In this post, we take inspiration from Kurt Gödel by looking at the system from an outsider’s point of view to detect malware.
Special thanks to my colleague Yochai Greenfeld for collaborating with me on this piece.
Kurt Gödel changed the face of mathematics by proving that a widely accepted truth about the completeness of the natural numbers system was actually unprovable. Computer science, which relies on the axioms of the natural numbers system, continues to bear the weaknesses exposed by Gödel’s findings. Modern software detection is one specific niche that suffers from this flaw.
Gödel was an Austrian mathematician, logician, and philosopher who specialized in the implications of logic for the foundations of mathematics. He studied at the University of Vienna and focused on the fundamental concepts of the natural numbers system (e.g., 0, 1, 2, 3…), which forms the basis of algorithmic logic and computer science. This system is built on axioms that define its logic. For example, one axiom states that 0 is a natural number and not merely a null representation.
Logical Systems: Completeness and Consistency
Logical systems rely on two fundamental principles:
- Completeness: Any claim within the system can be proven using the system’s axioms.
- Consistency: No two claims within the system contradict each other.
Gödel used these principles to construct the following paradoxical statement:
“CS cannot be proved within the system S.”
On the surface, this seems like a provable claim, but in practice, it is unprovable. The statement aligns with the logic of the system, but if it could be proven, it would refute the principle of completeness (since every claim should be provable). If it cannot be proven, it refutes consistency (since no claims should contradict one another). By demonstrating this, Gödel showed that logical systems have a limited ability to refer to or examine themselves.
Systems Have Limited Self-Attribution
Gödel’s mathematical proof mirrors what the linguist and philosopher Ludwig Wittgenstein described as the inability of language to refer to itself. Gödel showed that systems have a limited capacity for self-attribution because they depend on a closed logical subbase.
In the context of cybersecurity, this limitation explains why antivirus software and similar platforms cannot examine the entire system while being a part of it. These tools are subject to the same logical rules that govern the systems they aim to protect.
The Problem with Zero-Day Attacks
Zero-day attacks exploit vulnerabilities that were previously unknown, effectively operating outside the logical rules of the system. Cybersecurity platforms are unable to detect these threats because they cannot see beyond the logic of the operating system they are protecting.
Many cybersecurity companies continue to offer software-level solutions that promise advanced detection. However, these solutions are inherently limited by the logical inconsistencies Gödel described, leaving them blindsided to malicious activity occurring outside their scope.
A Flawed Arms Race
Enterprises continue to trust these limited solutions, accepting zero-day attacks as an unavoidable risk in an ongoing arms race between attackers and defenders. Despite this, the visibility limitations of software-based security solutions are an innate flaw that cannot be overlooked.
Final Thoughts
Gödel’s findings offer a valuable perspective on the challenges of cybersecurity. Just as mathematical systems have inherent limitations, so too do software-based solutions for detecting malware. To move beyond these constraints, cybersecurity must adopt approaches that consider the limitations of logic and strive for solutions outside the current scope of software-based visibility.