The Truth Of Axioms

There are some who claim that axioms cannot be proven, and here I will prove them wrong.  The issue is of such epistemological and ontological importance that I will abruptly dive into the matter instead of more lengthily elaborating on the topic.  I have defined axioms and discussed them elsewhere (I have links below), so check those if you need clarification about what an axiom is or about the nature of axioms before reading this.  It seems that these people believe that axioms are unproven or unprovable assumptions because they are the starting points of all knowledge and thus they are not conclusions based upon previous premises.  This is a great error.

Axioms are self-verifying, the greatest possible proof there is.  They are true no matter what else is, as I have explained multiple times.

Consider the following syllogism below:


1. If the sky is blue, the sky is not green.
2. The sky is blue.
3. Therefore the sky is not green.


Axioms do not have to be proven by syllogisms like the conclusion I stated above.  They are not reached by more foundational principles because there is no way to go back further into reality and epistemology than them; they are true by pure necessity and apart from their existence we would be unable to know anything at all about reality because we would have no starting point for knowledge.  If someone says that axioms are not proven by other premises, that person is correct.  But if he or she claims that axioms cannot be proven at all, then he or she either does not understand the concept of an axiom or is intellectually impaired.

Something that is provable either can be proven by a deductive argument or by the necessity of its own truth.  Simple reflection can provide knowledge that some things cannot be false.

Look at the statement below:


Truth exists.


This statement is not proven by preceding premises.  It is proven through the inescapable impossibility of it not being true.  It is impossible for truth to not exist.  Now, the questions of whether or not God exists, whether or not slavery is right or wrong, or whether or not we can know anything about truth beyond its abstract existence are all separate issues.  But regardless of the answer to any of these or other questions, truth still exists unavoidably.

See here for other examples of axioms [1].

If someone denies or doubts axioms, ask them simple questions that reveal the impossibility of their nonexistence or unreliability.  If someone claims that truth does not exist, ask "Is that true?"  If someone says that words cannot convey truth, ask "Then how are you communicating that truth using words?"  If a person insists that deductive reasoning is unreliable, ask "How do you know?"  He or she will inevitably use deductive reasoning in the answer, proving that either way deductive reasoning is reliable.  If someone tells you that due to our limitations we can't know anything, ask "How do you know that?"

This is a very effective method of demonstrating the existence and truth of axioms without defining terms precisely or explaining anything; if someone denies axioms, simply ask them brief questions that will illustrate how he or she is admitting axioms exist because it is impossible not to.

Don't listen to anyone who argues that axioms are unproven or unprovable.  Apart from them, no knowledge is possible whatsoever, regardless of what people may claim.  Axioms are not proven by other premises because they inherently possess the greatest possible proof--a self-verifying nature that is true independent of whatever else is.


[1].  See below:
  A.  http://thechristianrationalist.blogspot.com/2016/10/the-self-evidence-of-logic.html
  B.  http://thechristianrationalist.blogspot.com/2017/01/the-error-of-presuppositions.html