In logical reasoning, arguments play a fundamental role in evaluating the validity and soundness of an argument presented in a statement or passage. An argument is a set of statements, where one statement (conclusion) is supported by one or more other statements (premises). It is important to understand the structure of arguments to assess their logical coherence and validity. In logical reasoning, the structure of an argument consists of three parts: conclusions, premises, and assumptions. The conclusion is the main idea, the premises provide supporting evidence, and the assumptions are the underlying supporting elements.
- premises: Premise are statements that are provided as evidence or reason to support a conclusion. They are the basis on which the conclusion is made. The premises are considered true in the context of the argument.
- conclusion: The conclusion is the main statement that the argument aims to establish or prove. This is the claim that the compound is meant to support. The conclusion is what the arguer wants the audience to accept based on the given premises.
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meaning of logic
The structure of a logical argument is based on a collection of statements, known as premises, from which a logical conclusion is drawn. The conclusion is supported by the premises. Thus, an argument consists of both premises and the conclusion drawn from them.
For example:
premises,
- All humans are mortal.
- Socrates is a man.
conclusion:
In the given scenario, the first two statements are referred to as premises, and the last statement is identified as the conclusion. When taken together, these statements form an argument. The standard structure of the argument follows a sequence of premise 1, followed by premise 2, and ending with a derived conclusion.
form of argument
The structure of argument can be further divided into three categories, namely deductive, inductive and abductive.
deductive reasoning:
- Deductive reasoning is a type of reasoning where the conclusion logically follows from the premises.
- Its purpose is to provide conclusive evidence or proof for the truth of the conclusion.
- In deductive reasoning, if the premises are true, the conclusion must also be true.
- Deductive arguments are characterized by their validity, meaning that the conclusion necessarily follows from the premises.
Here is an example:
- Premise 1: All mammals are warm-blooded animals.
- Premise 2: The whale is a mammal.
- Conclusion: Therefore, whale is a warm-blooded animal. In this deductive reasoning, if we accept the truth of the premises, then the conclusion must also be true.
inductive reasoning
- Inductive reasoning is a type of reasoning where the conclusion is based on observed patterns, trends, or evidence.
- Its purpose is to establish the probable or probable truth of the conclusion.
- Unlike deductive reasoning, inductive reasoning does not provide absolute certainty. Instead, they rely on the strength of the evidence to support the conclusion.
Here is an example:
- Premise 1: Every cat I have seen has hair.
- Premise 2: Therefore, all cats have hair.
- In this inductive reasoning, the conclusion is based on observed examples, but does not guarantee that every cat in existence has fur. The conclusion is likely, but it is possible that there may be exceptions.
Abductive reasoning (or hypothetico-deductive reasoning):
- Abductive reasoning is a form of inference that involves generating the best possible explanation for a given observation or set of evidence.
- It seeks to identify the most plausible hypothesis taking into account the facts.
- Abductive reasoning often follows a pattern known as the hypothetico-deductive method, which involves proposing a hypothesis and then making predictions based on that hypothesis.
- These predictions are then tested to evaluate the validity of the hypothesis.
Here is an example:
- Observation: The ground is wet.
- Hypothesis: It rained last night.
- Prediction: If it rains tomorrow night there will be potholes on the roads.
meaning of categorical proposition
Categorical propositions express relationships between categories linked by “is” or “is not” using a subject and a predicate. They have four standard forms:
- “All S are P”
- “No S is P”
- “Some S are P,”
- “Some S are not P.”
Structure of hierarchical proposal
The structure of a categorical proposition has four elements: subject word, predicate word, copula, and quantifier. These components can be described as follows:
- Subject word: It refers to the first category or category mentioned in the proposal.
- Predicate term: It represents the second class or category mentioned in the proposal.
- Copula: It is a verb that joins or joins the subject and predicate words.
- Quantifiers: These are used to quantify or specify subject and predicate words.
For example, let’s consider the proposition “All cats are mammals.” In this proposal, the subject word is “cats”, the predicate word is “mammals”, the copula is “are”, and the quantifier is “all”.
Properties of Categorical Proposals:
The properties of categorical proposition can be understood through the following explanation:
- Quantity: The quantity property of a categorical statement is determined by the quantifiers used, such as “all,” “some,” “not,” etc. It indicates the extent to which the subject class is included in the predicate class. The quantity can be either positive or negative.
- Quality: The quality of a proposal is determined by whether it claims or denies overlap between classes. It can be positive or negative.
- Affirmative: A positive proposition is one that claims or affirms overlap between classes.
