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What if I say there are both two and three apples in the image above?
The honest assessment then is that you're insane or an imbecile
And on two separate occasions, I count 2 and 3 apples.
Well you've then lost touch with reality
Let's then go further to say that this would align with my logic
That then is not 'logic' but the denial of logic
that math is simply a set of approximations for a given value, rather than a definite unchanging result, so there would be 50% chance that I would count 2 apples, and a 25% chance I count 3.
If my logic leads me to fundamentally different conclusions, why does your logic, rationally speaking, have to be more valid than mine, besides a simple belief that it just is?
Well let's take 3 fingers instead of apples , if I asked you to count your 3 fingers and you counted only two then you would have no problem with me cutting of the finger you think is suddenly non existent and handing it to you , right?
I also asked you to give me a real world examples demonstrating this logical system you speak of and how it can be 'logical ' if it yields different results each time? You didn't supply an answer to my request give me real world examples please?
You don't create your own truths you create your own beliefs regarding truth claims this distinction you fail to see, reality is in contrast to fictional , illusory views of the world , truths are collective concepts having individual versions is insanity
As I said in my opening statement you're referencing Humes problem of induction and repeating it time and time again , I get it regards absolute certainties so all that remains is your claim regards creating your own truths the flaws of which I pointed out one or two
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What if I say there are both two and three apples in the image above? And on two separate occasions, I count 2 and 3 apples. Let's then go further to say that this would align with my logic that math is simply a set of approximations for a given value, rather than a definite unchanging result, so there would be 50% chance that I would count 2 apples, and a 25% chance I count 3.
There are two apples visible and one apple that is small and obscured from view by the other apples. The self-evident truth that might be held true is an apple can obscure the view of other apples when photographed.
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If you drop an apple, then either it will fall or it will not; no other options exist. You can drop an apple and see what happens, and then you will be able to say, "The apple fell", or "The apple did not fall". You cannot say "The apple fell and did not fall", or "The apple neither fell nor did not fall", in a meaningful way.
For your latter question, in natural science we build models, not prove theorems: physics is not mathematics. In physics certain assumptions are inevitable if we want to build any model whatsoever, and one of the core assumptions is that the Universe features certain laws that are discoverable. By observing patterns, reproducing them and failing to deny them we find approximations to those laws, and the more experiments we perform, the more certain we become that those approximations are very close to the actual laws.
If you have a better idea than this, feel free to propose it. I have never heard of one, but I am open to suggestions. Simply saying that lack of 100% certainty means that anything goes is lazy thinking. There is a difference between having 0 certainty, and having a lot of certainty, just not 100% - and you know it well from your own experience, when, getting into a bus or a car, you do not every time consider the possibility that the bus or the car will suddenly turn into a T-rex and eat you alive.
It is based on the very definitions of these terms, and it is not arbitrary at all.
It is not an axiom, but a consequence of definitions of these terms, as I have already explained. You are free to use other terms instead, but you keep using these ones, so please learn about their definitions if you do not want to keep making objectively wrong statements.
I am not sure what you mean by "more right". Logic is logic, and within it a statement is either true or false. Different systems of logic may lead to different statements, but they cannot lead to different interpretations of terms "true" and "false".
That is the problem though: you do not seem to follow those definitions. By 1, 2 and + I mean the same things as any mathematician does, while you seem to treat these as random symbols you can assign any meaning to.
Human communication does not work this way, my friend: if we are to communicate effectively, we have to be sure that we mean the same things by the same words. If you want to come up with your own language and speak it, then be my guest, but do not be surprised when other people do not understand what you are trying to say.
It does not need to be falsified or proved when it is baked into the system. It is like asking, "How do I know that I am alive?" Well, the very fact that you are able to ask this question is a testament to the fact that you are alive. Proof of your aliveness is not needed if it has already been explicitly demonstrated.
The fact that one's perceptions are not perfectly representative of reality does not at all imply that it is impossible to make accurate observations of reality. When you wear glasses, your perception of depth is distorted - yet your brain can correct for that, and you still can pretty accurately estimate distances, shapes of objects, et cetera. Every human, and every imaginable intelligent being at that, perceives the world through a system of filters, and nothing prevents him from studying those filters and correcting for the biases introduced by them.
As for how it can be objectively determined - life has a funny way of punishing people for being wrong. If you disagree that jumping off a cliff is hazardous to your health and decide to act on that disagreement, the Universe will slap you in the face and you will pay for your refusal to correct for the "bugs" in your understanding of the world. People who ignore the reality and live in their own imaginable world do not last long in this world, and history is full of examples of all kinds of ivory tower philosophers who made elementary blunders and died in hilarious ways because they thought that the weird constructs they built in their minds trumped the reality.
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