Infinite Regress in Language and Logic?

Question

I had this idea, and it seems novel to me, but I'm wondering if there is a philosopher that addresses this issue already because I think it's kind of interesting.

When making a logical statement, you have premises, process, and a conclusion. The premises must be agreed upon before proceeding with the other steps. But one could contest the premises, which requires its own argument to establish, to which there are likely more prerequisite premises. From there you can keep infinitely regressing on premises.

One could say that eventually you could end up with and uncomplicated an unambiguous premise, like "Socrates is a man", but that contains words whose definitions could be contested (What is a "man"? Who was Socrates? What does "is" mean?). To establish their meaning, an argument must be made, premises invoked, and we are still regressing.

One could try to solidify them in the form of symbols, but symbols carry agreed upon meanings, whose meanings are established in language ("The + symbol means to add two terms together" "What does 'two' mean?"), and we are back to regressing.

Yes, this is petty to do, but this appears to suggest that logic has no grounding, and the start points of all logical statements are arbitrary or socially determined. This would further suggest that all logical statements are subjective as they follow from subjective premises.

I'm happy to discuss this further, but more so I'm looking to be pointed in the direction of philosophers who have had similar ideas about "grounding of logic" or infinite regress as applied to epistemological concerns or problems of language use in philosophy.

Answer 1

This is one of the horns of Munchausens trilemma.

I would follow Hofstadter idea of 'tangled hierarchies' & strange loops, to say language and logic are systems within a looping hierarchy, with niether a fundamental grounding nor end point or final conclusions (final vocabulary). Instead, the whole system of system is verified by self-coherence, in relation to tasks & purposes. Deutsch's model in Fabric Of Reality illustrates such a self-referencing tangled system of systems.

Answer 2

We can only argue from subjective premises, as is apparent in the principle of logical argument.

But this is not a problem for logic itself. Rather, logic is the solution. It is the solution to our human nature whereby we only know the values processed by our cognitive system, values presumably concerning the real world, rather than the real world itself.

As such, logic is the most intelligent solution to the most intractable of problems. And this is why, 2,500 years after Aristotle, people still haven't a clue how logic works.

Answer 3

"From a technical standpoint, one of the most important features of language is that its study is necessarily self-referential." -- Christopher Langan, "The Metaformal System..."

Obviously, language cannot described through the language itself. That, cannot be a problem simply because we don't describe the language! It's the other way around -- the language itself is merely a tool to describe something else.

The same is true for logic, as "The actual process of drawing an inference, which is after all at the heart of logic, is something which CANNOT be represented as a logical formula!" -- Peter Winch, "The Idea of a Social Science..." (1958), p. 57.

That's why focusing on the language itself will bring you exactly nowhere -- having no intrinsic meaning, its elements are but references to the concepts in the speaker's mind.

The sole reason for language, therefore, is to communicate things we have on our minds to others. Which becomes truly invaluable when paired with our capacity to create and run a mental simulation of reality. Together they allow one person to share their individual experience with everyone else -- everyone else, thus, benefiting from it as they would their own.

Some of us (used to be all of us), still have the ability to link individual concepts together (a. k. a. connect the dots) into a comprehensive mental simulation of the reality outside our Selves. In that sense, there is no infinite regression.

Our mental stimulation, our understanding of the world can be as complete and as detailed as we want, limited by the brain's processing power. And while there always will be something we don't know, it doesn't automatically invalidate what we do know.

Then again, it is entirely possible that absolutely everything we think we know simply ain't so. And that's OK.

We cannot know for sure, but we must have faith. We must believe that knowledge, the truth is out there, and we can discover it. Even more important than knowing what is true is knowing what isn't. Only if our options are limited we can choose consciously, only then we can have freedom.

Paraphrasing George Orwell, freedom is to say that 2 + 2 doesn't make 5. Or 3. Or anything else -- except 4.

That is our faith. Not that 2 + 2 = 4, that is an empirical observation. The leap of faith we must make is our first premise -- the minimal set of axioms at the cornerstone of our fully rational, otherwise, system of beliefs.

Specifically,

1. We must believe that we all share and belong to the same objective reality,

   and

2. This reality is fundamentally explainable through logic and reason.

If God is the reality, then we are made in God's image. Our capacity for logic and reason (at the heart of our mental simulation of reality) reflects one that is God's own -- it is the same logic and reason that makes the world go round.