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:
- If I see something, then it exists;
- I see God;
- 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:
- If I reason logically, then logic exists;
- I am reasoning logically right now;
- 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.