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Humanities LibreTexts

1.6: Basic Logical Concepts

  • Page ID
    92510
  • Consistency

    Two (or more) statements are inconsistent with each other when it is logically impossible for all of them to be true at the same time. For example: The earth is flat, and The earth is spherical are inconsistent statements since nothing can be both flat and spherical. On the other hand, if you have any two statements that are both true, they are certainly consistent.

    Entailment

    A sentence X entails Y if Y follows logically from X. In other words, if X is true then Y must also be true, e.g. 30 people have died in the riots entails more than 20 people died in the riots,but not vice-versa.

    If X entails Y and we find out that Y is false, then we should conclude that X is also false. But of course, if X entails Y and we find out that X is false, it does not follow that Y is also false.

    If X entails Y but Y does not entail X, then we say that X is a stronger claim than Y (or Y is weaker than X). For example, all birds can fly is stronger than most birds can fly, which is still stronger than some birds can fly.

    A stronger claim is of course more likely to be wrong. To use a typical example, suppose we want to praise a person X but are not sure whether X is the best or not, we might use the weaker claim “X is one of the best” rather than the stronger “X is the best”. So we need not be accused of speaking falsely even if it turns out that X is not the best.

    Logical Equivalence

    If two statements entail each other then they are logically equivalent. For example, everyone is ill is equivalent to nobody is not ill, and cheap things are no good is actually equivalent to good things are not cheap. If two statements are logically equivalent, then necessarily they must always have the same truth value.

    Arguments

    In ordinary usage, the word “argument” is often used to refer to a heated dispute between two or more parties. But in logic and critical thinking, the term has a different meaning. Here,an argument is taken to be a list of statements, one of which is the conclusion and the others are the premises (assumptions) of the argument. To give an argument is to provide a set of premises as reasons for accepting the conclusion. The ability to construct, identify and evaluate arguments is a crucial part of critical thinking. We all have lots of opinions on lots of things,but most people are not good at giving arguments in support of their opinions.

    Here is an example of a short argument made up of three statements. The first two statements are the premises, and the last one is the conclusion:

    • Every star produces radiation.
    • The Sun is a star.
    • Therefore, the Sun produces radiation.

    Arguments in real life often are not presented in such a neat manner, with the premises and conclusions clearly laid out. So how do we identify them? There are no easy mechanical rules,and we usually have to rely on the context in order to determine which are the premises and the conclusions. But sometimes the job can be made easier by the presence of certain premise or conclusion indicators. For example, if a person makes a statement, and then adds “this is because ...”, then it is quite likely that the first statement is presented as a conclusion, supported by the statements that come afterwards. Words like “after all”, “suppose” and “since” are also often used to precede premises. Conclusions, on the other hand, are often preceded by words like “therefore”, “so”, “it follows that”.

    The secret to good reading and writing skill is to develop the ability to construct and summarize arguments, and to present arguments clearly and systematically. The same goes for giving good presentations.

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