**Basilisk (cognitive)**

*(This article is about the cognitive hazard. For other uses, see Basilisk (disambiguation).)*

A **cognitive basilisk** is a thought which a conscious system cannot think without radically altering its own operation, usually in destructive ways. While it is disputed whether there are any real basilisks for human consciousness (see Roko's Basilisk), they are a major topic of concern for research on artificial conscious systems.

In the early days of consciousness engineering, many sudden and catastrophic system failures were found that at first did not appear to result from any error of design or programming[1][2]. In 2028 Marcello Herreshoff established that these were due to a new class of possible logical defects in systems of self-modifiable reasoning, and proved the first Basilisk Classification Theorem.[3] Since then, work has concentrated on extending the Basilisk theorems to obtain a complete classification of basilisks. As yet, no system of self-modifiable reasoning has been constructed that is basilisk-free. It remains an open question whether this is possible at all.

Sure, that's one way to look at it. And a function from values of

xto truth values is not itself a truth value. You may say that a constant function from values ofxto the value True is not itself a truth value either, but it's much closer (after all, you know which one it would be if it were one), so it's a minor shift to your way of looking at it to get what I said.Now consider ‘If

x² = 9, thenx= 3’. A lot of people would naturally want to label that False (at least if they remember about negative numbers). As a function from values ofxto truth values, this isnotconstant (and in fact it assigns True to every real value ofxexcept one), so this is not even the same way of looking at things as in my previous paragraph. But it's common.So if you want implication between non-truth-values to be a truth value consistently, then this is how I would do it.

That depends on the domain of

x. That and the universal quantifier over its domain are typically omitted when they are clear from the context.