This author is trying to argue that one simply cannot dismiss the idea of an 'afterlife', whatever that may be. His main arguments?
Scientific and psychological reasoning and scepticism have yet to firmly counter the notion that there is an afterlife.
experiential evidence from around this world points to some form of existence in ‘the next’.
The first one is silly and just plain lazy. He's arguing that you can't prove that it doesn't exist. This is nonsense because it is the burden of a person arguing for the existence of something to show that it exists, not the other way around. So while his argument is to counter a previous article that appears to argue why it this afterlife doesn't exist, to turn around and argue that it does based on the point that "you can't prove it doesn't" really is extremely weak.
But the second part is what is more fascinating in terms of proving my continuing point that the general public, or at least those not in science, do not have any clue on the difference between anecdotal and scientific evidence. He is actually touting this "experiential evidence" as if this is something that is reliable and valid. It is a FACT that our minds can play tricks on us. It is a FACT that has been shown many times how people can believe that they saw something that never occurred (see here, here, and here). Therefore, experiential evidence is NOT RELIABLE as valid evidence. It is certainly less reliable when a person is under medical/physiological duress that he/she is near death! So to use those as justification for anything is extremely dubious.
It is ironic that he said that "... The afterlife may go against common sense, but twentieth century physics has taught us that common sense is often a poor guide to truth...." yet, he somehow ignored the rest of what physics has taught us of the nature of scientific evidence and what is valid. You'll notice a common thread here when someone who doesn't know much about physics will pick and choose what he/she wants to take from physics. The author of "The Secret" wants to use quantum mechanics to justify various part of it, and ignores the rest that will render the argument false. The same thing is occurring here. If this person is so respectful of what "twentieth century physics" has to teach us, then take the whole thing, rather than just what's convenient for him.
The fact that something like this continues to be presented as valid argument, and published in popular media without any hesitation, shows that (i) such fallacy is not seen as problematic to be accepted, and (ii) the readers and the general public probably won't catch what I've just mentioned here. Try reading the papers or watching TV. You'll see many more arguments being made that is based on simply a matter of opinion, or based on non-existent evidence, or an incomplete understanding. In many cases, no one is asking for evidence or justification of the point being made. So these things are being said as if they are "facts".
The nature and validity of the evidence being presented to support an argument is something that has been emphasized very little in public discourse. That is what is so discouraging.