2.5 Truth as an Outcome of Logical Argument
The purpose of this section is to make the very simple point that when we use the terms ‘true’ or ‘false’ about logical arguments what we are doing is stating our acceptance or rejection of particular inferences.
One can only say anything about the concept of truth in a logical sense by trying to understand the formalisations of logic, their expressive role, and the rational legitimisations of action that logic provides. In this section, as an explanatory convenience, I will make reference to the classic categorical syllogistic logic of ancient Greece, the propositional logic of normal language statements, modal logic of possibility and necessity.
2.5.1 Summary of Ideas
The reasoning used here is, in some places, not technically precise enough for professional logicians, however, the purpose of this simple section is to point out that:
a) It is convenient to think of human reasoning as falling into different types or styles. These include, practical, procedural and spatial reasoning, logical deduction, induction, abduction, associative, analogical and numeric reasoning, and so on. In addition, there are qualifications of ‘truth’ in modern logic.
b) Deductive logical arguments require truth or some degree of acceptability as the input to arguments if some worthwhile level of outcome is to be generated. Deductive ‘outcome’, 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 commonly said to be ‘truth-preserving’ although we could equally stipulate that it preserves acceptability. For me, the terms truth and acceptability are interchangeable when applied to logic, provided the same binary use is made of acceptable/unacceptable.
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 epistemic conception of truth is another matter.
d) Logic is based or the meaning of formal terms called ‘logical connectives’. The conjoined statements of deductive logic 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 commonly referred to as the binary criteria of truth and falsity on occasions 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 rain is possible that during the winter period. The assertion ‘it will rain here tomorrow’ will probably be true in the future (where ‘here’, ‘tomorrow’ and ‘future’ are contextual terms).
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. These terms are define the context or extent of the logical outcome.
h) Although we might think of the structure of an argument as logically valid and the conclusion of an argument as being deductively sound or ‘logically true’ (or acceptable) we still need to ask what is the source of the supposed truth or acceptability, if any, especially in deductive arguments.
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 logical binary outcomes of truth and falsity, such as plausibility or probability, and still reach useful or intellectually satisfying conclusions.
Logic is not just interesting (to some) but is also immensely important because it is required for our actions in the world and in mathematics, computer programming, and in science and its applications.
Deductive 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’ in deductive arguments 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.
The ‘logical test’ scene from the 1974 German-language film the Enigma of Kaspar Hauser, written and directed by Werner Herzog, cautions us to be careful about the claims we make about logic.
Steve Campbell
Glasgow, Scotland
2017, 2019, 2022, 2024