Now that I think about it, I care both about those currently living and about humanity itself, but with a small but non-zero discount rate (of the order of the reciprocal of the time humanity has existed so far). Also, I value humanity not only genetically but also memetically, so having people with human genome but Palaeolithic technocultural level surviving would be only slightly better for me than no-one surviving at all.
Now that I think about it, I care both about those currently living and about humanity itself, but with a small but non-zero discount rate (of the order of the reciprocal of the time humanity has existed so far). Also, I value humanity not only genetically but also memetically, so having people with human genome but Palaeolithic technocultural level surviving would be only slightly better for me than no-one surviving at all.