Logic: Conditional statement “if” as logical truth maker.

I hope to categorize functions of conditional statement in ordinary language and logical language into neat blocks.
But in this several posts about conditional statement, I will try to characterize it by two points of view: as logical truth statement maker, and as tracking signal of uncertainty like bookmark in the next post.

I think, at least now, that the goal from the attempt is to make a neat data format to describe scientific paper in “if ~ then” manner. The style provides visual key for what the paper actually assume without proof and how it infers the conclusion.
The format would be a good tool for scientific/ risk communication between citizens and specialists.

This post is about making logical truth statement by if ~ then statement.


The Basic:

A beneficial aspect of “if ~ then ~” statement is avoiding confirmation whether the premises are actually true.
When you put if on uncertain part, you can focus on how valid the definition of words and inferences are. And if all of them are valid, you can say it’s true.
For example, if you don’t certain whether it’s going to be a rainy day or sunny day, you can fix the assumption on either rainy or sunny by if statement, like “if it will be rainy tomorrow, then ~”.


The analogy:

The image is the analogy of this perspective of conditional statement.
In the CGI, “If” is an plug to prevent overflow of question whether it is true.



Continuity of axiom to common knowledge:

Ultimately, if all of the possible assumptions and inference rules are specified, it could be an axiom.

Inversely, if all of the possible assumptions and inference rules are not specified, it could be an definitive statement depending on common knowledge which everyone accepts.

Among the excessive two condition, in many cases, we argue something with a patch of implicit and explicit assumptions and inference


Usage and tricks of conditional statement:

Scale free:

“If ~ then” is like wrapping on a statement. You can wrap almost any statement including counterfactual things “if intelligent alien had already come”, or “if I were a wild bore”.

You can also nest “if”in multiple depths.

I call it “assumptionizaion”.

After assumptionize an statement, you don’t have to check if this is a true, instead, you should define the meaning of this and provide correct inference from it.

Unless trick:

“If ~ then” statement is not only for pinpoint assumptionzation. It can cover all except an pinpoint so than you don’t have to specify conditions in detail.
For example, “if ~ unless other conditions are not as usual, then ~”.

Of course, it remains a task to define what the usual condition is. But you can transfer the argument to the part of definition. If you convince the definition, you can pass the


Why do not all of scientific statement say that way?:

It it can provide true statement, why do not all of scientific statement obey the style?

There is enough reason not to use it. In many field, dividing into a few condition and inference in useful way is hardest part of scientific studies.
Moreover, many phenomenon can’t describe it such way in principle. It is similar problem with computer simulation. For example, chaos, randomness, lack of computability, hardness of detection data through experiments.


Relationship with logical positivism:

The point of view for conditional statement as true maker shares some overlapped idea to logical positivism. But this is not same as the idea in the post sequences.
logical positivism aims to construct true system by undoubtable empirical statement and logical inferences. I don’t sought such extreme purpose.

I want to check characteristics of “if ~ then”, and use it through actual data format for checking scientific papers about actual point that need to argue in public. And that would be a good format to scientific and risk communication between citizen and scientist.

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