Mental model "Automated Conveyer" in logic

Main thing

The "Automated Conveyor" mental model in logic is a mental representation of logic as a system that receives inputs, performs a series of sequential operations on them, and produces outputs.

The "Automated Conveyor" mental model can be applied to logic and reasoning in the following way:

1. Input: The premises, statements, or concepts that form the basis of an argument are like the raw materials or objects entered into the conveyor system. The quality and consistency of these inputs affect the final conclusion.

2. Movement through stages: The premises and concepts pass through a series of logical stages or inference rules, such as modus ponens, modus tollens, or syllogism. Each stage represents a specific logical operation applied to the inputs, similar to how objects move through different stages of a conveyor system.

3. Modification or transformation: At each logical stage, the premises and concepts are transformed or combined according to the rules of that stage. This process is analogous to the conveyor system modifying the inputs at each step.

4. Output: The final product of the logical reasoning process is the conclusion, which should follow necessarily from the premises and concepts if the argument is valid. The output should correspond to the intended goal of the argument, just as the final product of a conveyor system should meet the desired specifications.

Example: Consider the syllogism "All men are mortal. Socrates is a man. Therefore, Socrates is mortal." The premises "All men are mortal" and "Socrates is a man" along with the concept of mortality are the inputs. They move through the syllogistic reasoning stage, where they are transformed into the conclusion "Socrates is mortal," which is the output.

Variables in the model for logic:

• Premises

• Concepts

• Inference rules

• Validity

• Soundness

• Conclusion

Examples of applying the model to logical reasoning:

1. Deductive reasoning (reversed conveyor): Start with general premises (finished product) and apply inference rules (movement through conveyor backwards) to reach a specific conclusion (raw material).

2. Inductive reasoning (conveyor with quality control): Begin with specific observations or premises (raw materials) and use logical principles (conveyor stages) to infer a general conclusion or concept (finished product). The conclusion is subject to verification (quality control) based on further observations.

3. Abductive reasoning (conveyor with multiple outputs): Start with an observation or set of premises (raw materials) and seek the most likely explanation or conclusion (one of several possible finished products) that accounts for the given information. The conveyor system may have multiple paths leading to different conclusions.

4. Analogical reasoning (conveyor with parallel lines): Identify similarities between concepts or premises in one domain (raw materials on one conveyor line) and apply the same logical principles (conveyor stages) to another domain (parallel conveyor line) to reach a conclusion (finished product).

5. Causal reasoning (conveyor with cause-effect stages): Examine premises or observations (raw materials) to determine cause-and-effect relationships (conveyor stages linked by causality) and draw conclusions about the causal factors (finished product).

Terms

• Logic - the study of correct reasoning, focusing on the principles and criteria for valid inferences and demonstrations.

• Mental model - a simplified, conceptual representation of a complex system or process that helps in understanding, reasoning, and decision-making.

• Statement - a declarative sentence that is either true or false, serving as a building block for logical arguments.

• Argument - a series of statements, called premises, that are used to support or justify a conclusion.

• Premise - a statement or proposition that forms the basis of an argument. Premises are assumed to be true for the sake of the argument. Example: "All dogs are mammals."

• Conclusion - the final statement in an argument that follows logically from the premises. Example: "Therefore, Socrates is mortal."

• Inference rule - a logical principle or operation that allows the derivation of a conclusion from premises. Examples include modus ponens, modus tollens, and syllogism.

• Modus ponens - an inference rule that states if a conditional statement ("if P, then Q") is true, and the antecedent (P) is true, then the consequent (Q) must be true.

• Modus tollens - an inference rule that states if a conditional statement ("if P, then Q") is true, and the consequent (Q) is false, then the antecedent (P) must be false.

• Syllogism - a form of deductive reasoning that consists of a major premise, a minor premise, and a conclusion. Example: "All men are mortal. Socrates is a man. Therefore, Socrates is mortal."

• Validity - the property of an argument where the conclusion necessarily follows from the premises. If an argument is valid and its premises are true, the conclusion must be true.

An analogy

Logical reasoning is like a car assembly line. The premises and concepts are the raw materials, such as the chassis, engine, and wheels. The inference rules are the various stages of the assembly process, such as welding, painting, and quality control. Each stage modifies or combines the components according to specific rules. The conclusion is the final product - the assembled car. If the inputs (premises and concepts) are of good quality and the assembly process (inference rules) is followed correctly, the output (conclusion) will be a well-functioning vehicle.

Just as a defect in the raw materials or an error in the assembly process can result in a faulty car, flawed premises, concepts, or invalid reasoning can lead to a false or unsound conclusion.

A main misconception

A common misconception is that a logically valid argument always yields a true conclusion. However, validity only ensures that the conclusion follows necessarily from the premises. If one or more premises are false, the conclusion can be false even in a valid argument.

For example, consider the valid argument: "All cats are reptiles. All reptiles are cold-blooded. Therefore, all cats are cold-blooded." Although the reasoning is valid, the conclusion is false because the premise "All cats are reptiles" is false. This misconception highlights the importance of verifying the truth of the premises in addition to the validity of the reasoning.

Cases how to use it right now

1. When reading an opinion piece, identify the author's main assertions (premises) and trace how they logically lead to the conclusion. Evaluate the reasoning for validity and the premises for truth.

2. When making a case for a project proposal, start with the desired outcome (conclusion) and work backwards to determine what evidence (premises) and reasoning (inference rules) you need to support it.

3. In a debate, listen carefully to your opponent's argument and break it down into premises and conclusion. Look for flaws in their reasoning or false premises to counter their position.

4. When teaching a complex concept, present the information as a series of logical steps, each building on the previous one, to help students follow the reasoning and arrive at the intended understanding.

5. When faced with a challenging problem, clearly define the given information (premises) and the desired solution (conclusion), then apply logical principles to bridge the gap and derive the solution step by step.

6. When analyzing a scientific theory, identify the initial hypotheses (premises) and how they are logically combined and transformed through the scientific method to yield testable predictions (conclusions).

7. In a legal case, examine how the evidence (premises) is presented and connected through legal reasoning to support the verdict (conclusion). Identify any gaps or inconsistencies in the logic.

8. When developing a philosophical argument, start with basic assumptions (premises) and apply logical inference rules to derive intermediate conclusions, which then serve as premises for further reasoning, until the final conclusion is reached.

9. In a mathematical proof, begin with the given axioms and definitions (premises) and apply valid logical steps to arrive at the theorem (conclusion), ensuring each step follows necessarily from the previous ones.

10. When troubleshooting a malfunctioning system, gather data on the symptoms and possible causes (premises), then use logical deduction and process of elimination to identify the most likely culprit (conclusion) and devise a solution.

Interesting facts

• The ancient Greek philosopher Aristotle is credited with developing the first formal system of logic, which forms the basis of deductive reasoning.

• The "modus ponens" inference rule, meaning "the way that affirms," has been called the most basic rule of logic. It states that if a conditional statement ("if P, then Q") is true, and the antecedent (P) is true, then the consequent (Q) must be true.

• The "affirming the consequent" fallacy is a common logical mistake that assumes if a conditional statement ("if P, then Q") is true, and the consequent (Q) is true, then the antecedent (P) must be true. However, there could be other reasons why Q is true besides P.

• In propositional logic, there are 16 possible binary connectives or logical operators, such as "and," "or," "if-then," and "not," that can be used to combine or modify propositions.

• The "liar's paradox" is a famous logical problem that arises from self-referential statements like "this sentence is false." If the sentence is true, then it is false, but if it is false, then it is true, creating a paradox.