Logical issues in reasoning (conclusions)

Main thing

Logical issues in reasoning about conclusions are mistakes that happen when we try to figure out if something is true. These mistakes can cause us to reach conclusions that aren't correct, even when our starting ideas (premises) are right.

These mistakes occur when the steps we take to reach a conclusion don't line up properly with our starting ideas. It's like putting together a puzzle where the pieces don't quite fit, so the final picture is off. It's important to spot these mistakes to make sure our conclusions are solid and make sense.Here are some typical mistakes:

• Thinking a starting idea must be true just because the result is true. For example, "If it rains, the ground gets wet. The ground is wet, so it must have rained." But there could be other reasons for the wet ground.

• Thinking a result can't happen because the starting idea didn't happen. For example, "If it rains, the ground gets wet. It didn't rain, so the ground can't be wet." But the ground could be wet from a sprinkler.

• Believing there are only two choices when there might be more. For example, "We must either win or lose," but a game could also end in a tie.

• Jumping to a broad conclusion from a small amount of information. For example, "One apple was bad, so all apples from this store are bad."

• Believing that one thing will definitely cause another without enough evidence. For example, "If kids play video games, they will do poorly in school."

To avoid these mistakes:

1. Check if the conclusion really follows from the starting ideas.

2. Look for any hidden assumptions.

3. Think about other possible reasons or outcomes.

4. Make sure the conclusion matches the amount of evidence we have.

5. Break down the argument into parts and examine each step.

Terms

• Reasoning – The process of thinking about something in a logical way to form a conclusion or judgment.

• Conclusion – The final decision or judgment that comes from reasoning; the end point of an argument where you decide if something is true.

• Premise – A starting idea or fact that an argument is based on.

• Logical issue – A problem or error in the way an argument is made or reasoned that can lead to incorrect conclusions.

• Starting idea (antecedent) – The first part of a statement that suggests a result will follow if this part is true.

• Result (consequent) – The outcome or second part of a statement that follows from the first part.

• Hidden assumption – An unstated idea that is taken for granted in an argument but may not be true.

• Evidence – Information or facts that are used to support whether a conclusion or belief is true or valid.

• Argument breakdown – Analyzing an argument by separating it into its individual parts to better understand how it works and to check for errors.

An analogy

Logical issues in reasoning related to conclusions are like leaks in a pipe system. Just as a small leak can compromise the integrity of the entire system and lead to water loss, a single logical fallacy can undermine the soundness of an argument and lead to an unjustified conclusion. Even if the premises (the water source) are true and the conclusion (the endpoint) is desirable, flaws in the reasoning process (the pipes) can render the argument invalid.

Example: An argument that relies on a false dilemma is like a pipe system with a faulty valve that only allows water to flow in two directions, ignoring other possible paths. Just as this faulty valve restricts the efficient distribution of water, the false dilemma restricts the range of possible conclusions and leads to an unjustified either-or choice.

A main misconception

Many people believe that if an argument's premises are true and its conclusion aligns with their beliefs or intuitions, then the argument must be logically sound. However, this is not always the case. An argument can have true premises and a believable conclusion, but still be invalid if the conclusion does not follow necessarily from the premises.

Example: Consider the argument: "Most people prefer chocolate ice cream. John is a person. Therefore, John prefers chocolate ice cream." Although the premises may be true and the conclusion seems plausible, the argument is invalid because it assumes that what is true for most people must be true for John. This is a hasty generalization fallacy.

The history

1. In the 4th century BCE, Aristotle developed the first formal system of logic, which included identifying valid and invalid argument forms.

2. In the 3rd century BCE, the Stoic philosophers further developed propositional logic and studied logical paradoxes.

3. In the 12th century CE, Averroes and other Islamic philosophers made significant contributions to Aristotelian logic and syllogistic reasoning.

4. In the 17th century, Gottfried Leibniz envisioned a universal system of reasoning and symbolic logic.

5. In the 19th and 20th centuries, logicians like George Boole, Gottlob Frege, and Bertrand Russell developed modern formal logic and the foundations of mathematics.

"Logic takes care of itself; all we have to do is to look and see how it does it." – Ludwig Wittgenstein, influential 20th-century philosopher who made significant contributions to logic and the philosophy of language.

Three cases how to use it right now

1. When analyzing a complex argument, break it down into its component premises and conclusions. Identify the logical form of the argument and check if the conclusions follow necessarily from the premises. Look out for any formal fallacies, unjustified assumptions, or leaps in reasoning.

2. When constructing your own arguments, start by clearly stating your premises and conclusion. Double-check that your conclusion follows logically from your premises and that you haven't relied on any unsupported assumptions. Consider potential counterarguments and address them proactively.

3. When evaluating arguments in public discourse, such as political debates or media commentary, be on the lookout for common logical fallacies. Don't be swayed by appeals to emotion or authority. Focus on the logical structure of the arguments and the strength of the evidence presented.

Interesting facts

• The study of logical fallacies dates back to ancient Greek philosophers like Aristotle and the Sophists, who were interested in the principles of valid reasoning and argumentation.

• The "post hoc ergo propter hoc" fallacy (Latin for "after this, therefore because of this") is a common logical error in which people assume that because one event followed another, the first event must have caused the second.

• Confirmation bias, the tendency to seek out information that confirms one's preexisting beliefs, can lead to the logical fallacy of cherry-picking evidence to support a conclusion while ignoring counterevidence.

• Some researchers have argued that humans' susceptibility to logical fallacies may have evolutionary roots, as quick and dirty heuristics for decision-making that prioritize efficiency over accuracy.

• In the field of artificial intelligence, researchers are working on developing systems that can recognize and avoid logical fallacies in reasoning and argumentation.