I think most people will intuitively accept the first premise. Although the scientific community is somewhat divided on the subject, data from NASA's Wilkinson Microwave Anisotropy Probe (WMAP), along with other experiments, suggest that the universe is flat within a 2% margin of error. This data, coupled with WMAP's other finding that the universe's rate of expansion seems to be accelerating, indicates that the universe will continue to expand forever and is thus infinite. Regardless, if you accept that reality exists, then there always must be something to house reality and this something must be infinite if the concept of reality is consistently believable.
The second premise is probably harder to accept. Again, the scientific community is divided on the subject. The equations that form the foundations of physics seem to indicate that time travel should be possible. These equations have proven reliable in the past, so it is reasonable to presume that they would be reliable in this case as well. Even if you are extremely hesitant to allow for the possibility of time travel, perhaps you would allow at least a .00000000001% chance that it could happen.
If you are still hesitant, consider the implications of time travel. It is a well-known fact that if someone were to travel back in time and alter something, the resulting changes to the chain of causality could have disastrous implications to our present, including, but not limited to, causing mankind to stop existing. Surely these most dire of consequences would allow you to consider the possibility of the possibility of time travel existing, if only to err on the side of caution? To use another example, Gregg Easterbrook argues in The Atlantic that although the scientific community is divided on the possibility that a meteor will strike the Earth (anywhere from an infinitesimally small possibility to as much as 10%), the calamitous results of such a strike necessitate preventative measures. To wit,
". . . in 1908, a huge explosion occurred above Tunguska, Siberia. The cause was not a malfunctioning alien star-cruiser but a small asteroid or comet that detonated as it approached the ground. The blast had hundreds of times the force of the Hiroshima bomb and devastated an area of several hundred square miles. Had the explosion occurred above London or Paris, the city would no longer exist."Therefore, if there is any chance of this happening again, even if that chance is extremely small, then we should at least spend some amount of time and money planning for the possibility since the consequences would be so horrible. Surely the same argument can be made for the existence of time travel. Although science is decidedly more mixed on the possibility of time travel than on the possibility of a meteor striking the Earth, the consequences of time travel could be far more cataclysmic than a meteor strike, so why not at least allow for the possibility? Can you afford not to?
If you are now willing to accept both of my premises, that the universe is infinite and that time travel is possible (no matter how small the possibility), then consider the fact that, in an infinite universe, anything that has any probability of occurring will inevitably occur. Therefore, if you accept my first two premises, then you accept the premise that time travel will inevitably occur at some point in time in the future.
Additionally, since we are dealing with time travel, it doesn't matter at all when it occurs, it can still have an effect on our present. If time travel is not mastered until a billion years into the future, someone could travel a billion and one years into the past and alter something in 2009 that would affect our 2010 reality.
Therefore, we must immediately begin taking steps to prevent time travel from happening or at least prevent a time traveler from altering anything should he travel into our time. Since a time traveler could conceivably completely wipe out human existence by his actions, then our efforts to prevent this from happening must be international and must take precedence over any other national or global initiatives. All of the world's resources must immediately be devoted to this task; there is nothing more important.
Time is of the essence. Since time travelling is an inevitability, many changes have undoubtedly already been made to the course of human history by time travelers. During the time that you were reading the previous two sentences in this paragraph, it could have been the case that John Adams was the first president of the United States. Between the time you finished those sentences and the time you began the next sentence, someone could have travelled back in time and rigged the election so that George Washington won. The you reading this sentence believes that George Washington was always the first president of the United States, and there's nothing anyone could do to change your mind, but you would be wrong. Thus, our entire world can change in a split second.
All of the changes that have been made to our past by time travelers already have caused us to arrive at the world in which we exist right now. This world is, at worst, tolerable, and is undoubtedly preferable to a random alternative, considering how truly disastrous the worst of those alternatives could be. Therefore, we have to act at once to prevent any additional changes from being made. We must preserve our present world at all costs.
To do this, we must prevent people from time travelling not only to our present, but also to our past and future. The only way to achieve this is by installing video surveillance cameras in every single physical location in the entire world, both inside and outside of buildings, as well as underwater. We will also need to create an international organization responsible for viewing and policing the camera feeds.
This will immediately solve the problem of anyone from the future time traveling into our midst. The cameras will recognize a human instantly materializing and then notify the proper authorities to apprehend this person and prevent him or her from altering anything. Nobody will be able to time travel into any time after the camera network is built without being immediately apprehended.
That would take care of people time travelling into our present and future, but we would still have the problem of people time travelling into our past. Fortunately, the camera network, by its very existence, will solve this problem easily. Once the network is built, we can expect a slew a time travelers to begin travelling into our present (like moths to a bug light) with the express purpose of destroying or somehow subverting the camera network, so that people of the future could once again resume time travelling with impunity. using the camera network, we will easily capture these people and force them to give us the secrets of time travel, which we will use to travel back to the point at which Earth was created in order to install another network of cameras throughout the planet in order to police the entire history of the planet and prevent anyone from travelling to a time before the first camera network was built.
Obviously, speed is of the essence in building the camera network, which is why we must mobilize all of the Earth's resources and people. Again, since the worst possible scenario is someone travelling back in time and causing the entire human race to cease existing and since this could literally happen at any moment, the only rational decision is to begin the mobilization immediately. Any opposition to the worldwide camera network or any negative externalities produced by its existence (e.g. lack of privacy, reduced freedom, etc.) pale in comparison to the prospect of humanity ceasing to exist and must be ignored.
In all likelihood, the mere fact that I was born and have written this blog post is proof that my plan has been adopted and is successful, so any remaining opposition to the camera network is futile. Since I am the first person to ever publish these ideas, surely someone must have travelled back in time to try and kill me before I wrote this or perhaps to try and kill my parents or their parents, and so on. Clearly, the overseers of the camera network have already apprehended several time travelers and gleaned the secrets of time travel from these people and used it to ensure my safety. So, as you can see, the very existence of this blog post is enough to prove the validity and inevitability of the camera network. The argument is true because I have made the argument. The camera network must be adopted; there is no other future available.