An introduction to the use of the term ‘logical truth’ in the processes of assertion and argument
This is a simple introductory essay about the use and meaning of the term ‘logical truth’. Reference is made to the classic syllogistic logic of ancient Greece, the propositional logic of normal language statements, modal logic of possibility and necessity and very superficial mention is made about logical probability.
Logic Part 1: Summary of Ideas
The reasoning used here is, in some places, not technically precise enough for professional logicians, however, the purpose of this simple essay is to point out that:
a) There are different types of argument that are commonly taken to be ‘logical’. These are often referred to as
- Deduction, which reaches a conclusion given starting ideas
- Induction, which produces generalisable conclusions from related observations
- Abduction or argument to the best explanation in a particular set of circumstances
(This is a somewhat arbitrary classification of mental processes that are in everyday life not truly independent of each other.)
b) Deductive logical arguments require truth or some degree of truth as the input to arguments if some level of truthful outcome is to be generated. Deductive truth in that sense is merely a product of the ‘rules’ of argument that we are prepared to accept or we consider to be intuitively valid. Deduction is therefore said to be ‘truth-preserving’.
c) Logical deduction is valuable in the sense that it produces useful conclusions (or composite ideas) given certain starting points or premises. Whether or not, or under what conditions that process can generate an idealised philosophical (epistemic) conception of truth is another matter.
d) Conjoined statements are created by the use of words called ‘logical connectives‘ (such as AND, OR, IF and THEN) that join assertions into composite ideas. In order to make any form of useful logic we also require the use of negation, which allows us to declare when something is NOT the case.
e) Logic requires some form of implied or explicitly stated outcome based on some criterion for rejection or acceptance of the arguments or composited statements that are produced by the connectives and NOT. These are often the binary criteria of truth and falsity modified by some degree or strength of belief. For example, logically arrived at assertions might be regarded as absolutely true or probably false.
f) There are very important modifiers of the concept of logical truth such as necessity and possibility. The modifiers are known technically as alethic modalities. It can be enormously important to know, for example, if a conclusion must be true, can not possibly be true or is instead possibly true in certain circumstances only. We might believe that is possible that during the winter period the assertion ‘it will rain here tomorrow’ will probably be true.
g) Another set of logical truth modifiers are known as quantifiers. A statement or logical conclusion might be modified by the words ‘all’ or ‘every’, ‘each’, ‘some’, ‘many’, ‘most’, and ‘few. It matters a great deal if an idea or a logical conclusion is modified by such words.
h) Although we might think of the conclusion of an argument as being ‘logically true’ we still need to ask what is the source of the supposed truth, if any, especially in deduction.
i) Repeated observations can be used to argue the existence of causes when it is accompanied by deductively mechanistic thinking.
k) We can use some kind of surrogate for the idealised conceptions of logical binary outcomes of truth and falsity, such as plausibility or probability, and still reach useful or intellectually satisfying conclusions.
Of course, our appreciation of logic need not end there, since we can learn much from others including professional logicians who have been developing ideas about logical systems since antiquity. Logic is not just interesting (to some) but is also immensely important because it is required in mathematics and computer programming, in science and its applications, and in everyday life.
Logic by itself, tells us nothing about the world since it is only concerned with the relationship or rationalised connection between different ideas, observations or assertions. However, in the absence of some kind of logical reasoning or argument, we cannot form explanations about the way things are. Nevertheless, the meaning of the term ‘Logical Truth’ is somewhat illusory and can vary depending on the particular conception of logic that is being used. Thomas Hofweber argues that “Overall, we can … distinguish four notions of logic:
- (L1) the study of artificial formal languages
- (L2) the study of formally valid inferences and logical consequence
- (L3) the study of logical truths
- (L4) the study of the general features, or form, of judgements”
Our brains seem both hard-wired and culturally endowed to reason in particular ways. The reason for believing that logic is to some extent innate is that we feel that we know when a compound sentence or a simple argument makes sense when we understand the correct use or meaning of the logical terms. This view of logic is called ‘intuitionist’. This is the outlook that I adopt.