On The Nature Of Logic

There was an age old argument from philosophers about the nature of logic. Some philosophers said logic is derived from experience, whereas others said it arises out of our own conceptualising of the world. What should have been obvious, even in the corridors of history, is that what was being presented was a false dichotomy.

A quick consideration of our engagement with reality shows us that humans first have the experience and then we construct the conceptualisations through relational thoughts, of which logic is one. There is no reason why these should be mutually exclusive. To say that those conceptualisations in any way deny the origin of experience is about as misjudged as arguing that the heat of the candle's flame denies the existence of the candle.

Let me tell you about a milestone moment in philosophical history where the matter was settled comprehensively by David Hume. In his Enquiry Concerning Human Understanding Hume posited something that has shocked many, and it has confused numerous laypeople who like flirting with heterodoxy in order to appear subversive or ultra-sceptical, but it remains one of the most important observations in philosophy.

The underlying summary of what Hume gave us is that everything (and I do mean everything) we can classify as knowledge is acquired only through experience of the natural world. We have what Hume called 'matters of fact' which are facts about reality gained from sensory perception that enable us to make propositions about reality out there, and we have 'relations of ideas' which are about formulations of ideation (ideas) and concepts related to those facts.

What Hume's Enquiry laid out better than anyone that preceded him is that we could not possibly have acquired any single bit of human knowledge without experience, and as a consequence we never predict anything that is not already presented to us through some experiential pathway.

Of course, we can elaborate on previously discovered things, and we can make forecasts ("Africa will be more prosperous in 300 years' time" is a forecast, as is "Any two objects in nature attract each other with a force according to an inverse square law", albeit a different kind of forecast) - but we can never predict anything previously undiscovered about nature herself (for further detail of this, this Blog post - Why We Never Have, & Never Will, Predict Anything New)

The key thing here is that we build on experiences through those 'relations of ideas' which involves extrapolating from the data of experience and building concepts, ideas and views about our sensory experiences of the natural world, but every bit of new knowledge is a discovery, because everything new comes from experience.

So the same applies to logic then?

Yes, it is by this method that we deal with logic too. Logic amounts to human extrapolations from our engagement with physical reality - it is a formal construct derived from experience of how the world is. So we can say that all our empirical knowledge is built on logic, but equally our logic is derived from our experiences of the world. I don't mean, of course, that logic gives us new information about the world - I mean that it provides us with a system that reflects how the world works. 

Logic works like this; If, for a deductive argument, the form of the syntax is valid ("If P then Q; P, then Q") then all we need to do insert some rationally consistent and factual premises in place of P and Q , and we can arrive at a true conclusion. If the argument form (the syntax) is valid and the semantic components (the premises) are true, then the argument is sound.

Here's a simple explanation of deduction and induction. When looking at an argument, two things are considered - whether it is valid and whether it is sound.  An argument is valid when the conclusion logically follows from the premises.

All politicians wear glasses

Bill is a politician
Therefore Bill wears glasses

That is a valid argument, because if all politicians wear glasses, and Bill is a politician, it logically entails that Bill wears glasses. But while it is a valid argument, it is not a sound argument. A valid argument becomes sound when the conclusion logically follows from the premises, provided the premises are true. Clearly the above argument is not sound because the first premise is wrong (all politicians do not wear glasses). For an argument to be deductive, it must be valid as well as having premises that are known to be true. Here's an obvious one:

All men are mortal.

Bill is a man.
Therefore, Bill is mortal.

As you can see, all arguments and observations rest on there being a logical underpinning to the proceedings. Let's take a well known principle to show how inextricably linked to the physical logic is - the law of non-contradiction. Since the days of Socrates, Plato, and Aristotle many people have been employing the correspondence theories of truth, which states that how we deal with the formulation of truth is to do with our perception of the relationships between our inner thoughts and the external reality with which we interface.

The tools of logic apply so well to our world because they are based on how the physical world works - and the law of non-contradiction is a prime example. The law of non-contradiction takes the form “A is not not-A”, which basically means that one cannot logically predicate of a thing a quality which is its contradictory. 

In other words, something cannot be A and not A at the same time, and our brains literally can’t conceive of reality any other way. Close your eyes for a second and try to imagine a triangle that is also a circle, or a woman who has short ginger hair and long black hair. Why did you find that impossible to conceive? Because it would require us to simultaneously have the physical constituents of the thought A and not A at the same place at the same time - something which is physically impossible, because nature permits that it is not possible.

If by our understanding of perception of colour a woman has entirely short ginger hair she cannot simultaneously have entirely long blond hair. Our ideas of mutual contradiction are based on our experiences and on associative ideas. Try to picture a head of hair that is fully ginger and fully black at the same time and you'll find you won't be able to. Picture a head that is a mixture of ginger and black and the world makes sense again.

The law of non-contradiction has to be self-evidently valid, because any attempt to disprove it assumes its efficacy and proves the thing you're trying to disprove. To propose it is false is to presuppose that it is not at the same time true, and to propose it is true is to presuppose it is not at the same time false. Ergo: the law of non-contradiction is valid - to attempt to refute it only confirms it.

Given the foregoing, it should be clear that we derive our understanding of logic from how things are in nature. We don't choose to invent the law of non-contradiction, we find that it holds because of the way nature is. The same is true of the truth conditions of a proposition. Even though we derive logic from experience and form those conceptualisations as a consequence, we still require an inner criterion for making such judgements. 

Think of it as being a bit like the rules for chess or grammar - there isn't anything wrong with them within the confines of their constituent parts, because they serve the purpose of acting as a supporting strap for the players. Similarly, the language of logic is a human construct that provides a supporting strap for the players involved in engaging with the world and how it works.

We know that logic requires experience because no one has ever been able to convey a logical truth that can be understood without invoking some example abstracted from the world of experience. In actual fact, the logic part is relatively straightforward compared with the subjects it contains.

The logical rule "If P then Q, not P then not Q" is easy to understand. If a man is married then he is not a bachelor. John is married, therefore John is not a bachelor. But experience might tell us something more complex while still obeying the logical principles. If it is raining then the roads are wet, it is not raining, therefore the roads are not wet. I can conceive of situations in which the road is wet while it is not raining.

A lorry containing a tanker of water could crash and spill its load all over the road. Moreover, I have known roads to still be wet long after it has stopped raining. The reason I need experience to demonstrate this is because logic gives no indication of causation – only experience presents us with causation. Logic can tell me that John cannot be a bachelor and not a bachelor at the same time, but only experience can tell me when John gets married. 

Not only is logic derived from experience – it is the structure of interpretation that underpins almost all of our enquiries. Without logic, our attempts at knowledge would fall down. That’s why we couldn’t come up with a different system of logic that we could use to govern our epistemology – because we have grafted on to our thinking a system that provides us with rules for attaining knowledge, but also because the attainment of knowledge is built around having formal structures that provide us with consistency to attain knowledge.

Logic is like the ground on which our objects of knowledge can be placed. It also acts as a set of formal tokens which is then employed as a vehicle that reflects external reality. That is why I think it is accurate to say that logic is a true reflection of what is found in nature. Unlike mathematics, logic doesn’t have truths outside of a universe, because every form of logic with which we interface is based on facts about our universe. Logic is to the universe as paint is to the canvas.