Table of contents | |
Introduction | |
Identifying Arguments | |
Arguments - Types of Reasoning | |
Validity | |
Soundness | |
Inductive Reasoning | |
Good Arguments |
Signal words in text help indicate arguments. For instance, the word "because" signals that a premise or reason is being provided to support a claim.
Examples of words and phrases that may signal a premise include as, due to, as indicated by, for the reason that, owing to, through, in the view of, and as a result of.
The word "therefore" and its synonyms are clues that a conclusion or claim is being made. Other words that signal a conclusion include accordingly, consequently, infer that, hence, prove that, and conclude that.
For instance, consider the argument "The internet is a good invention." This claim can be supported with reasons like "It is a source of endless information" and "It is a hub of entertainment." Finally, a conclusion wraps up the argument.
Deductive reasoning is a logical process where a conclusion is drawn from a set of premises with certainty. It involves starting with general statements and applying them to specific instances. Let's explore this concept further.
In deductive reasoning, the conclusion is a necessary outcome of the premises. For example, consider the following premises:
Premise 1: All humans are mortal.
Premise 2: I am a human.
Conclusion: Therefore, I am mortal.
In this example, the conclusion is logically derived from the premises. Deductive reasoning can involve multiple premises, and there is no strict limit to the number of premises that can be used to reach a conclusion. For instance, instead of just "I," we could have "you," "he," "she," and so on, making the premises more specific.
Deductive reasoning is often considered more scientific and is associated with formal logic, which is the "science of deduction." It is deterministic, meaning that the conclusion follows necessarily from the premises without exception.
Deductive inference can be further categorized into immediate and mediate reasoning:
Immediate Reasoning: This involves drawing a conclusion from a single statement.
Mediate Reasoning: This involves drawing a conclusion from two statements, known as syllogism. Syllogism will be discussed in more detail later.
Deductive reasoning is akin to analysis, where a whole is separated into its constituent elements. It is a systematic and rigorous approach to drawing conclusions based on established premises. Deductive Reasoning vs Inductive Reasoning
Validity refers to the logical strength of deductive arguments, indicating how well the premises support the conclusion. A deductive argument is considered valid when, if all its premises are true, the conclusion must also be true by necessity.
Consider the following argument:
This argument is valid because if the premises were true, the conclusion would necessarily follow. Validity is determined by the form of the argument, not the truth of the premises.
Valid Arguments Can Have
However, valid arguments can never have true premises and a false conclusion. In a valid deductive argument, if the premises are true, the conclusion cannot be false.
Example of Invalid Argument
Consider the following argument:
In this case, the premises are true, and the conclusion is also true, but the reasoning from the premises to the conclusion is not valid. The conclusion does not necessarily follow from the premises, making the argument invalid.
Soundness in deductive arguments refers to the combination of valid reasoning and true premises. A deductive argument is considered sound when it meets two criteria:
Consider the following argument:
This argument is sound because:
It is important to note that while all sound arguments are valid, not all valid arguments are sound. Validity only considers the logical structure of the argument, while soundness takes into account the truth of the premises as well.
For instance, the earlier example with dogs, dragons, and birds is valid because the form of the argument is correct. However, it is not sound because the premises are not true.
Inductive reasoning is a method of reasoning that involves drawing general conclusions from specific observations or instances. It is often used in the fields of informal logic and critical thinking, particularly in social sciences.
Inductive strength refers to the strength of an inductive argument. An argument is inductively strong if, assuming the premises are true, the conclusion is likely to be true as well.
To assess whether an inductive argument is strong or weak, follow these steps:
Example of Inductive Strength:
In this example, the argument is inductively strong because if the premises are true, the conclusion is highly likely to be true as well.
In summary, a strong inductive argument makes it unlikely for the conclusion to be false if the premises are true. Conversely, a weak inductive argument suggests that the conclusion is unlikely to follow from the premises, assuming they are true.
Cogency refers to the quality of an inductive argument based on the truth of its premises and its logical strength. An inductive argument is considered cogent when it meets the following criteria:
In this example, the argument is cogent because:
On the other hand, an argument may demonstrate inductive strength without being cogent if it lacks true premises. For instance, the peacock example used earlier is not cogent because it does not have all true premises.
In summary, an inductive argument is cogent when it is improbable for the conclusion to be false given the truth of the premises. Cogency combines the strength of the argument with the truth of its premises to establish a compelling case.
The key takeaway regarding the attributes of deductive and inductive arguments is that a good argument proves its conclusion and possesses two essential features:
Logical strength refers to the level of support that the premises, if true, provide for the conclusion. This characteristic is relevant to both deductive arguments (through validity) and inductive arguments (through inductive strength).
For example, consider David Hume's question, "Will the Sun rise tomorrow?" While the laws of nature suggest it will, there is still uncertainty about the future.
Let's explore examples of deductive and inductive arguments:
Logical reasoning is a fundamental aspect of human thought, but humans are not always purely logical reasoners. The deductive method leads to definitive accept or reject decisions, while the inductive method results in tentative conclusions that may seem subjective. Inductive and deductive theorizing are complementary stages in constructing any theory, with induction preceding deduction.
According to Aristotle, the distinction between deductive and inductive arguments lies not in the words used but in the intentions of the arguer. If the intentions of the arguer are unknown, both aspects are assessed. This involves evaluating whether the argument is deductively valid and inductively strong.
Syllogism, based on propositions, can be categorized into four types:
Categorical Syllogism focuses on categorical relationships. There are exactly 256 distinct forms of categorical syllogism, derived from:
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1. What is the definition of an argument in logic? |
2. What are the main forms of an argument? |
3. What is a categorical proposition and how is it structured? |
4. What are the properties of a categorical proposition? |
5. What is a categorical syllogism, and how does it relate to the classical square of opposition? |
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