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Statements and universality really come into play when you start creating arguments. An argument is not what we associate with the word in everyday life, a back-and-forth exchange of opinions. But instead, an argument is a presentation of a series of premises or statements that together form a conclusion. In its simplest form, the logical argument takes this shape. All cupcakes are baked goods. This dessert is a cupcake. Therefore, this dessert is a baked good.
Through logic, we can use two or more statements to create a new statement. Whether the new statement is true or false, depends on whether the premise statements are true. And whether the structure of our argument is logically valid. This is a classic argument known as a syllogism. It has a mathematical structure that looks like this. All A are B. C is an A. Therefore, C is a B. Knowing this, we can start judging the validity of arguments.
All cupcakes are baked goods. This dessert is a cupcake. Therefore, this dessert is a baked good. This is a true statement or logical conclusion, because it follows the syllogism structure. The premises are sound and structure is valid. If you flip the order of the premises, it becomes pretty obvious why. This dessert is a cupcake. All cupcakes are baked goods. Therefore, this dessert is a baked good. Now consider another argument. All cupcakes are desserts.
This donut is a desert. Therefore, this donut is a cupcake. This statement is not true, because the logical structure is incorrect. And the reason it is incorrect, is because we are making an inference from one particular to another. While both donuts and cupcakes belong in the dessert category, they are in separate subcategories that do not overlap. If we flip the order of the premises, you'll see just how ridiculous this statement really is. This donut is a dessert.
All cupcakes are desserts. Therefore, this donut is a cupcake. In this order, it's clear that donuts and cupcakes are two different groups of desserts that don't necessarily have anything else in common. This previous argument is untrue because it's logically invalid, but you can also make logically valid arguments that are untrue because the premises are untrue. All birds can fly. The penguin is a bird. Therefore, the penguin can fly. This argument is logically valid, but it's conclusion is false because the first premise; all birds can fly, is false.
It takes a property of the particular, flying and applies it to the universal. All birds. Bizarrely, this means you can get a factually accurate conclusion from this argument even though the first premise is false. All birds can fly. The eagle is a bird. Therefore, the eagle can fly. What we have here, is a false positive. This conclusion is true in spite of the false premise, because of a happy accident. Some birds can fly and the eagle falls into that subcategory.
Had the first premise been, all birds are made of cheese, the conclusion would be false in all cases. This syllogism is the most basic form of a logical argument and the simple example shows you just how powerful and how important logic is in communication. It also highlights a fundamental difference between humans and computers. A human will often accept a logically invalid argument based on fact as true, and will also often accept a logical conclusion from false premises.
Because she knows more about the situation, or is willing to extend her trust to the person presenting the argument. A computer on the other hand, will only accept logically valid arguments and will always find a logically invalid argument false, even if the conclusion is true. The human prioritizes context, the computer prioritizes formal structure. For now, we can conclude that knowing how to make logically valid arguments and understanding the value of factual statements, and universality.
Will help you, not only when speaking to people, but also when dealing with computers.
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