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These are propositions I take to be true:

  • Our knowledge is based purely on empirical observation.
  • There is no way to directly observe reality or objective truths.
  • Therefore, there is no way to say for sure that the laws of logic exist beyond human reasoning.

So, wouldn't any 'proof' of the laws of logic, imply the need for logic to prove its own existence?

(Please correct any mistakes, I do not possess a complete understanding of any of this)

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  • "Our knowledge is based purely on empirical observation." Yes, and also our knowledge about logic's existence. Jun 21, 2021 at 14:14
  • In general, we do not prove the existence of something: logic, God, world,... An for sure we cannot prove the existence of "empirical" entities by logic alone. Jun 21, 2021 at 14:19
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    "Our knowledge is based purely on empirical observation." That's clearly false. If it were true, there would be no knowledge at all beyond "I am experiencing this sensation right now". You would have no way to know that your memory is true, no way to know mathematics, no way to know that what you experience is of a real world instead of just an illusion, no way to know that other minds exist, no way to predict that what happens in the future is going to be similar to what happened in the past, now way to even know that one thing is similar to another. Jun 22, 2021 at 0:17
  • @DavidGudeman Yes, I have thought of this before. But, in that case all knowledge comes from a mix of empirical observation and imagination. We use observation and try to interpret it in all ways we can. Jun 22, 2021 at 1:20
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    – J D
    Nov 19, 2021 at 19:25

4 Answers 4

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Short Answer

So, wouldn't any 'proof' of the laws of logic, imply the need for logic to prove its own existence?

No, and the reason for that is tied to the idea of 'proof'. Not all proof is rational. Some, in fact, consider proof an empirical matter, like the intuitionists in mathematics.

Long Answer

It is arguable that there is a deep-seated psychological need to claim that certainty can only be derived from rationalism, particularly deductivism which seems to have reached a technical apex with the hypothetico-deductive model. But long before the logical positivists sought to abolish metaphysics from reason, Descartes and his methods advocated for introspection as the best path to truth. In fact, rationalism can be thought of as a philosophy that relies heavily on the notion of logical truth. But there are multiple theories of truth, of which the theory of coherence is but one. In fact, there are several theories of truth, and many people use those theories to determine what exactly constitutes truth. So, married to one type of truth, one has to accept one type of proof. But, I suspect, most philosophers embrace aspects of various theories of truth.

But against this Cartesian ideal of the rational, particularly the logical, being the path to truth, other schools have pushed back largely motivated by arguments made by the empiricists. Among empiricists, theory has always been held suspect and subordinate to experience particularly those of the senses. In fact, the marriage of logic and experience, which stretches back to the ancient Greeks, but perhaps reach a culmination in theory with Kant and his Critique, seem to suggest that knowledge is not just a priori, but also a posteriori. That is theory and experience strike a balance.

In mathematical and logical circles, great stock is placed in logic as a means to truth, but other philosophers have sought to tie truth of logic to what is often referred to as states of affairs, a phrase wielded by early Wittgenstein, particularly in his Tractatus Logico-Philosophicus. Here, a theory truth resulting from correspondence is dominant. That is to say, truth is not based in logic, but in the physical reality we all seem to participate in.

In this realm of truth, many of the first principles assumed by philosophers historically are rejected. A good example of this is mathematical intuitionism which is a collection of philosophical positions that posits that mathematical truth comes from the brain, and is not some sort of 'objective thing'. From WP:

In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied, but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possible independent existence in an objective reality.

So, is logic true because it is logical? Perhaps, but maybe logic is true and functional because it works, like in describing the state of affairs or as in any use of language, as a tool, a view known as instrumentalism.

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  • I'm glad you mentioned Kant here JD; are you keen to expand on why his Critique has been interpreted as a culmination of previous work on this topic, and how it addresses the circularity objection?
    – Paul Ross
    Nov 20, 2021 at 13:06
  • @PaulRoss No, and I'm tempted to remove the normative modifier just to avoid obligation. :D However, I'll tell you what I had in mind when I wrote it. Rationalism and empiricism as more formal doctrines were popular for quite awhile before Kant, but I think Kant, particularly in his contribution of the analytical and the a priori dichotomies, is seen at least by subsequent German Idealists as settling the question on how to reconcile empirical and rational epistemologies. I have noticed that even here on PhilSE, a lot of contributors rely on that terminology despite The Two Dogmas.
    – J D
    Nov 20, 2021 at 14:50
  • Because transcendental idealism seems to have impacted thought and language so thoroughly, it seemed like an allowable simplification, or better perhaps conjecture, to describe the CPR. If you have any objections to the use, or think I've missed some relevant point, go ahead and edit so that I might see. I am certainly no expert on Kant or CPR.
    – J D
    Nov 20, 2021 at 14:51
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human consciousness implies existence of reality and its logic
but human's non consciousness doesn't imply that there is no existence of such (specific) reality
You don't need logic to prove logic, Logic exist without a need for a proof, without logic there is no meaning to life But no meaning to life doesn't mean there is no logic!
logic exist objectively , logic exist in all dimensions.
there is no reality without logic, but logic exist even if there is no reality .

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  • Welcome to the site. Please see philosophy.stackexchange.com/help/how-to-answer We expect a philosophical context, and references where appropriate. Who says these things? What schools or traditions are they part of? You seem to be 'arguing by lack of imagination', without awareness of alternatives to your position, enough to be sure you can eliminate them.
    – CriglCragl
    Jun 21, 2021 at 19:23
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there is no way to say for sure that the laws of logic exist beyond human reasoning

There is no way to say for sure that anything exists beyond your own personal experience.

