Justify intuitionistic logic through the BHK interpretation could be problematic
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Assessment
- Difficulty
- 5/5
- Estimated time
- Over a week
- Newbie friendliness
- 25/100
- Issue type
- Documentation
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- Needs clarification
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- Stale
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- tex
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- documentation
Research direction
The issue does not name a file, test, or entry point. Start by locating the OLT's BHK justification and compare it with the cited discussion from van Dalen and Troelstra. Done means adding a clear, agreed-upon explanation of what constructive functions or transformations mean and why the classical reading is insufficient.
Written by the indexing model from the issue text.
Description
Using the BHK interpretation to justify intuitionistic logic requires a discussion on what we mean by a "function" that transforms a construction of A to a construction of B. van Dalen and Troelstra writes (in Constructivism in Mathematics):
This exercise shows that the BHK-interpretation in itself has no "explanatory power": the possibility of recognizing a classically valid logical schema as being constructively unacceptable depends entirely on our interpretation of "construction", "function", "operation".
The OLT is justifying the ND-rules for intuitionistic logic using the BHK-construction, but a similar BHK based argument justifies the RAA rules as well (interpreting "function" as a classical set theoretic object).
I think this should be commented on in the text together with a discussion on what a constructive transformation could mean. I'm afraid I won't be able to do it good enough.
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