… Correct reasoning? The nature of thought or language? The structure of the world?…
What’s the subject matter of logic?That question has been answered in many different ways by many different philosophers and logicians over the centuries.
Take these examples:
(1) Logic’s subject matter includes propositions, entailment, implication, inference, validity, soundness and consistency.
(2) Logic’s subject matter is the structure of thought itself.
(3) Logic’s subject matter is the structure of language.
(4) Logic’s subject matter is “the structure of the world” in that it deals primarily with world’s (to use Ludwig Wittgenstein word from the Tractatus) “form”.
(5) Logic doesn’t have a subject matter in that logic is what is used to deal with literally all subjects (e.g., from maths to language to science to everyday arguments or statements).
Number (1) above is (in broad terms) the usual account of logic’s subject matter. It’s also a less philosophical — and more formal — account. Yet it’s the case that none of these accounts necessarily contradicts all the others. Indeed perhaps logic is accounted for by the sum of at least some of these seemingly distinct positions.
(1) Formal Logic’s Subject Matter
One can take a purely formal and technical position on logic.
This basically means that it can be said that inference, consequence, validity, soundness, consistency, entailment, etc. are the true subject matter of logic. Having said that, even if formal logic does indeed give us the pure and unadulterated subject matter of logic, it’s still nevertheless the case that nearly all language and thought abides by the principles of formal logic. And when thought and language don’t do so, then this effectively renders them incoherent, meaningless or simply useless. In other words, almost everyone in their everyday thought and talk commits him or herself to the law of identity, the law of non-contradiction and the law of excluded middle. Laypersons also infer things, deduce logical consequences and they believe in validity and consistency. It just so happens to be the case that laypersons (i.e., non-logicians) don’t use the former technical terms when they do so.
Of course laypersons can improve their logical skills by studying logic in some form or even acquire brand new logical techniques. On the other hand, it’s hard to believe that the majority of people reason correctly solely because they’ve previously sat down and thought about, say, the laws of logic or “correct inference”.
The pragmatists John Dewey (1859–1952) and C. S. Peirce (1839–1914) looked at these issues in another way. They believed that logicians and philosophers should codify and notate logical principles and rules simply by studying the way people actually reason in their everyday lives. Peirce, specifically, believed that it is scientists and the methods of science which should be the true subject matter of logic. Dewey, on the other hand, concentrated on what he called “everyday inference”.
We now come across the problem of which way the arrow points. Does it point from language users to logic or from logic to language users? That is, do people learn to reason correctly by self-consciously using logical laws and rules? Alternatively, does (much) logic simply codify the way people naturally reason and think?
It can now be said that the arrow actually points in both directions.
So even if formal logic needn’t (or doesn’t) study everyday reasoning, we can still safely say that everyday reasoning rarely breaks the rules of logic. This state of affairs is not unlike the philosopher Donald Davidson’s argument that we must simply assume that the beliefs of all other cultures (as well as people from the past) or even aliens have been — or are — largely true. Similarly, we must also assume mass rationality rather than mass irrationality. Indeed if mass and systematic irrationality were ever the case, then that would make (what Davidson’s called) the “radical interpretation” of other communities (or even aliens from outer space) impossible from the outset. (See Davidson’s paper ‘Radical Interpretation’.) Either that or we’d need to assume that such communities were collectively insane. And that, according to Davidson, would be an illogical position.
(2) Logic’s Subject Matter is the Structure of Thought
It should immediately be said that many philosophers would say that the structure of thought mirrors the structure of language. Yet many others reverse this “binary opposition” by arguing that the structure of language mirrors the structure of thought. Whatever the reality is, these statements don’t in themselves tell us what is logical about either thought or language.
So let’s firstly take thought.
Aristotle (384–322 BC) offered us what he called the laws of thought.
These laws are captured in terms of basic logical terms.
Take the law of excluded middle. (In symbols: p or not-p.)
In terms of thought, we can say that we can either think that p is true or that p is false (or not true).
Now take Ludwig Wittgenstein’s expression of what he — and many others — have called a “tautology”:
“It will either rain this afternoon or it won’t rain this afternoon.”
Perhaps this is a bad example because Wittgenstein himself said that the above “tells us nothing”. However, it’s still the case that we must think that either p is true or not-p is true. Aristotle, on the other hand, argued that this shows us that we can’t think contradictories. Thus thought is structured around the basic and fundamental fact that we can’t think both p and not-p — at least not at the same time.
(3) Logic’s Subject Matter is the Structure of Language
Despite what was said earlier about the (possible) mutual relatedness of thought and language (or, in Donald Davidson’s words, “thought and talk”), it can be said that many philosophers have believed that natural languages (or at least natural expressions) have their own “logical grammar” (or logical form). More relevantly, they’ve also said that such logical grammar is often hidden by the “ordinary grammar” of natural expressions.
