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What is the difference between valid and sound argument?

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A valid argument is an argument whose conclusion follows logically from the truth of the premises. It is impossible for the premises to be true and the conclusion false. An example of a valid argument is:

1. If Thales was right, then everything is made of water.
2. It's not the case that everything was made of water.
3. So, Thales wasn't right.

This argument has the form: If P then Q, ~Q, therefore ~P. The conclusion is derived using Modus Tollens. All of the premises are true, and so is the conclusion.

However, the validity of an argument does not entail the truth of its conclusion. Consider another example of a valid argument:

1. If Socrates was a Philosopher, then Socrates was a happy alligator.
2. Socrates was a Philosopher.
3. So, Socrates was a happy alligator.

This argument is valid: it is of the form If P then Q, P, therefore Q. The conclusion is derived using Modus Ponens (a rule for logical inference which preserves truth).

However, the conclusion is false. Because it is valid, one of the premises must also be false: and, we can see, premise 1 is the culprit. If we replace it with a better premise, such as "If Socrates was a Philosopher, then Socrates existed", we derive a different and true conclusion (that Socrates existed).

A sound argument is an argument with two features: (i) it is valid, and (ii) its premises are all true.

It is not clear whether we ought to include other features, like non-circularity, in the necessary conditions for soundness; convention has yet to determine it.
In my opinion, a valid argument is any argument that opens a dialogue (without anger of course) where the opposing side can see and understand your side and may actually cause doubt as to whether they were right at all.

Opposing argument:
Arguments begin with a premise or premises and end with a conclusion. Take the argument above, here we have a premise that states a valid argument is one that opens a dialog, qualifying that opening as non emotional, and concludes that by opening with a non emotional argument of non specified nature the opposing side will understand the correctness of this argument and thereby have doubt about its own argument. Of course, since the premise is far too vague to even lead to a conclusion, there is no doubt by the opposition that another definition is required to effectively explain what a valid argument is.

In order to have a valid argument, the truth of the conclusion must be a logical consequence of the premise. Take this argument, for example, that has declared the original argument not valid as a valid argument because the truth of the conclusion quite clearly is not a logical consequence of its premise. That would be the premise. Now this argument will lead to a logical conclusion proving that the above argument was not valid. The above argument may be a deductive argument that has, in that contributors opinion, deduced that the conclusion of that argument is a logical consequence of the premise. Or it may be a inductive argument that claims the conclusion is supported by the premises and if a deductive argument the above argument may or may not be valid or may or may not be sound. In this case, the above argument is neither valid nor sound.

The only kind of argument that can logically be called a valid argument is one where the the truth of the conclusion is actually a logical consequence of the premise or premises and its corresponding conditional is necessarily true. An argument then, can only be valid if the negation of the corresponding conditional is a contradiction. For example:

It is either good or bad

It is not good

Therefore it is bad.

In its application we can test if an argument is valid or not by translating the premise and conclusion into sentential or predicate logic sentences. Then constructing from these the negation from the corresponding conditional and finally see if from this a contradiction can be obtained. Or a truth table if feasible can be used to test if the premises come out false in every row. This truth table usually relies upon Boolean functions in terms of true or false. Then alternately construct a truth tree to test if all the branches are closed. If successful this proves the validity of the original argument.

In attempting to test the original argument we find that argument is lacking in sufficient premises to test it. We could break the premises down to this:

In his opinion any argument is a valid argument

Any argument that opens a dialog with out anger

An argument that allows the opposing side to see his argument

The opposing argument then doubts their own reasoning.

Broken down this way, the premises do not lead to a logical conclusion. If any argument is a valid argument then the opposing argument would be valid as well. Let's try breaking it down this way.

Any argument is a valid argument that opens a dialog

Without anger, where the opposing side can see that argument

Thus, or possibly causing doubt in the opposing arguments reasoning.

Of course, if the original premise is true then there is no point in arguing as any opposition by definition is non valid since it did not open the dialog. However, the conclusion is a logical consequence of the original premise. It is the second premise that makes no sense if the original premise is true, because no opening argument need be made in order for an opposing argument to see that it is an opening argument and by definition the only valid argument made. Thus, the premise must original premise must be false, but the second premise is clearly true leaving the conclusion in a state of illogic.

The original argument really can not be broken down by any truth table or truth tree. It is merely an opinion offered for lack of a better explanation. In any argument, if the one making the argument assumes the game is to prove the other person wrong, then the game is lost. Arguments should only be used to derive a truth or truths. When this is understood, those making arguments are never wrong. The premise itself may be either true or false but never wrong. May be valid or not, sound or not sound but never wrong. Since the original argument was offered as merely an opinion it is of course, not wrong. It his however, not a valid argument.
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