Philosophy
Immanuel Kant was born in 1724 in Königsberg.
- Logic And Language
Let me try to get to some of the logic and language questions today: Nick + Adam ask, "After a week of debate, we come to you with this question: Is there an example of an argument that one should believe that is inclusive of one or more premises that...
- Logical Fallacies Examples ? Appeal To Novelty And Age
As always let's begin with a simple definition. A logical fallacy is an error in reasoning which usually relies on a wrong assumption made in the argument. Appeal to emotion is one of the most popular types of logical fallacies ? examples of these...
- Propositional Logic - Using Truth Tables To Evaluate The Validity Of Complex Arguments
In our previous lesson on propositional logic, we learned that we can take arguments in natural language (English, Spanish, German, whatever) and translate them into symbolic form through the use of variables to represent statements, and connectives to...
- Peter Singer - Evolution Vs. Ethics
From its very inception, the theory of evolution by natural selection has been misinterpreted by social reformers of all kinds. Opponents argue that it endorses a psychopathic 'nature red in tooth and claw' approach to social problems. Proponents...
- Jon Stewart And The Glenn Beck Reductio Ad Absurdum
A reductio ad absurdum is an awesome and powerful logical tool in which you can either a) disprove the assumptions of a given argument by showing that its premises lead to a conclusion that contradicts one of the premises (proving that the original premise...
Philosophy
Valid arguments vs. sound arguments
Validity and soundness are one of the most important terms in logic. How to distinguish between deductively valid and invalid arguments as well as between sound and unsound arguments? The definition is very much straightforward and it is all that is needed to grasp the idea. However, this post will also give you a brief description of a few examples which will provide you with a more practical approach to the problem. And at the end of the post I will reveal to you a little secret which will turn this logical issue into a piece of cake!
Valid argument means an argument whose conclusion cannot be false if its premises are true. Consider the following example:
Immanuel Kant was born in 1724 in Königsberg.
In 1724 Königsberg was in Prussia.
Therefore, Immanuel Kant was born in Prussia.
The conclusion follows from the two premises so the argument is deductively valid. Provided the two premises are true (and by the way ? they are), the conclusion cannot possibly be false. Now consider the following argument:
Plato was born in Greece.
Everybody who is born in Greece have two heads.
Therefore, Plato had two heads.
Does the conclusion follow from the premises? It certainly does. Is it possible for the conclusion to be false when the premises are true? It is not. Therefore, the argument is valid. However, something seems to be wrong with the above argument ? obviously, its second premise is not true! This argument is unsound. The argument is sound only if all its premises are true and the argument is valid. Therefore, the argument about Plato is a deductively valid and unsound argument (the argument about Kant is both valid and sound). Now let?s deal with the last example:
Products containing sugar are sweet.
Bananas are sweet.
Therefore, it shouldn?t rain tomorrow.
You didn?t expect that conclusion, did you? Both premises are true but the conclusion does not follow from the argument?s premises. Undoubtedly, this argument is both invalid and unsound (although the premises are true, the conclusion is false).
Just in case you want to be sure that you are able to correctly classify arguments, here is the promised surprise ? a little diagram which will make the whole process much easier. And remember ? there are no false or true arguments ? arguments are either valid/invalid or sound/unsound. The argument may have true/false premises and conclusion but in logic terms true and false do not apply to arguments! Never!
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- Logic And Language
Let me try to get to some of the logic and language questions today: Nick + Adam ask, "After a week of debate, we come to you with this question: Is there an example of an argument that one should believe that is inclusive of one or more premises that...
- Logical Fallacies Examples ? Appeal To Novelty And Age
As always let's begin with a simple definition. A logical fallacy is an error in reasoning which usually relies on a wrong assumption made in the argument. Appeal to emotion is one of the most popular types of logical fallacies ? examples of these...
- Propositional Logic - Using Truth Tables To Evaluate The Validity Of Complex Arguments
In our previous lesson on propositional logic, we learned that we can take arguments in natural language (English, Spanish, German, whatever) and translate them into symbolic form through the use of variables to represent statements, and connectives to...
- Peter Singer - Evolution Vs. Ethics
From its very inception, the theory of evolution by natural selection has been misinterpreted by social reformers of all kinds. Opponents argue that it endorses a psychopathic 'nature red in tooth and claw' approach to social problems. Proponents...
- Jon Stewart And The Glenn Beck Reductio Ad Absurdum
A reductio ad absurdum is an awesome and powerful logical tool in which you can either a) disprove the assumptions of a given argument by showing that its premises lead to a conclusion that contradicts one of the premises (proving that the original premise...