For example, both Ludwig Wittgenstein and Bertrand Russell (at least in their early years) believed that many everyday expressions (if only of a particular type) hide their logical grammar.
To repeat: we’re asking what is the subject matter of logic. In this case, then, it’s the logical grammar of everyday — and also metaphysical — expressions.
Now take Russell’s theory of descriptions in which he uncovered the logical grammar (if the following is the correct word) underneath statements such as “The king of France is bald”.
Russell argued that the English sentence (or statement) “The king of France is bald” hides it true logical grammar. Thus by careful analysis he showed that because of the use of the definite article “the”, there’s an implicit commitment to the actual existence of the king of France. The king of France didn’t in fact exist at that time. Thus someone (or some x) who doesn’t exist can’t be either bald or not bald. So, to cut Russell’s long and complex story short, this sentence is effectively “meaningless” because of its “empty definite description”.
Other philosophers have said that the statement “The king of France is bald” is simply false (for more or less the same reasons), rather than meaningless.
And yet I myself have just used the description “The king of France” in my own sentences. I’ve also predicated baldness of this person (or non-person). So perhaps all I needed was to use quotation marks to escape from what Quine called Plato’s beard.
Alternatively, it can be argued that rather than the logical grammar of everyday expressions being (in surely metaphorical terms) hidden beneath their everyday grammar, their grammar (both logical and everyday) is explicit and therefore on the surface. (This is more or less what the “late Wittgenstein” argued. See the book Nothing is Hidden: Wittgenstein's Criticisms of His Early Thought.)
So instead of offering an analysis, what Russell actually did was offer us a new version of the analysed expression. More strongly, it can be said that Russell offered us a philosophically kosher alternative to the suspect expression. That alternative, however, was deemed — by Russell — to be free of logical and ontological complications or ambiguities.
Similarly, the logical positivists’ verifiability principle was supposed to show us that certain “metaphysical” expressions are “meaningless”. That was either because they can’t be verified or because they have no observational or experiential content and/or consequences. The logic of such expressions, therefore, rendered them meaningless (yes, that word again!).
In these cases, then, the subject matter of logic is the logical and philosophical mix-ups of metaphysical and ordinary-language expressions. So, as the logical positivists once argued, only the expressions of science, mathematics and logic are (at least in principle) free from such faults.
(4) Logic’s Subject Matter is the Structure of the World
Another point to make about Aristotle's laws of thought is that they apply to the world — not just to propositions (usually symbolised as p and/or q). More than that: they apply to everything. So instead of the propositional
p or not-p
we can also have:
A or not-A
Here the A above symbolises any situation, fact, condition, event, or state of affairs in the world.
So take Wittgenstein’s rain example again. We can make his tautology be about a thought/belief. Thus:
We can’t think [or believe] both that it will and it will not rain this afternoon.
However, we can also say of the world itself:
It can’t both rain and not rain at one and the same time.
We can say here, again, that either the structure of thought mirrors the structure of language or that the structure of language mirrors the structure of thought. Yet we can now also say that both thought and language abide by the structure of the world in that neither thought nor language can break (to speak metaphorically) the world’s own logical rules.
So if a ball is painted blue all over it can’t also be painted red all over. And that is a (to use 20th-century jargon) de re statement about the world.
We can also offer a de dicto version. That is, we can’t think or say
“That ball is red all over.”
at the same time as thinking or saying
“That [same] ball is blue all over.”
Again, the question many philosophers have asked (vis-à-vis thought and language) is whether or not our thoughts about the ball are determined by the logical structure of our language. Or do both language and thought somehow shape how we perceive and understand the world? Alternatively, does the world somehow impose its structures on both thought and language?
Now let’s take another Aristotelian law of thought: the law of identity: A = A.
This has something of the blindingly obvious about it. However, this law lies at the very heart of all thought, language and… well, everything. Therefore it deserves to be notated logically (as Aristotle did) and commented upon.
For example, if the (propositional) contents of all thoughts weren’t equal to themselves, then thought itself would cease. Perhaps more relevantly: if we didn’t know that one thought were identical to itself when expressed at a different time, then this would certainly impact on thought itself. In ontological terms, we need to recognise the identity of a thought-about-an-object over time, which itself provides us with the very basis of thought itself.
A may well (obviously) equal A. Yet at one point people didn’t know that, for example, the Evening Star is the same thing as the Morning Star. (The phrases “the evening star” and “the morning star” were descriptions which later became names — see Ruth Barcan Marcus’s paper ‘Names and Descriptions’.) More relevantly, the names “Morning Star” and “Evening Star” have the same (to use Gottlob Frege’s term) reference but difference senses. That self-identical reference being the planet Venus.
To sum up: without the stability of the law of identity, thought itself would be rendered incoherent, if not void.
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