In 2005, a foundation called The Edge posed an irresistible question: "What do you believe is true even though you cannot prove it?" The responses from serious thinkers numbered more than one hundred. So provocative were the answers that the whole endeavor garnered international media attention.
Argues Randolph Nesse:
I can't prove it, but I am pretty sure that people gain a selective advantage from believing in things they can't prove. I am dead serious about this. People who are sometimes consumed by false beliefs do better than those who insist on evidence before they believe and act. People who are sometimes swept away by emotions do better in life than those who calculate every move. These advantages have, I believe, shaped mental capacities for intense emotion and passionate beliefs because they give a selective advantage in certain situations.
I am not advocating for irrationality or extreme emotionality. Many, perhaps even most problems of individuals and groups arise from actions based on passion. The Greek initiators and Enlightenment implementers recognized correctly that the world would be better off if reason displaced superstition and crude emotion. I have no interest in going back on that road and fundamentalism remains a severe threat to enlightened civilization. I am arguing, however, that if we want to understand these tendencies we need to quit dismissing them as defects and start considering how they came to exist.
Says Terrence Sejnowski:
If memories are stored as changes to molecules inside cells, which are constantly being replaced, how can a memory remain stable over 50 years? My hunch is that everyone is looking in the wrong place: that the substrate of really old memories is located not inside cells, but outside cells, in the extracellular space. The space between cells is not empty, but filled with a matrix of tough material that is difficult to dissolve and turns over very slowly if at all. The extracellular matrix connects cells and maintains the shape of the cell mass. This is why scars on your body haven't changed much after decades of sloughing off skin cells.
We will find ways to circumvent the speed of light as a limit on the communication of information.
I believe that animals have feelings and other states of consciousness, but neither I, nor anyone else, has been able to prove it. We can't even prove that other people are conscious, much less other animals. In the case of other people, though, we at least can have a little confidence since all people have brains with the same basic configurations. But as soon as we turn to other species and start asking questions about feelings, and consciousness in general, we are in risky territory because the hardware is different.
Other answers are worth reading too -- see John McWhorter's unproven hypothesis for one of the weirder examples.
In conclusion, I ask you, dear reader: what do you believe that you cannot prove? Send answers to firstname.lastname@example.org