Types of Reasoning and Syllogisms

Question 1

Reasoning

Answer 1

Logic/Reason is the primary tool of the philosopher

A good philosopher needs to be able to use reason to make clear, relevant and precise points as well as to detect bias and logical flaws in their ideas or in the statements of others.

Logic and reason can act as a sort of filter that allows truthful ideas pass through while blocking untruthful or flawed ideas.

Question 2

Arguments

Answer 2

In the philosophical sense, an argument is a sequence of 1 or more premises (statements) that rationally support or lead to a conclusion.

Philosophers can also use the conclusions from a series of smaller arguments as premises to prove an even bigger point.

Question 3

Types of Reasoning and Argumentation

Answer 3

There are 2 main types of reasoning and arguments. These are Deductive and Inductive reasoning and arguments.

These both lead to logical conclusions, however, they arrive at the conclusions in different ways and the types of logical conclusion drawn by one type of reasoning might not be available using the other type.

Question 4

Deductive arguments

Answer 4

Deductive arguments start with general statements and end with a specific, inevitable conclusion. If the premises logically support the conclusion, the argument is deemed “valid” (though not necessarily correct if the premises are false). When a deductive argument is both logically valid and factually true, it’s termed “sound.” Syllogisms serve as prime illustrations of deductive reasoning.

Question 5

Inductive arguments

Answer 5

Inductive arguments use specific premises to move towards general conclusions (ie. The opposite of deductive arguments)

Unlike deductive arguments, an inductive argument might have numerous possible logical conclusions.

There are several different methods of inductive reasoning. 2 examples are Enumerative Induction and Inference to the best explanation.

Question 6

Enumerative Induction

Answer 6

This type of reasoning looks at a lot of information and makes a reasonable guess based on the patterns noticed. (general conclusion based on specific instances or observations)

For example, if I cut open 1000 peaches and find each has a pit, I might guess that all peaches have pits. Each peach I check gives a specific piece of information (like Peach #1 has a pit, Peach #2 has a pit, and so on), but my conclusion is a generalization about all peaches. While it’s likely that all peaches have pits, it’s not absolutely guaranteed, unlike in deductive reasoning.

Question 7

Inference to the Best Explanation

Answer 7

This method looks at various pieces of information to come up with the most probable explanation for something, based on what’s known. It doesn’t give a conclusion that’s absolutely certain, but uses logic to suggest the most likely cause.

For instance, if I find my garbage can overturned with bags ripped open and garbage scattered, and I know raccoons live under my deck, find raccoon fur and tracks nearby, and know raccoons often eat garbage, then I can reasonably conclude a raccoon got into my garbage. While other explanations are possible, based on the evidence, raccoons are the most likely culprit.

Question 8

Syllogisms

Answer 8

The most common form of deductive argument is a syllogism.
There are 3 main types of syllogism: Categorical, Disjunctive and Hypothetical
Each category is named based on the types of proposition that the statements contain

Question 9

Categorical (Syllogisms)

Answer 9

statements about whether things belong to certain categories. Each syllogism includes a major premise, a minor premise, and a conclusion, with specific requirements for terms and their positions.

For example, in the syllogism “All humans are mortal; Socrates is a human; therefore, Socrates is mortal,” the terms “human,” “mortal,” and “Socrates” are positioned according to strict rules. These syllogisms follow a standard format: “All A are B; C is an A; therefore, C is a B.”

While a syllogism can be logically valid based on its structure, it can still be factually untrue if the premises are false, as demonstrated in the example where all humans are wrongly stated to be professional wrestlers.

Question 10

Disjunctive (Syllogisms)

Answer 10

In philosophical logic, “disjunctive” refers to a choice between alternatives. Disjunctive syllogisms begin with an either/or statement, presenting two possible options, one of which is usually negated in the minor premise. The conclusion then affirms the remaining option. For example, if the major premise states “Either Jane or Annette is a doctor,” and the minor premise states “Jane is not a doctor,” the conclusion follows that “Annette is a doctor.”

Question 11

Hypothetical (Syllogisms)

Answer 11

In philosophical logic, a hypothesis is a proposition suggested for reasoning, regardless of its eventual truth. Hypothetical syllogisms typically employ “If-then” statements, where at least one premise begins with “if.” For instance, if the premises are “If you study, you will do well on the test” (If A then B) and “If you do well on the test, your average will improve” (If B then C), the conclusion is “Therefore, if you study, your average will improve” (If A then C).