# 1.2 Defining a proof  (Page 2/5)

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 1 All griznoxes chorble happily. Premise 2 A floober is a type of griznox. Premise 3 Therefore, floobers chorble happily. Syllogism, lines 1,2

You don't need to be a world-class floober expert to evaluate this argument, either.

Lewis Carroll, a logician, has developed many whimsical examples of syllogisms and simple reasoning. (Relatedly,note how the social context of Carroll's examples demonstrates some feminist issues inteaching logic .)

As you've noticed, the form of the argument is the same in all these.If you are assured that the first two premises are true, then, without any true understanding,you (or a computer) can automatically come up with the conclusion. A syllogism is one example of a inference rule that is, a rule form that a computer can use to deduce new facts from known ones.

## Some non-proofs

Of course, not all arguments are valid proofs. Identifying invalid proofs is just as interesting as identifying valid ones.

```Homer: Ah, not a bear in sight. The Bear Patrol must be working. Lisa: That's specious reasoning, Dad. Homer: Thank you, honey.Lisa: By your logic, this rock keeps tigers away. Homer: Oh? How does it work?Lisa: It doesn't work. Homer: Uh-huh.Lisa: It's just a stupid rock. Homer: Uh-huh.Lisa: But I don't see any tigers around here, do you? [pause]Homer: Lisa, I want to buy your rock! [A moment's hesitationand money changes hands.]``` (From The Simpsons Much Apu About Nothing .)

If Lisa isn't around, who will identify specious reasoning for us? We can certainly use her approach of finding other particular examplesthat follow the same argument, yet lead to a clearly erroneous conclusion.

Suppose that my friend makes the following argument:

 1 Warm cola tastes bad. Premise 2 Warm salt-water tastes bad. Premise 3 Therefore, mixing them together tastes bad. Common-sense conclusion, lines 1,2
I'm skeptical, so I have a sip; sure enough, the conclusion is indeed true. But is the proof correctdoes thecommon-sense conclusionrule actually hold? In order to refute the form of the argument, we can trysimilar arguments which have the same form but a false conclusion (as Lisa did).
 1 Ice-cold coke tastes good. Premise 2 Ice coffee tastes good. Premise 3 Therefore, mixing them together tastes good. Common-sense conclusion, lines 1 and 2.
After another unfortunate sip, I verify that this conclusion is not true, and therefore my friend's reasoning is at fault.

My friend responds by claiming that thecommon-sense conclusionis too valid; the rule is that bad-taste is preserved upon mixing,not that any taste is preserved. While I'm inclined to believe that, we realize we can stilltest this more refined rule: can you come up with an instance of mixing together bad-tasting thingsand ever getting a yummy result? (Say, salt and flour, which can be mixed and baked to get delicious saltines!The argument continues, about whether the form of the argument precludes baking, and so on.)

The end result (after I take some antacid) is that we have a clearer understanding ofthe initially vaguecommon-sense conclusion, and stricter rules about when it applies.Thus, refining the argument has led us to a greater understanding.

what is Economics
the branch of knowledge concerned with the production, consumption, and transfer of wealth and has Influence by sociology!!!!
Ajay
Economics is the study of how humans make decisions when they want to fulfil their requirements and desires for goods, services and resources.
Abdullah
Economics is the study how humans make decisions in the faces of scarcity.
Rose
economic is the study of how human make decision in the fact of scarcity.
Toang
Economics is a social science which study human behavior as a relationship between earn and scarce mean which have alternative uses
Juliet
what is market structure
Fatima
what is demand
demand is the willingness to purchase something
Mohamed
demand is the potential ability or williness to purchases something at a particular price at a given period of time..
Ahmed
Demand refers to as quantities of a goods and services in which consumers are willing and able to purchase at a given period of time. Demand can also be defined as the desire backed by ability to purchase .
what is demand
is the production of goods in scarcity
David
thanks
John
Demand refers to as quantities of a goods and services in which consumers are willing and able to purchase at a given period of time.
what is demand of supply
What is the meaning of supply of labour
what is production?
Production is basically the creation of goods and services to satisfy human wants
Anthonia
under what condition will demand curve slope upward from left to right instead of normally sloping downward from left to right
how i can calculate elasticity?
What is real wages
what are the concept of cost
what is the difference between want and choice
Want is a desire to have something while choice is the ability to select or choose a perticular good or services you desire to have at a perticular point in time.
Dalton
substitutes and complements
Substitute are goods that can replace another good but complements goods that can be combined together
nkanyiso
account for persistent increase in lnflation
what is opportunity cost
opportunity cost reffered to as alternative foregone when choice is made
niwahereza
government measures to control inflation?
control populationk growth rate by using family planning to reduce faster increase of people than job creation
niwahereza
in a comparison of the stages of meiosis to the stage of mitosis, which stages are unique to meiosis and which stages have the same event in botg meiosis and mitosis
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