This is the most basic foundation of analytic truth:
New concepts are created and they are assigned a Name
The axiomatic argument of the Münchhausen
states: "accepted precepts are merely asserted rather than
The axiomatic argument, which rests on accepted precepts (i.e. we
reach some bedrock assumption or certainty)
We can know with certainty that a gross pay amount of $400 is correct if the number of hours worked was 40 and the $ per hour was 10. The semantic meaning of the product of decimal integer 10 multiplied by decimal integer 40 is defined by its algorithm to be 400.
This example proves that some knowledge is defined by an algorithm that has been assigned to a term. The "product" of two integers is defined by its algorithm.
Analytic propositions are true solely by virtue of their meaning
We can overcome this objection by realizing that when brand new ideas are created or discovered they are assigned to a term. This is the beginning of their foundational basis. The term: "the big bang theory" has been assigned to a connected set of ideas.
At the point in time when the ideas have been assigned to a term they are merely asserted rather than defended. The assignment of these ideas to a term however, is known with logical certainty.
We can also know with complete certainty that the term: "the big bang theory" has been assigned to the category of possibly true rather than definitely true because it is called a theory. So the big bang theory itself cannot be construed as knowledge because knowledge must be definitely true. Analytical knowledge must be definitely true entirely on the basis of its meaning.
The big question is how do we know that an expression of language is definitely true?
We can definitely know that the connected set of ideas the define the concept of arithmetic makes this expression true: "3 > 2".
Isn't that just an example of an expression that is merely asserted rather than defended?
No it is not. The connected set of ideas of the knowledge of arithmetic form a subset of the body of analytical knowledge. It is a set of ideas that fit together to mutually define each other.
None of these ideas are merely asserted they all fit together to specify an algorithm (definite sequence of operations). From this algorithm we can decide whether or not an expression such as "3 > 2" belongs to the set of expressions comprising the knowledge of arithmetic.
When we look at this using mathematical terms we are establishing some expressions of language as axioms of the formal system of that language. For all practical purposes the axioms of a formal system are stipulated relations between the objects of that formal system. These stipulated relations comprise the basic concepts that the formal system operates with. They are the building blocks of the system.
The arithmetic of natural numbers depends upon the concept of an ordered set of numbers. At some point in time someone had to create this concept and assign it to a name. So the way that the axiomatic argument of the Münchhausen trilemma is overcome is that new concepts are created and assigned a name.