use the direct and the counterexample methods to show that these arguments are invalid? For the counterexample method, display the form used.
1. There could be lightening without thunder. So, there could be thunder without lightening.
2. Nothing its better than liberty. Prison life is better than nothing. Therefore prison life us better than liberty.
3. Saying that women earn less than men because women interrupt carers to gage children, work fewer hours, obtain fewer degrees in technical areas than men, and the like of course serves the interests of successful men in the workforce who do not want their own privileges to be challenged. So, those are not the real reason for women's reduced earnings.
4. If I would make any proposition whatsoever; than by that I would have a logical error. But I do not make proposition; therefore I am not in error.
Keep in mind that no one here will write your assignment for you. Please post what YOU THINK, and someone here will be happy to critique your thinking and writing.
To determine if an argument is invalid using the direct or counterexample method, we need to look at the logical structure of the argument and see if it follows a valid form.
1. There could be lightning without thunder. So, there could be thunder without lightning.
Direct Method: To show invalidity using the direct method, we need to find a scenario where the premises are true and the conclusion is false. In this case, we can imagine a situation where there is lightning without thunder, such as in a silent lightning storm. However, this does not necessarily mean that there could be thunder without lightning. Thunder is generally caused by the rapid expansion and contraction of air surrounding a lightning bolt, so it is unlikely to have thunder without lightning. Therefore, the conclusion does not logically follow from the premise, making the argument invalid.
2. Nothing is better than liberty. Prison life is better than nothing. Therefore, prison life is better than liberty.
Counterexample Method: To show invalidity using the counterexample method, we need to find a specific case where the premises are true, but the conclusion is false. In this argument, the first premise states that nothing is better than liberty. The second premise claims that prison life is better than nothing. However, this does not mean that prison life is better than liberty. It simply means that prison life may be better than having nothing at all. This argument fails to show that prison life is better than liberty in general. Therefore, the argument is invalid.
3. Saying that women earn less than men because women interrupt careers to raise children, work fewer hours, obtain fewer degrees in technical areas than men, and the like of course serves the interests of successful men in the workforce who do not want their own privileges to be challenged. So, those are not the real reasons for women's reduced earnings.
Counterexample Method: In this argument, the author claims that the reasons provided for women's reduced earnings (interruption of careers, working fewer hours, fewer technical degrees) are not the real reasons and that they serve the interests of successful men in the workforce. To show invalidity using the counterexample method, we need to find a specific case where the premises are true, but the conclusion is false. However, the argument does not provide any evidence or counterexamples to support the claim. Merely stating that the reasons are not real without providing counterexamples or supporting evidence is not enough to invalidate the argument. Therefore, the argument is not proven to be invalid based on the given information.
4. If I would make any proposition whatsoever, then by that I would have a logical error. But I do not make propositions; therefore, I am not in error.
Direct Method: To show invalidity using the direct method, we need to find a scenario where the premises are true and the conclusion is false. In this argument, the first premise states that if the speaker makes any proposition, it would result in a logical error. The second premise claims that the speaker does not make propositions, therefore concluding that the speaker is not in error. The argument follows a valid form known as modus tollens (if P then Q, not Q, therefore not P). Since the premises are true and the conclusion logically follows from them, the argument is valid.