A semantic digression is necessary in order to pre-empt irrelevant criticism. The word 'universe' traditionally denotes 'everything there is'. Therefore if we envisage that physical reality could embrace far more than traditionally believed - for instance, other domains of spacetime originating in other big bangs, or domains embedded in extra spatial dimensions - we should really define the whole ensemble as 'the universe', and introduce a new word - 'metagalaxy' for instance - to denote what observational cosmologists traditionally study. However, so long as this whole idea remains speculative, it is probably best to continue to denote what cosmologists observe as 'the universe' and to introduce a new term, 'multiverse', for the whole hypothetical ensemble.
If our existence - or, indeed, the existence of any 'interesting' universe -depends on a seemingly special cosmic recipe, how should we react? There seem three lines to take: we can dismiss it as happenstance, we can invoke 'providence', or we can conjecture that our universe is a specially favoured domain in a still vaster multiverse.
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