Do Animals Prove the Existence of Mathematics and Logic?
It’s a common question: does the ability of animals to count and understand basic mathematics and logic prove that these concepts truly exist? But what does it mean to exist, and exactly how is logic proven to exist in our subjective world?
Existence in Our Subjective World
Logic, like empirical proof, is deeply enmeshed in our subjective experience. Every piece of evidence we gather through experience is filtered through our minds. This means that logic’s existence, as Aristotle knew, is a property of the mind rather than an external entity. Fish, for instance, can infer strength by observing fights between males, showing a form of logical reasoning that suggests logic is a property of the brain. However, logic as it is applied and understood, clearly exists within the framework of the brain.
A Philosophical Perspective on Mathematics
A lot hinges on our philosophy of mathematics. Within the Platonic school, mathematical entities are seen as abstract, eternal, and unchanging, independent of human witness or discovery. If animals can count, it reveals nothing more than their capacity to understand a specific aspect of mathematics, but it doesn’t prove that the broader concept of mathematics exists in an eternal, separate entity.
If you're a Formalist, mathematics is a construct, a solution to a string manipulation problem. In this view, if there were no mathematicians, very little of modern mathematics would exist.
Logic and Mathematics in Everyday Life
Counting and understanding logical concepts are human activities, not unrelated entities. Mathematics in grocery stores, determining costs, handling payments, and measuring fuel for cars are all examples of how humans use and apply mathematics. It is the activity and practical application that define mathematics and logic, not an abstract, permanent existence.
Do animals' mathematical skills prove the existence of mathematics and logic in the same way that Platonic truisms? Perhaps not, but the fact that these concepts are utilized by living, breathing creatures certainly demonstrates the utility and basic principles of these ideas. The notion of “more” or “less,” and the concept of possession are rudimentary forms of understanding quantity and ownership, which are foundational to mathematics and logic.
Limitations and Realities
Animals, like fish observing males fight, display limited logical ability but not the deep, abstract reasoning required for complex mathematics. Their understanding of quantity and possession is a starting point, albeit basic, for more advanced mathematical and logical reasoning. Yet, the ability to see and utilize these concepts is a testament to the universality and importance of such reasoning.
The Role of Human Activity
Ultimately, the existence of mathematics and logic as we understand them is a human activity. We measure, count, and calculate every day, and these actions define and prove the existence of these concepts. Mathematics rules over much of our lives, from the simple act of paying for groceries to the complex calculations involved in engineering and technology. Logic is a tool we use to communicate, make decisions, and understand the world around us.
Conclusion
The complex and abstract nature of mathematics and logic makes it difficult to provide empirical proof of their existence. However, the practical application and the rudimentary understanding displayed by animals do not prove their existence but do validate their importance in the natural world. Logic and mathematics are not separate, abstract entities; they are integral to human activity and the understanding and interpretation of the world.
Understanding the existence and utility of mathematics and logic, therefore, lies in our daily activities and the ways we use these concepts, not in an abstract proof of their existence. This realization underscores the essential and deeply human nature of these concepts.