Infinity, comes from the Latin infinitas, and essentially means ‘unboundedness’. Mathematics has tended to deal with this concept in literal, quantifiable terms – infinity as an indefinitely great number; an unyielding incremenation (or decrementation). Philosophy, on the other hand, has attempted to decipher the ontological outcome of this concept. For example, to be infinite is not only to continue indefinitely, but to have no decipherable patterns; no perceivable limitations.
So, what is an idea anyway? Are the electrical impulses in our brain that represent¹ ‘getting up from our chair’ an ‘idea’? In the strictest sense, no. But, if this act is explicitly part of something larger, we could say yes. First, let us define an idea as the creation of a mental algorithm – an approach that purports to solve an issue or problem. In other words, the creation of a spear to take down a woolly mammoth would count as an idea. In fact, that idea would contain several other ideas: the conceptualization of the spear, the determination of materials needed to create the weapon, the finalization of planning and strategy needed to take down the game, etc. Even the failed concepts in this enormous undertaking would hold ideas: failed weapon designs, failed strategic maneuvers, etc. So, looking back, we can say that ‘getting up from our chair’ could count as a genuine idea if we were doing so in a conscious effort to fulfill a specific mental algorithm (or plan) – say, during musical chairs. The concept here is that general actions with no overarching purpose will not be viewed as ideas, while plans dealing with creation, execution, or innovation will.
So, armed with our system of categorization for ideas, I would have to conclude that human ideas are finite in nature. Our ideas are based off of pre-existing, finite data, and grow in response to situations which are also finite in nature. We could only build a spear for game if there were game to be hunted, and if the concept of ‘weapon’ already existed. Conversely, one could only decide to stand up from ones chair if a game called ‘musical chairs’ had already been invented, and the idea of that game could only exist if chairs and easily controllable music were already in existence. Even when one adds the possibility of future problems/situations or the fact that ideas are the permutations of old ideas and current data, the result is still finite ideas – because the input is always finite.
Although our conclusion leads to finitude, this is no reason to worry about the ultimate ability of our cognitive power. As alluded to earlier, the world is in no short supply of pressing issues, and only our dedication to human ideas will be of assistance. Luckily the combination and permutations of past instances with current and future data yields impressive returns. And, with the aid of the internet, the rate at which individuals and collectives can create these needed grand ideas is continually increasing.
¹or create, depending on your inclination