An argument is a structure that comprises a conclusion, namely a proposition that one wants to uphold, and some premises, as reasons to support the belief in the conclusion. Logic is about whether and how a conclusion follows from the premises. What it means for a conclusion (a certain proposition B) to follow’ from a premise (another proposition A) is sometimes cashed out as whether whenever the premise (A) is true, the conclusion (B) is also true. Arguments come in many forms in real life; sometimes they are easy to spot but sometimes the covert. We thus need first of all some training to heighten our awareness of and ability to identify arguments.
An argument contains one and only one conclusion. In fact, an argument is individuated by its conclusion. If we want to make more than one conclusion, then there must be more than one argument. An argument can be represented in the following standard form: the premises are listed on the top followed by the conclusion at the end and each sentence is numbered for easy reference. We also use a line to separate the premises and conclusion.
A conclusion is supposed to be supported by the premises. There may be many premises in an argument. Indeed, there is no limit to the number of premises. However, is there a minimum number of premises in an argument? If so, what is it? One, two, or three? Surprisingly, formally, the answer to the minimum number of premises required is zero! This is surprising because premises are reasons to support a conclusion and allowing zero premises would mean that the conclusion is supported by nothing, and that seems to directly contradict the goal of reasoning, namely, to accept an argument only if one can provide a reason to believe in it. These are legitimate points. Yet when logicians allow an argument to have no premises, it merely means that nothing goes against the conclusion, rather than that the conclusion is supported by no reason. We regard such a conclusion as self-evident. The following are some examples of self-evident truths.
Example (1): Everything is identical to itself.
Example (2): Something is the case or it is not the case. Example (3): It cannot be true that something is both the case and not the case at the same time.
Example (4): An object cannot be red and green all over at the same time.
Self-evident truths are obvious truths that do not need anything to support them. Equally, it can also be said that everything supports them because nothing counts as a reason to reject them, and they do not contradict with anything. I will discuss in this blog the idea that an argument is valid if it preserves truths from the premises to the conclusion. Given this definition, because a conclusion containing a self-evident truth is always true, any statement serving as its premise, if true, will lead to the truth of the conclusion. Thus, every argument supporting a self-evident truth is a valid argument.
Self-evidence: Is self-evidence just the same as having nothing to go against it? How do you take it?
The question of self-evidence is more complicated than it looks Self-evident truths are intuitive. It is difficult to argue against widespread intuition, especially when many other judgments are based on it. Consider what I am to do if I really doubt that these hands are mine? I will also need to doubt many other things that we so take for granted in our lives. Yet we do know that sometimes what we believe is true may turn out to be false: for example, I could mistake a robot dog seen in the distance for a real dog. How to distinguish various types of intuition and more importantly, how to justify those very general and foundational ones? These are not easy questions!
A philosopher Ludwig Wittgenstein once described the situation as: : “If I have exhausted the justifications I have reached bedrock, and my spade is turned. Then I am inclined to say: “This is simply what I do Ludwig Wittgenstein (1958), Philosophical Investigations, section 217)
Moreover, should we treat self-evidence the same as having nothing to go against it? When we do so, don’t we already assume that a proposition is either true or false, and then nothing is both true or false? Yet these laws of logic (the Law of Excluded Middle and the Law of Contradiction respectively) are exactly some of the self-evident truths that we claim to exist. So we would be defining self-evident truth using some self-evident truths. Isn’t that begging the question?
For our very question is that although we do not usually challenge; self-evident truths, it seems hard to explain why self-evident truths cannot be challenged. Indeed, some laws of logic are challenged under different systems of logic. The three logical laws stated above are the laws for classical logic. There are non-classical logic systems that try to answer these questions in a different way. For instance, paraconsistent logic does not accept the Law of Contradiction – some paraconsistent logicians claim that there: are true contradictions in reality, such as a group of people holding opposing moral views; some claim that all contradictions are trivially true.