Axioms are subjective (?), and, since propositions are based on axioms, isn't everything subjective? (of course, the answer should be from the perspective of someone who believes in objectivity)
Or am I wrong in the assumption that axioms are always subjective?
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What does it even mean that "axioms are subjective"? That each have their own? What difference does it make? Reality hits men with a brick on the head the same way, regardless of their axioms. Please provide more context, it is unclear what your words mean and what you are asking.– ConifoldCommented Feb 12, 2022 at 6:33
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We need always assumptions as starting points for our discussion, communication, understanding of the world. Mostra of them are simply unnoticed. In mathematics they are explicitly stated and shared and thus they are not "subjective" in the sense you are alluding.– Mauro ALLEGRANZACommented Feb 12, 2022 at 10:00
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Propositions are not based on axioms. You seem to be confusing the different types of logic as if it was all one. Axioms are a math thing. Philosophy does not need axioms nor does deductive reasoning. We can reason with zero axioms.You are also probably confused with TRUTH as if that two ot had one type. Truth has multiple contexts. Objective truth is the highest form of truth humans have so far. Objective truth is constant & never changes.Because you are unaware of something doesn't mean there is no truth. Propositions are supposed to be only objective. Doing subjective thinking is Psychology– LogikalCommented Feb 13, 2022 at 16:32
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1 Answer
You can fix any group of axioms you like and start deducing consequences. You built a theory in that way. Your theory is useful if there are models of the theory that are interesting to someone and you were able to deduce non trivial consequences from the set of axioms you have chosen. I would say that in order to discuss sets of axioms you need to introduce the notion of model. Otherwise things get messy. Looking at things on this way I would say you don't have to worry about subjectivity and objectivity. An axiomatic theory does not tell you how the world is. It gives you tools to deal with the aspects of reality it models.
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1To tell how the world is Vs to deal with the aspects of reality it nodels. What is the difference ? Commented Feb 13, 2022 at 9:36
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Look at the following situation: a highway is empty. Thousand cars start moving all in the same direction. After some time groups of cars have to slow down, maybe even stop. Why? There is lots of space... You can make some assumptions about how the cars behave (isolate a set of axioms), deduce some properties from those assumptions and built a computer model that verifies the axioms and in a sense reproduces the phenomena. At this point I feel like I understood this aspect of reality. This understanding presupposes many beliefs I have about how the world is.– Just meCommented Feb 13, 2022 at 10:54
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I have and I will always have many unsubstantiated beliefs about he world. When I stumble in a problem, maybe I will question some areas of my system of beliefs. Maybe I will explicit them, examine them, replace some, produce a theory and use it to illuminate some part o reality. My understanding of this part of reality is based on the theory I developed and in a series of beliefs, many of them I am not even conscious of.– Just meCommented Feb 13, 2022 at 11:35