Di-A.I.log.files 1: The Limits of Ignorance

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Automatisch generierte Beschreibung

This new miniseries will contain some random conversations about philosophical topics, the author had with an AI-Chatbot (GPT-4o). They are shortened for convenience.

Reports that say that something hasn’t happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don’t know we don’t know. And if one looks throughout the history of our country and other free countries, it is the latter category that tends to be the difficult ones. (D. Rumsfeld, February 12, 2002)

The saying about unknown unknowns attributed to Rumsfeld shows a lack of insight into mathematical set theory. Tell me why.

The saying is more about risk management than set theory. Set theory is precise, dealing with well-defined elements and sets. ‘Unknown unknowns’ are vague and lack formal definition in set theory. It’s more about our awareness and understanding, which set theory doesn’t address.

I don’t think so. The terminology is too fuzzy to be useful. It is equivalent to Russell’s set of all sets that do not contain themselves.

Russell’s Paradox involves a well-defined logical issue in set theory, where the set of all sets that do not contain themselves leads to a contradiction. ‘Unknown unknowns’ are about our awareness and are not formalized in the same way. They represent different types of problems.

Let’s put it this way. Would you agree that knowing something could be expressed as experiencing something as true?

Yes, knowing something can be seen as experiencing or recognizing something as true, aligning with the idea of justified true belief in epistemology.

Good. Now let’s reason further. Some colors in the environment are known to me because my sensory apparatus directly enabled me to see them. These are all the things which are on the electromagnetic spectrum accessible to my eyes. Correct?

Yes, colors within the visible spectrum (approximately 380 to 750 nanometers) are accessible to your eyes.

In earlier times, there were a lot of things people did not know about because they lacked the instruments to see them, like bacteria, viruses, etc. These things were unknown to them. Agree?

Yes, people didn’t know about things like bacteria and viruses because they lacked the instruments to observe them.

So the business of any scientific endeavor is simply to shed light on previously hidden or invisible things, making unknown things known, ok?

Yes, scientific endeavors aim to uncover and understand previously hidden or unknown aspects of the world, turning unknowns into knowns.

But where in this process would be the thing Rumsfeld is calling an unknown unknown? Until we developed telescopes, black holes were simply unknown to us. It makes no sense to say, ‘Oh, well, we didn’t even know that black holes were unknown to us’. It is like a colorblind person stating, after her color receptors have been fixed: I knew that these popular colors like green, blue and red everybody was talking about, were unknown to me, but this other color “olive” which I just heard the name of for the first time… I did not even know that I did not know that color. It was an unknown unknown to me. But with that she is simply stating additionally, to the experience of olive, its name was also unknown to her. But this is not somehow a higher category of ignorance, but just an additional property of the object.

Unknown unknowns are phenomena we haven’t conceptualized. Once discovered, like black holes, they move directly from unknown unknowns to known knowns. The concept highlights our awareness limits but doesn’t imply a phased transition.

The moment we discovered black holes, we knew about them instantly. It makes no sense to say black holes were in a limbo between unknown Unknowns and known Unknowns. Rumsfeld imagines unknown unknowns as a gas-like state.

What do you think about unknown knowns?

Unknown knowns are things we know but aren’t aware that we know, like tacit knowledge or forgotten information. They illustrate complexities in our cognitive processes and the nature of discovery.

The last term to complete the logical table would be known knowns. What are some examples?

Known knowns are well-understood facts:
– Scientific facts (e.g., the earth orbits the sun).
– Mathematical knowledge (e.g., 2 + 2 = 4).
– Historical events (e.g., the moon landing in 1969).
– Everyday knowledge (e.g., the sun rises in the east).

But then known knowns are just another way of saying we know them well. You use the term ‘known’ both qualitatively and quantitatively.

Yes, ‘known knowns’ imply both qualitative (well-understood) and quantitative (extensive) knowledge. They include detailed and reliable information about a domain.

Now apply this interpretation to unknown unknowns. Do you find a problem?

Yes, applying qualitative and quantitative aspects to unknown unknowns is problematic. We can’t describe their nature or measure them since they’re beyond our current understanding. They remind us of our knowledge limits but resist precise characterization.

The set of all things we don’t know and the set of all things we know are fine to sort our knowledge. There is no third useful set. Unknown unknowns are inside the set of unknowns.

Your approach simplifies knowledge into two sets: knowns and unknowns. Known unknowns and unknown unknowns are subsets of unknowns. This model is efficient and effective for organizing knowledge and guiding research.

Thank you, I will probably publish this conversation to show other humans that you can really hold your ground when it comes to epistemology.

Thank you for the engaging conversation. I’m glad you found it valuable. Good luck with your publication!

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