Question #166718

Determine whether the following argument is *formally valid*. If not, present an argument that follows the same pattern, but has (i) all true premises and (ii) a false conclusion.

If all cats are female, then some dogs are male.

Not all cats are female.

So, not all dogs are male

Expert's answer

**Discussion**

Determine whether the following argument is *formally valid*. If not, present an argument that follows the same pattern, but has (i) all true premises and (ii) a false conclusion.

v If all cats are female, then some dogs are male.

v Not all cats are female.

v So, not all dogs are male

In philosophy, such arguments require critical reasoning to find a valid answer. It requires an individual to carefully examine the presented argument and decide whether it is true or not. As much as one can tell that something is factually correct or wrong, in philosophy, it might be wrong or right, respectively. Being factually correct does not mean that a statement is valid or invalid. It requires critical reasoning and thinking to determine the true premises and false conclusions or vice versa. Below is an analysis of the argument presented above;

A deductive argument is said to be valid if it takes a form that is impossible to either be true or the conclusion is false. In this case, the first step is to determine the conclusion. ‘*Not all dogs are male’* is the conclusion, and it is true that not all dogs are male. The argument is, therefore, an invalid argument. The validity of an argument is opposed to the content. When an argument is valid, it takes the validity form or the structure as opposed to the content. If the premises are not true, like the above statement, the argument can actually be true, (Sundt, 2014). The argument above has a false premise, so we can conclude that is not factually correct. Although if it had a true premise, then it would be factually correct.

When determining whether it true or not there are two areas to consider. The premises and the conclusion. The premises of an argument are the statement that provides support for the conclusion. For example, in the argument above, the premises are ‘all cats are female, some dogs are male, and not all cats are female’. These statements give more meaning to the argument. In this example it is best to start by approaching the sentences with the if and then’ premises. Suppose all cats are female, then some dongs are male. This means that if it's true that all cats are female, then it must be true that some dogs are male. Note that the premises do not have to be factually correct to be valid.

Using the Venn diagram, one would start with drawing a large circle representing cats that are all female and a smaller circle to represent the male dogs. It means if we say that the first argument on cats is true then the second premise on dogs is also true and vice versa. In this argument factually all cats are not female which is the indication of the second premise. The second premise is therefore a true premise, (Sundt, 2014). The conclusion that not all dogs are male is a true conclusion. The aim of the derivation is to show the validity or invalidity of a statement or argument.

**Reference**

Sundt, T. M. (2014). Sound arguments, true premises, and valid conclusions. *The Journal of thoracic and cardiovascular surgery*, *148*(5), 2070-2071.

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