I think therefore I am - Rene Descartes

REASON (logic) It has been said that man is a rational animal. All my life I have been searching for evidence which could support this. Bertrand Russell (1950)

In a very general sense, reasoning is a collective endeavor by which people construct meaning together by exchanging, modifying and improving their ideas and opinions. When someone makes a claim to know, it is legitimate to ask for reasons and to expect that these will be coherent. Arguments require consistency.

Reason is perhaps as present in everyday decision making and problem solving as it is in mathematics, sciences and other areas of knowledge. The requirements of logical validity and rigor serve these various purposes.

In different degrees and in different ways, it is arguable that reason has its place in many, if not all, areas of knowledge as well as in the everyday experience of individuals and the groups to which we belong. It may be worth considering how reason is used in these different domains * to discover and create, * to articulate, * to justify and * assess knowledge claims. For when disputes arise, what is at issue is not only the substance or facts of the matter, but also the appropriateness of the reasons given for acceptance of the facts, and the validity of the logical procedures used in reaching the conclusion.

$29 Three people check into a hotel. They pay $30 to the manager and go to their room. The manager finds out that the room rate is $25 and gives $5 to the bellboy to return. On the way to the room the bellboy reasons that $5 would be difficult to share among three people so he pockets $2 and gives $1 to each person. Now each person paid $10 and got back $1. So they paid $9 each, totalling $27. The bellboy has $2, totalling $29. Where is the remaining dollar?

Answer Each person paid $ 9, totaling $ 27. The manager has $ 25 and the bellboy $ 2. The bellboys $ 2 should be added to the managers $ 25 or subtracted from the tenants $ 27, not added to the tenants $ 2

Three kinds of reasoning Deductive reasoningDeductive reasoning Inductive reasoningInductive reasoning Informal reasoningInformal reasoning

DEDUCTIVE REASONING Moves from the general to the particular. Eg: All dogs are mammals Fido is a dog Therefore Fido is a mammal

Syllogisms: The above kind of deductive argument is known as syllogism. A syllogism consists of 1.Two premises and a conclusion 2.Three terms, each of which occurs twice (‘dogs’, ‘mammals’ and Fido) 3.Quantifiers, such as ‘all’, or ‘some’ or ‘no’, which tell us the quantity that is being referred to.

Truth and Validity Truth is concerned with what is the case, validity with whether conclusions follow from premises. Truth is a property of statements, validity of arguments. To avoid confusion, you should not say that an argument is true or false, but rather that it is valid or invalid. More formally, we can say that an argument is valid if the conclusion follows logically – i.e, necessarily – from the premises. And it is invalid if the conclusion does not follow logically from the premises

The main point to grasp is that the validity of an argument is independent of the truth or falsity of the premises it contains. Eg. All panthers are pink. Che Guevara is a panther. Therefore Che Guevara is pink.

Both premises and the conclusion of the argument are false, but the argument itself is valid.

All ostriches are teachers. Richard is an ostrich. Therefore Richard is a teacher. We can construct valid arguments for almost any combination of true and false premises and conclusions. The only situation that is impossible is a valid argument with true premises and false conclusions.

Inductive reasoning From particular to the general. Eg: Metal A expands when heated Metal B expands when heated Metal C expands when heated Therefore all metals expand when heated.

Terms to know Premises Assumptions Conclusions Truth (content) Validity (process) Syllogism Deductive vs Inductive reasoning