- Negative: A negative proposal is one that denies overlap between classes.
- Distributed: A proposition is said to be distributed when it refers to the entire class.
- Undistributed: A proposition is considered undistributed when it refers only to a class or part of a class rather than the entire class.
Types of hierarchical proposal
Categorical proposals can be classified into four types, which are described as follows:
Universal Affirmative (denoted by A):
- This type of proposal considers the entire class and confirms the overlap of the classes. It states that every element of the subject class is also a member of the predicate class.
- The structure of this proposition is “All S are P”, where S represents the subject and P represents the predicate.
- For example, all cats are mammals.
Universal negative (denoted by e):
- This type of proposal considers the entire class but denies overlap of classes.
- It states that no member of the subject class is part of the predicate class. The structure of this proposition is “No S is P”.
- For example, no cats are dogs.
Special Positive (denoted by I):
- This type of proposal focuses on a section or subgroup of the class rather than the entire class, but still confirms the overlap of the classes.
- It states without specifying the entire subject class that some members of the subject class are part of the predicate class.
- The structure of this proposition is “Some S are P.”
- For example, some dogs are black.
Special Negative (represented by O):
- This type of proposal also focuses on a segment or subgroup of the class, rather than the entire class, but denies overlap of classes.
- It states that some members of the subject class are not part of the predicate class.
- The structure of this proposition is “Some S is not P.”
- For example, some cats are not black.
categorical syllogism
Categorical syllogism is a logical argument consisting of three categorical propositions that form two premises and a conclusion. Every proposition has a subject, a predicate, and a conjunction connecting them. Here is a brief explanation of categorical syllogism with an example:
A hierarchical syllogism follows the structure:
- Major Premise: It states the relationship between the major term (predicate) and the middle term (common term) in the conclusion.
- Minor Complex: It states the relationship between the minor term (subject) and the middle term in the conclusion.
- Conclusion: It logically traces the relationship between the major term and the minor term.
Example of categorical syllogism:
- Major premise: All humans are mortal. (All S are P)
- Short premise: All philosophers are human beings. (All M are S)
- Conclusion: Therefore, all philosophers are mortal. (All M are P)
In this example, the major word is “mortal”, the minor word is “philosopher”, and the middle word is “man”. The major premise establishes the relationship between “human beings” and “mortals”, while the minor premise establishes the relationship between “philosophers” and “human beings”. Based on these grounds, the conclusion is that “philosophers” are also “mortal”.
classical class of opposition
A class of opposition is a logical conclusion drawn from propositions that share the same terms but differ in terms of quality and quantity. Proposals in formal opposition must have the same conditions. The class of contradiction reveals the logical inferences that can be made from one type of proposition (A, E, I, or O) to another type of proposition. There are four types of relationships depicted in the category of opposition, which are explained in detail below:
Contradictory:
- Contradictory relations exist between A and O propositions as well as between E and I propositions.
- These relationships involve offers that vary in both quality and quantity. If one proposition is true, the other is obviously false.
- For example: A – All dogs are mammals. O – Some dogs are not mammals. If A is true, then O cannot be true, and the same applies to the relation between the propositions E and I.
Subaltern:
- Subaltern relations exist between proposals that have the same quality but differ in quantity.
- This means that the truth of propositions goes from A to I and from E to O, but not vice versa.
- Falsification of proposition goes from I to A and O to E.
- For example: A – All dogs are mammals. I – Some dogs are mammals. If A is true, then I is also true, and similarly, if E is true, then O is also true. If I is false, then A is also false, and if O is false, then E is also false.
Adverse:
- Paradoxes are propositions that contradict each other.
- They have the same quantity but differ in quality, and both are universal in quantity. If one is true, the other must be false, so they cannot both be true.
- However, when one is false, the truth value of the other proposition remains uncertain.
- For example: A – All dogs are mammals. E – No dog is a mammal. If A is true, then E is false, but if A is false, then the truth status of E is indeterminate.
Sub-contrast:
- Subcontrastive relations exist between propositions that differ in quality but have the same quantity.
- This relation occurs between particular affirmative and particular negative propositions. If one is false, the other must be true, so they cannot both be false.
- However, when one is true, the truth value of the other proposition remains uncertain.
- For example: I – Some dogs are mammals. O – Some dogs are not mammals. If I is false, then O is true, but if I is true, then the truth state of O is indeterminate.
The classical class of contradictions helps in understanding logical relations and drawing conclusions based on clear propositions. It helps in assessing the validity of arguments and drawing conclusions.
Structure of Arguments Download Study Notes PDF
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