. Ignore other conditions

• For example: It is believed that "oyster (A) is a sufficient condition for combustion (B), but in fact, oxygen is only one of the necessary conditions for combustion.

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Summarize

• Sufficient conditions: Establishment of A can ensure that B is established, but establishment of B does not necessarily require A to be established.
• Necessary conditions: A must be established when B is established, but A is established not necessarily guaranteed to be established.
• Fully necessary conditions: A and B depend on each other, A is established if and only if B is established.

Through logical relationships and practical examples, the differences and connections between sufficient conditions and necessary conditions can be better understood.