Logic: how do you analyse the structure of deductive arguments? - Chapter 3

Frustration often plays a role in discussions with others. This frustration comes from two sources. First of all, when confronted with an argument, it is often difficult to keep this clearly in mind. To counter this, argument reconstruction is important. Secondly, it is often difficult to state what exactly is wrong about another's argument. Techniques and conception with regard to argument assessment are important for this. The argument assessment is first discussed below.

The charity principle

An argument consists of a set of propositions, or premises. However, these premises are not always explicitly stated. That is why the first step in evaluating an argument is clarifying and supplementing the literal words of the speaker / writer. Reconstructing an argument is largely a matter of interpretation, but with the charity principle we can still do this in a systematic and conscious way. The charity principle firstly includes the context and circumstances in which someone says something. Together with the actual words that the speaker / writer uses, the context and circumstances form the basis for assessing an argument. If we want to find out the truth (and not just win the discussion), we must always choose the best reconstruction of the argument. If you show that something is a bad argument, that does not mean that the conclusion is not correct. However, if you show that something is a good argument, you will learn something about the correctness of the conclusion. Hence the charity principle. However, this principle has limits; the only evidence you can rely on is the context, circumstances and words of your discussion partner. If you start thinking too much about what that person might mean, there is a chance that you will insert new arguments yourself. If you only want to reconstruct the other's argument, that is not very handy. If your goal is to get closer to the truth, however, this may be the right approach.

Truth

Truth should not be confused with the beliefs (beliefs) that someone has. When person A says, "fish live in the water", he means that he believes that fish live in the water. If person B says, "that's true," this person means he believes that too. Whether it is true that fish live in water does not, however, have to do with whether people believe it or not. The truthfulness of a statement says something about whether a statement is true or not. In the formal study of logic, it is important that a proposition cannot be both true and false at the same time.

Deductive validity

Deductive validity is the derivation of a specific statement by making assumptions. An example of this is:

P1) The president's dog is infected with fleas

P2) All fleas are bacteria.

C) The president's dog is infected with bacteria.

That such a reason is valid does not necessarily mean that the conclusion is true . If the reasoning is correct while one of the premises is incorrect, the reasoning is valid, but not true. Validity is therefore about the connection (inference) between the premises and the conclusion, not about the truth content. However, if the premises are all true, the conclusion is necessarily true. If it is not, then the reasoning must be invalid. Logic is therefore about constructing perfectly reliable procedures to detect validity, or the lack thereof.

Prescriptive claims versus descriptive claims

Descriptive claims are claims that only describe the facts (The cat is lying on the mat). Prescriptive claims are claims that say how things should be based on, for example, wishes, values, norms or moral rules (You must ensure that the cat is on the mat)

Conditional propositions

Conditional sentences are often expressed in the if-then form (for example: if it rains, then it is cloudy). You have different forms of conditional sentences:

1. If not .. then not ..

If P is Q, then also applies:

If not P, then not Q.

2. Or .. Or ...

This form can be used inclusive , where applies; or P is true, or Q is true, or they are both true. This form can also be used exclusively , whereby; or P is true, or Q is true, but not both. For both exclusive and inclusive, both P and Q cannot be false.

3. Only if ...

Hereby it applies that if P, then Q, but the other way around it does not. For example, if you say: It only rains when it is cloudy, you cannot say: it is only cloudy when it rains. This should not be confused with 'if and only if'. For example, if you say: "Sarah only comes to the party when Joop comes too," it is possible that Sarah will not go to the party when Joop goes. However, if you say that Sarah comes if and only if Joop comes, it means that if Joop comes to the party, Sarah will come anyway.

4. Unless ..

It is easiest to see 'unless' as equal to 'if not'. For example: "I don't make the bus unless I run" is the same as "I don't make the bus if I don't run".

The antecedent and consistent of a conditional sentence

The relationship between two parts in a conditional sentence can be represented in the form of an arrow, for example: It's raining à It's cloudy. The part where the arrow comes from is called the antecedent and the part where the arrow goes is called the consistent .

A conditional sentence does not necessarily have to be an argument. If you say, "If it rains, it is cloudy", is not the same as saying that it rains. In argument form this would be: It's raining, so it's cloudy. This is sometimes confusing because in everyday language a conditional sentence often implies that the antecedent is actually true. Arguments can, however, have a conditional sentence as a conclusion.

Argument trees

An argument tree is a tool that is used to present arguments in diagram form. The claims and premises are represented by Cs and Ps in circles, with an arrow going to C1 from P1 and P2, and an arrow to C2 from C1 and P3. If a C can be derived independently from P1 and P2, a separate arrow goes to both from P's. If C can only be derived in combination from, for example, P1 and P2 or P3 and C1, a joint arrow goes to C2. See p. 84-85 of the book for examples of an argument tree.

Deductive accuracy

A deductively correct argument means that an argument is valid and that all premises are true. In result,  that it is not possible for two opposing points of view to have a deductive argument, because that would mean that two opposing conclusions are both true. If an argument is deductively incorrect, it means that the argument contains either an incorrect premise, that the conclusion is invalid, or both.

The connection with formal logic

There are several valid argument schemes, the argument being valid regardless of the content (so it says nothing about the truth content):

1. Modus ponens :

P1) If P, then Q.

P2) P.

C) Q.

2. Modus tollens:

P1) If P then Q.

P2) not-Q.

C) not-P.

3. Disjunctive syllogism:

P1) P or Q.

P2) not-P.

C) Q.

In addition, formal logic uses surrogate characters instead of the logical language expressions:

Brackets are also used to distinguish arguments: for example, P (Q v R) means that if P is true, or Q or R is true, and (PQ) v R that is, or “If P, then Q” is true, or R is true. However, certain logical words are often used, such as "all". The use of surrogate signs is sometimes more convenient than the linguistic constructions that we use in everyday language, because in formal logic there is only one way to express a certain argument.