Let me start with the inference then we will come back to valid argument. What is an inference? An inference is formed from some presuppositions and a conclusion. For example,
(1)
Every man will die.
John is a man.
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John will die.
(1) is a classical instance of inference. "Every man will die." and "John is a man." are our presuppositions in (1), and "John will die." is our conclusion. Furthermore, if we need a more complex argument than (1), we must build up an argument chain, which is composed of more than one inference, and in other words, building up two arguments will required more presuppositions and result in two or more conclusions. As (2),
(2)
Every human will die.
John is a human.
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John will die.
John's wife is a human.
Martina is John's wife.
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Martina will die.
.
.
.
and so on.
In this manner we had roughly explained the inference, and it is time to concern valid argument, which is an argument comprises some true presuppositions and a necessarily true conclusion. However, true presuppositions would not guarantee a valid argument definitely valid, and the true presuppositions are not absolutely effective to build up a valid argument. That is to say ,we say the validity of an argument does not mean the truth of an argument. Therefore, valid argument does not mean the presuppositions must be true.
The end, valid argument is very useful to philosophy. It is pertinent to say that philosophers are good at using valid argument and it has become a widely fact.
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