Argument

An argument is composed a sequence of multiple 202204281244#. The last sequence of it is the conclusion of the argument. All previous statements are called premises, assumptions or hypotheses. For an argument to be valid, both conclusion and premises must be valid in form and #logically sound.

To test the validity of an argument, follow the procedure below:

  • Identify the premises and conclusion of the argument
  • Construct a 202205061151# showing all the truth values of them.
  • Verify that the truth values for conclusion for every critical row are all true.

Critical row means a row of truth table which all the premises are true. If the conclusion is true in every critical row, then we can say that the argument is valid. However, if it is false in one of the critical rows, then the conclusion is false, which implies the argument is invalid#.

There are various form of arguments that is valid which they are called the rules of inference. They are shown as below:

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  • Universal Statement

    To disprove this, one could use counterexample, to show that at least one \(x\) in the set of \(H\) is false. To prove that the statement is true, one could not avoid proving that all of them are true, which is called the method of exhaustion. You can see the difference between it and 202204281254.

  • Transitivity

    Transitivity is a valid #202205062050 form where if A implies B and B implies C, A must implies C. Its form is shown as below:

  • Syllogism

    Syllogism is a valid #202205062050 form which consists of two premises and a conclusion. The first premise is referred as major premise whereas the second premise is called minor premise.

  • Specialisation

    Specialisation is a valid form of #202205062050 which we can deduce a premise to a narrower context. The form is shown below:

  • Proof by Division into Cases

    Proof by Division into Cases is a valid form of #202205062050. As the name suggests, the proof can be done if we exhausted all possible cases and all of them come up with the same 202204281244. This will be shown below:

  • Modus Tollens

    We can prove the validity of it by contradiction. Suppose we are analysing the following #202205062050:

  • Modus Ponens

    It can be proved to be valid by examining its #critical row using 202205061151.

  • Logical Fallacy

    #Logical Fallacy happen when a reasoning resulted in an invalid #202205062050. It is an error in logic.

  • Logic

    Logic does not determine the truth or falsify of 202205061208#. It helps only link the separate pieces of information into a coherent whole. This means that in an 202205062050#, the conclusion could be true regardless of the content of the premises. If the reasoning resulted in a invalid argument, it is called a 202206172053#.

  • Generalisation

    Generalisation is a valid form of #202205062050 where we can deduce a premise to a wider context. It has the following form:

  • Existential Statement

    To prove this, one can just show that at least one \(p\) in the set of \(P\) is true. To prove that the statement is wrong, one could not avoid proving that all of them are false, which is called the method of exhaustion. You can see the difference between it and 202204281245.

  • Elimination

    Elimination is a valid form of #202205062050 where one must be the case when the other has been ruled out. It includes two premises and a conclusion (similar to 202206101739), shown in the following:

  • Contradiction Rule

    Contradiction Rule is a valid #Argument which states that if \(p\) is false leads to a contradiction, then \(p\) must be true. This is shown as below:

  • Conjunction

    Conjunction is a valid #202205062050, stated that if a statement is true, and another statement is true, then the conjunction of them (which is an and statement) is also true.

#logic #philosophy