What is the difference between empirical experience and deduction? Certainly it is direct or sensually experiencing the stimuli on the basis of which we deduce. But our sensory experience is not everything, below I will present an example:
I feel that it is cold and shivering, but touching the radiator I find it cold and I can see that the weather is nice outside, that I'm feeling warm and that my sensations are inadequate in relation to the weather. But I am cold, what can I do? I put a thermometer under my arm and after some time it indicates 34.09 C. I find that I have a cold and it is nice outside.
My deduction is based on three sensory modalities: touch, sight, body temperature. Which one gives us adequate data? We dedicate based on sensory experience. "This view was already expressed by Bertrand Russel, stressing that" Kant observed that his contemporary geometers could not prove their claims with the help of no additional reasoning (unaided argument), but needed a reference to the drawing, he created a theory of mathematical reasoning, according with which inference is never purely logical, but always requires the support of what he called, ''
Visualizations in mathematics in the face of epistemological tradition. To reach the conclusion, we had to confront with each other, four epistemic modalities.
p - I feel that it is cold, shivers penetrate
q - By touching the radiator, I find that it is cold,
r - The weather is nice outside
g - It's warm
m - My sensory feelings are inadequate to what the weather is like
v - The thermometer indicates 34.09 ° C.
g - I find that I have a cold
d - The weather is nice outside
Some of the premises mentioned above support each other in the deductive system
The above formalization is made in the KRZ, let's try to add epistemic modalities.
@ - I feel
# - I touch
$ - I see
% - I know
(((@p ^ #q ->% (r ^ g)) ^ $ m ^ - v ^ k)) ^ (b ^ c)) -> (g ^ -d)
& - smell
^ - taste
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