What is Logic?
'Contrariwise,' continued Tweedledee, 'if it was so, it might be;
and if it were so, it would be; but as it isn't, it ain't. That's logic.'
-Through the Looking Glass
We most often think of logic as one element of sound reasoning. Other key elements might include: verifiable and relevant evidence (including appropriately used statistical information), repeatable demonstrations, applicable analogy or comparison, and inference through circumstantial evidence.
In one sense, logic appears to function without the other elements of sound reasoning (as in mathematics), but the other elements (such as evidence) generally require logic to make them applicable to an argument. This suggests the conclusion that logic is essential to argument.
- Formal logic requires our thoughts to be presented into structured sequences of propositions. However, we sometimes find it difficult to organize our thoughts and ideas into formal propositions. But when the formal propositions are structured and presented, there is an elegant inevitability to the results, although there is a legitimate question whether the conclusion of a formal logical argument was already contained within its initial proposition.
- Informal logic is used much more often in our reasoning and argumentation; however, even if significant fallacies are avoided, there are inevitable debates on assumptions, premises, definitions and context.
- Mathematical logic represents the foundations of mathematics as a scientific endeavour aimed at discovering new valid propositions.
Prior to logic as the basis for argumentation, we can also think of logic as the infrastructure for coherent communication, an apparatus without which argument would not be possible. If the infrastructure of logical reasoning is not sound, then the reasoning may itself be suspect. Consider certain basic assumptions we make in our conversation:
1. We talk about things which exist (even as ideas or dreams)
2. A thing is what it is
3. A thing is not at the same time another thing
4. A thing has at least one property or characteristic
5. A thing either has or does not have a property or characteristic (the middle is excluded)
6. A thing cannot both have and not have a property or characteristic (non-contradiction).
These assumptions concern the existence, identity, uniqueness and specificity of things, demanding that something be one thing or another and not both. These assumptions are, in effect, the axioms of rational discourse. But they are assumptions.
We might propose certain tests of these basic assumptions to assure ourselves of their validity (if we can set aside the difficulty that our tests themselves may rely on the assumptions we want to test). This is a good field for discussion but to start off consider, as examples, whether the assumptions:
• could be contradicted by experience (observation)
• form a consistent whole within themselves; i.e., they do not appear to contradict one another.
• provide a complete explanation of things and their properties.
The foundations of logic, for the most part, appear to meet these tests.
However, some argue that the principles of quantum physics suggest that our assumptions fail all three tests.
If, for example, there is a possibility that one thing can both exist and not exist at the same time, or can exist in two spaces at the same time, or can both have and not have certain properties, then one could challenge the assumptions of existence, non-contradiction and can be challenged.
For one other challenge to the distributive law in logic, consider the following citation from Wikipedia:
- "Quantum logic has some properties which clearly distinguish it from classical logic, most notably, the failure of the distributive law of propositional logic:
- p and (q or r) = (p and q) or (p and r),
- where the symbols p, q and r are propositional variables. To illustrate why the distributive law fails, consider a particle moving on a line and let
- p = "the particle is moving to the right"
- q = "the particle is in the interval [-1,1]"
- r = "the particle is not in the interval [-1,1]"
- then the proposition "q or r" is true, so
- p and (q or r) = true
- On the other hand, the propositions "p and q" and "p and r" are both false, since they assert tighter restrictions on simultaneous values of position and momentum than is allowed by the uncertainty principle. So,
- (p and q) or (p and r) = false
- Thus the distributive law fails."
If these challenges are valid, then our traditional infrastructure of logic may only describe how we experience our consensual and social reality. The rules and principles of logic are, in this view, neither immutable nor ineluctable; they are a human creation.
As well, in fuzzy logic systems propositions may be based on probability and likelihood rather than truth or falsehood. Where there are ‘degrees of truth’, the certainty of traditional logic is weakened.
There is an interesting further challenge which suggests that, even if the foundations of logic were unassailable, they remain a subjective cultural artifact: the principles were ‘discovered’ by humans, and are applied in argumentation by humans; there is nothing beyond human experience, so the argument goes, that suggests the foundations have any immutable or eternal value. However, this challenge can be applied to any human experience or thought, and basically maintains that there is no objective reality beyond human experience. Such may or may not be the case, but it does leave the scent of solopsism in the air.
For our discussion, we could start with these questions:
- Do the principles of logic have objective value, or are they subjective human creations used to explain our experience?
- Is it important whether logic has objective reality?
- How do we test any logical principles or assumptions for validity?