What must be defined and what must be left to intuition?

[Werg22]

Lately, I've been interested in logic, mainly to get answers to many questions I ask myself that I feel if left unanswered, I will never be satisfied with how I understand the way things work and are. One thing bothers me: I haven't found an author who makes a proper treatise of "where to start". I know nothing can be ever said or done if we constantly try to give definitions and meanings to things that refer to previously established definitions and meanings - one has to stop at the intuitive level. But the question is, where do we set this "intuitive level"? What words, aspects of our speech and logic should should we delegate to intuition, and which ones should we clearly define?

 

[JoeDawg]

I haven't found an author who makes a proper treatise of "where to start".

Descartes.

 

[Werg22]

In which of his work? Meditations on First Philosophy?

 

[JoeDawg]

In which of his work? Meditations on First Philosophy?

Well, yeah. That's where everything starts.

 

[HallsofIvy]

Before you can talk about an "intuitive level" you will first have to define "intuition". What do you mean by that?

(I know one person who define "intuition" as "prejudice"!)

 

[JoeDawg]

(I know one person who define "intuition" as "prejudice"!)

Is it something else?

 

[moving finger]

(I know one person who define "intuition" as "prejudice"!)

intuition : the power or faculty of attaining to direct knowledge or cognition without evident rational thought and inference

prejudice : an (adverse) opinion or leaning formed without just grounds or before sufficient evidence

what is the difference?

The problem that Werg22 faces is that, to answer any question about anything, we must start with some premise(s) - and the truth of these premises in turn must be based either on some other logical/rational/coherent argument, or they must simply be assumed to be true. To avoid infinite regress, our arguments must ultimately be grounded in assumed premises - call them intuitions or prejudices if you like.

 

[JoeDawg]

To avoid infinite regress, our arguments must ultimately be grounded in assumed premises - call them intuitions or prejudices if you like.

Either that or they can be grounded in what is called 'self-evident' premises... which brings us back to Descartes.

 

[Moridin]

To avoid infinite regress, our arguments must ultimately be grounded in assumed premises - call them intuitions or prejudices if you like.

Self-refuting since it is self-referentially incoherent.

 

[octelcogopod]

Usually an assumption holds true if it works into the system in a way that works for us, it neither assumes be to true or false 'in reality', it just works then and there.
This is usually where intuition comes in, we intuitively assume something based on what works or not, and then maybe science can figure out how it really works.
And also about infinite regress.. I don't think that's an issue, because as long as the system works, and we are able to study something, we will either find out that studying it is fruitful, or that it is not, and as such we could hit many results before infinite regress ever becomes an issue.

I guess an analogy would be that just because the lake is 10,000 meters deep, doesn't mean we can't bathe on the surface, or even dive a little bit, you see what I'm saying?
Infinite regress is only a problem when we actually see that it might be true, the concept itself before that fact is harmless.

 

[Hurkyl]

I know nothing can be ever said or done if we constantly try to give definitions and meanings to things that refer to previously established definitions and meanings - one has to stop at the intuitive level.

False dichotemy. An axiomatic definition requires neither an appeal to intuition, nor an appeal to previously established definitions and meanings.