Our brains learn as newborn babies to make sense of our stream of consciousness, for example it is thought to take a couple of years to build a sense of self. We have no control over that, it happens to us as we grow.

Similarly, the rules of logical thought grow in us. But they do not grow the same in everybody. People from very different cultures and environments can have very different modes of what they regard as reasoning.

And indeed there are many logics to choose from. It is one of the logician's fields to strip away one "law" after another and see what thinking can still be done without it. There is usually a common residuum, such as the notion that if I make a statement today, it will still be the same statement when I revisit it tomorrow, or if I negate it then the negation is not the same statement any more. But it is amazing how low you can get and still come up with a rational system on its own terms. What you add back in to create your personal baseline is a matter of choice - of horses for courses, as they say.

ZFC - Zermelo-Fraenkel set theory with the axiom of Choice bolted on - has seen much popularity in certain academic circles (though not with me).

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Is Logic necessary to prove its own existence?

All logical arguments (logical proofs) start from some premise which is assumed true. The general form is "A, therefore B", or, hypothetically, "If A, then B".

Consequently, any proof that something exists has to assume some premise that implies the existence of this thing. Example of a logical proof of God:

  1. If I see something, then it exists;
  2. I see God;
  3. Therefore, God exists.

I'm not sure why nobody ever offered it as an ontological proof but it is perfectly logical. The only problem of course is whether we can say that we know that the two premises are true.

A logical proof that logic exists then could go like this:

  1. If I reason logically, then logic exists;
  2. I am reasoning logically right now;
  3. Therefore, logic exists right now.

Again, the main issue here is whether we can say that we know that the premises are true.

Our knowledge is based purely on empirical observation.

Empirical data is all we have to form an idea for ourselves about the material world. If we see a tree, we are convinced that the tree we see is a real part of the material world. However, this is not enough to claim knowledge about the material world, for our visual perception of the tree is not the tree itself. Thus, at best, empirical data allow us to arrive at plausible beliefs. It is more plausible that there is a tree in my garden if I can see it that if I cannot. We live our lives trusting our perception of the world and this seems to be sufficient to prosper and reproduce. Our fallacious claims to knowledge are driven by competition between human beings and our dependence on social interactions for our survival.

There is no doubt that we knows things. We don't know the material world, but we know the beliefs that we have about it. When we see a tree, we know the visual perception that we have of what we assume is a tree. In other words, we know the contents of our mind. If we assume that our mind is somehow a property of our brain, and if we assume further that our brain is the result of natural selection, then we can understand why trusting our perception data is a good idea if we want to survive in the natural world. There is no certainty, though, and therefore no actual knowledge beyond the knowledge of our perception data.

Empirical data are our perception data. So our beliefs are based on empirical data, while our knowledge is limited to knowledge of empirical data, that is, knowledge of our perception data.

There is no way to directly observe reality or objective truths.

There is no way to observe directly the material world, but there is no doubt that our subjective experience is knowledge of reality. Reality in this case is circumscribed to the contents of our own little mind, but from that we are satisfied to somehow infer that the whole material world must exist. Not bad.

Therefore, there is no way to say for sure that the laws of logic exist beyond human reasoning.

The laws of logic don't exist beyond human reasoning. Logic is the basic language of the animal brain, and human logic only exists inside the human brain, although it is very likely that all animal brains have essentially the same logic as we do.

That being said, the human brain is an integral part of nature, so logic essentially exists in nature. However, since nature is part of the material world, we don't actually know that this is true, but it seems good enough that it be very plausibly true and there is empirical evidence to support this belief: Sword fish have been shown to infer which male fighter is strongest based on the observation of fights between other males. If A beat B and B beat C, then A must be stronger than C. Isn't that good enough?

So, while we couldn't actually know that logic exists beyond our own mind, we can be pretty sure that it does. Of course, we don't need to look at fish, we can observe other human beings. Aristotle's Prior Analytics should be good enough. Ignore the syllogisms, but read the more than twenty pages of his logical reasonings about syllogisms. The mere fact that you can understand somebody else's reasoning should be enough to feel certain that logic exists outside your own mind. Indeed, without Aristotle, most likely you wouldn't even be aware of your own logical sense. But you will probably never actually know that logic exists outside your own mind because you cannot know that anything exists outside your own mind.

So, wouldn't any 'proof' of the laws of logic, imply the need for logic to prove its own existence?

Logic is not the kind of thing that needs to prove anything. We are. All logical proofs amount to the same thing: start from assumed premises, derive a conclusion logically. However, there are things whose existence we don't need to prove logically. If you know something, then it exists and this is your own proof. I know the colour blue whenever I have the impression of the colour blue. There may not be anything actually blue outside my mind, most likely not, but I can report that the colour blue as I enjoy it is really lovely. And we can also enjoy reasoning logically. This is how we know that logic exists. We could not actually know that it exists in other people's minds, simply because we don't even know that other people exist themselves, but it has to be good enough that it seems most plausible that it does.

The pretence that we know stuff leads very many people to ask metaphysical questions impossible to answer, such as this one. Do things really exist? Where is the proof that things really exist? Well, there aren't any "absolute" proof of anything outside our own mind, but there is all the empirical evidence that one could possibly need to feel very confident that logic exists in other people's minds, and very plausibly in pigs' and cows' minds as well.

And you should ask yourself: How would you even guess what it is that other people mean when they don't actually say it? If we didn't all have the same logic, there would be no way to tell. And we all have the same logic because human logic is the result of natural selection and so comes with our DNA, and we share most of our DNA with other people. Without a common logic, there would be no reason for us to understand Aristotle's reasonings across the more than twenty pages of Prior Analytics. This is good empirical evidence and there is no other.

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