Formal Fallacy: Propositional Fallacy

A propositional fallacy occurs when an error in logic arises due to the structure of compound propositions. In essence, for a compound proposition to be true, each of its component propositions must also be true. Errors arise when the logical connectives within the compound proposition—such as 'and', 'or', 'not', 'only if', and 'if and only if'—are misapplied, leading to incorrect conclusions. These fallacies can lead to incorrect conclusions, often because the truth values of the individual components do not align with the logical connectives used. 

Common types of propositional fallacies include 'affirming the consequent' and 'denying the antecedent'. 

• Affirming the Consequent

The fallacy of affirming the consequent is a common error in reasoning where one assumes that if a certain outcome is observed, then a specific cause must be true. This is a formal fallacy in propositional logic, often resulting from a confusion of necessity and sufficiency.

• Examples:

1. If a medication is effective, patients recover quickly. Patients have recovered quickly, therefore the medication is effective. This reasoning is flawed because quick recovery could be due to other factors, not necessarily the medication. 
2. If gravitational waves exist, we will detect them with sensitive equipment. We did not detect them, therefore gravitational waves do not exist. This is a fallacy because the failure to detect could be due to insufficiently sensitive equipment, not the absence of gravitational waves.
3. If a scientist hypothesizes that a specific chemical causes a reaction in plants, and then observes the reaction, they might conclude that the chemical was present. However, this is not necessarily true, as other factors could produce the same reaction. 
4. A specific drug treats a disease by targeting a particular pathway, and patients taking the drug show improvement, one might conclude that the drug's effectiveness confirms the hypothesis. However, this reasoning is flawed because the improvement could be due to other factors unrelated to the drug's mechanism of action.

• Denying the Antecedent

Denying the antecedent involves an incorrect inference made from a conditional statement. This form of reasoning is invalid because the falsity of the antecedent does not necessarily lead to the falsity of the consequent.

• Example

1. If a substance is an acid, then it will turn litmus paper red. If we deny the antecedent by saying the substance is not an acid, it does not logically follow that the substance will not turn litmus paper red, as there are other substances, like bases, that can also affect the color of litmus paper. 
2. If a creature is a bird, then it can fly. If we deny the antecedent by stating the creature is not a bird, we cannot conclude that the creature cannot fly, as there are other flying creatures like bats and insects. 
3. If a creature is not a mammal, then it is not warm-blooded, which is incorrect because birds, which are not mammals, are also warm-blooded.

This fallacy is particularly problematic in scientific reasoning because it can prevent the consideration of alternative hypotheses and impede the progress of scientific understanding.

Conclusion:

This fallacy can lead to confirmation bias, where researchers only look for evidence that supports their hypotheses, neglecting data that could disprove them. It's crucial for the scientific community to remain vigilant against such fallacies to ensure research integrity and the advancement of knowledge.  It is important to be able to spot propositional fallacies in order to avoid being deceived or misled by faulty reasoning.

Points to Ponder:

If a substance is an acid, then it will turn litmus paper red.

In this argument can you explain why it is fallacious?