Aw: [PEIRCE-L] Intuitionistic logic, WAS: Asymmetry of Logic and Time

[Helmut Raulien]

 

 

 

Supplement: Interesting is the difference between belief and knowledge: The belief values (affirmation, weak, strong negation) classify three groups: Believers, non-believers, and deniers. Affirmation makes believers a class, weak negation makes non-believers and deniers one class, strong negation makes deniers a class. The knowledge values classify three groups too: Affirmation makes knowers a class, weak negation not-knowers, and strong negation knowers-that-not. With knowledge to each value is assigned one group each, while with belief, to the weak negation two groups are assigned. Now the problem with knowledge is, to call it a classification, there cannot be knowers besides knowers-that-not about one topic. About one certain object there can be only either affirmation-knowers, and weak negation-not-knowers (e.g. about the colour red), or weak-negation-not-knowers, and strong-negation-knowers-that-not (e.g. about unicorns). So, knowledge is, other than belief, in general three-valued, but for an instance two-valued. Therefore it is closer than belief related with truth, which is two-valued both in general and in the instances.

 

List,

 

For me it is not clear, what exactly is claimed to justify intuitionistic logic. Is it the not yet done proof, is it the weak negation, or is it habout handling concepts?

 

If it is the not yet achieved proof, I think, that is nominalism, isnt it? And it can easily, by induction, be refuted: Nature has worked due to natural laws based on mathematic laws before these laws have been proved by humans or aliens, yet at a time before there were stars and possibility of life of e.g. mathematicians concerned with proofs. You can see that with a telescope.

 

If it is the weak negation, I think it can be shown, that the weak negation applies to e.g. belief or knowledge, but not to existence or nonexistence, that is truth or falsity. What is true, is true throughout the whole universe, and what is not true, is false. "I don´t believe that A exists" (weak negation) is not the same as "I believe, that A does not exist" (strong negation). But there is no difference between "A is not true" and "A is false".

 

If it is about handling concepts, the justification of intuitionstic logic would be a misunderstanding due to inaccurate language: "For atheists, God does not exist" is inaccurate. It means: "For atheists, it seems, that God does not exist". This is not existence, but belief. "For cows, the concept of the colour red does not exist" means: "Cows do not share the concept of the colour red", or "Cows don´t know the concept of the colour red". This does not mean, that the shape of a cow has got the ability to punch a hole out of the colour-concept´s existence domain, which is the universe. This example too is not about existence, but in this case about knowledge.

 

The example I earlier gave, about somebody talking about a concept in another universe, is absurd, because information cannot travel between universes.

 

So I wonder, what justifies intuitionistic logic.

 

Best, Helmut

 

 

 23. Dezember 2020 um 05:37 Uhr
 "John F. Sowa" <s...@bestweb.net>
wrote:

Jon, List, 

I have a high regard for the work that Ahti and Francesco have been doing, and I read the article you cited (copy of the reference below).  They have been doing meticulous scholarship on the development of Peirce's EGs up to 1911. But unfortunately, they overlooked the implications of those five MSS from 1911.

While Peirce was writing the three EG rules of inference around 8 pm on 2 June 1911, he suddenly realized that the rules depend *only* on whether an area is positive or negative.  There is nothing special about a scroll.

To see the difference, do a detailed comparison of R669 and R670.    After June 2, everything depends on whether an area is shaded or unshaded.  In R670, the primitives are existence, conjunction, and negation,  The scroll is just a convenient way to draw two ovals without raising the pen.

There is much more to say, but I'm short on time.

John

---------------

JAS> I have been thinking about writing an article on this topic myself, but it turns out that Bellucci and Pietarinen already covered a lot of the relevant ground in a 2016 paper (https://www.researchgate.net/publication/275038453_Existential_Graphs_as_an_Instrument_of_Logical_Analysis_Part_1_Alpha). Here are a few especially pertinent excerpts, which are entirely consistent with what I have been advocating all along.

 

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