Truth, Validity, and Soundness in Arguments

Truth, validity, and soundness are important concepts for evaluating an argument. For the purposes of this essay, argument will refer specifically to a list of reasons (henceforth called premises) which are provided in support of a conclusion. This differs from its definition in common usage, which denotes aggressive bickering between people. In an argument, truth refers to whether the statements are factual, validity refers to whether the premises can logically support the conclusion (regardless of their truth-value), and soundness refers to an argument that is both true and valid.

Truth and validity are the two fundamental components to an argument; deprived of either, the argument is not worth believing. Truth is fairly easy to grasp, so more time will be spent on the discussion of validity. Put tersely, truth refers to whether the statements of an argument are actually factual. If somebody argues that, because dogs are mammals and mammals are warm-blooded, that dogs must therefore be warm-blooded, evaluating the truth of an argument means questioning whether it is a fact that “dogs are mammals” or that “mammals are warm-blooded.” Truth has nothing to do with the form of the argument but instead to do with whether the statements provided are factual. Now, if someone were to argue that, because dogs are mammals and cats are warm-blooded, that dogs are warm-blooded, all of these statements would be true, but there is clearly something wrong here. Even if we accept that “dogs are mammals” and “cats are warm-blooded,” does this give us any reason to accept the conclusion that “dogs are warm-blooded?” We know the conclusion is true, but the reasons do not support it. This is where validity comes in.

Validity is all about whether the premises provided actually do logically support the conclusion, regardless of the truth-value of the statements. Take the following argument as an example: dogs are cats and cats are lizards, so dogs must be lizards. These are clearly false statements. It is untrue that dogs are cats and that cats are lizards, but if they were true, would it support the conclusion? The answer is yes. If it is true that dogs are cats and if it is true that cats are lizards, then it must be true that dogs are also lizards. We can think of this as a kind of equation: if A = B and B = C, then A = C. This is what validity is all about. Validity is about whether the conclusion is logically supported by its premises, regardless of whether the statements are true or not. A common argument form written abstractly: If A, then B. A. Therefore B. More concretely: If gas prices go up, car-pooling will be more popular. Gas prices have gone up. Therefore car-pooling will be more popular. We’re not concerned with whether gas prices have gone up or whether it is factual that car-pooling will be more popular if they do go up. Instead, we see if the premises (i.e. the facts) support the conclusion. If it is true that car-pooling will be more popular if gas-prices go up and if it is also true that gas-prices have gone up, then it absolutely must be true that car-pooling will become more popular. A valid argument, thus, is an argument whose conclusion logically follows from its premises regardless of whether its premises or conclusion are true.

A sound argument is an argument whose premises and conclusions are true and whose form is valid. For the purposes of demonstrating this, we will explore three arguments which differ in their validity and their truth-value. The first: all animals that live in the water are fish. Whales live in the water. Therefore, whales are fish. This argument is valid because, regardless of whether the statements are true, the conclusion must be true if the premises are true. The first argument is unsound, however, because its premises are untrue. It is not true that all animals that live in the water are fish, as whales live in the water and are mammals. The second argument: all humans with a terminal illness will die. Socrates is a mortal. Socrates will die. This argument is true, but it is invalid. While it is true that all humans with a terminal illness will die and that Socrates is a mortal, these two statements do not support the conclusion. The argument, although it is true, is unsound because it is not also valid. The third argument: all dogs are mammals. All mammals are warm-blooded. Therefore, all dogs are warm-blooded. This argument is both true (because the statements are factual) and valid (because the conclusion must be true if the premises are). Given that the third argument is both true and valid, it is therefore sound. Soundness refers to an argument which is both true and valid.

When evaluating arguments, it is not sufficient for an argument to be solely valid or solely true. An argument worth believing is one that is sound, merging both truth and validity. When considering the arguments that people present, it is worthwhile to evaluate these two components of the argument separately as a seemingly-convincing argument may not be so convincing upon closer inspection. There are different techniques for evaluating the truth and validity of arguments, however these techniques fall outside of the scope of this essay and will not be explored. For techniques on how to evaluate the truth of an argument, it may be worthwhile to search for “techniques on determining credibility.” For techniques on how to evaluate the validity of an argument, it may be worthwhile to search for “valid argument forms.” As a note of advice, it is often easier to evaluate validity than truth. It is easier to determine whether the premises are relevant to the conclusion and whether they align with valid arguments forms as opposed to determining what is factual, especially if you are not an expert in the material. In an age of specialization, it is very easy to become overwhelmed by complex information, to find conflicting sources, and to be suffocated by jargon. With validity, it is often much easier to phrase the argument as a hypothetical (i.e. if this is true, then that must be true) for the purposes of evaluation. Truth must still be evaluated but beginning by analyzing the validity of an argument is usually a good way of beginning to understand and criticize otherwise complex material. Lastly, evaluating arguments is more of an art-form than an exact science. Some areas of evaluation, such as validity, are more clear-cut, but evaluation can largely be a process of interpretation; the evaluation of arguments may not be as straight-forward as the ones presented in this essay. Typically, arguments have implied premises or conclusions, they’re buried in irrelevant commentary, or they’re vague or ambiguous to begin with. Evaluation can often be a difficult task, but the only way to get better at it is with practice. Regardless, it is important to understand the concepts of truth, validity, and soundness, as they form the bedrock of what makes an argument worth accepting.

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