Stephen Hawking says universe can create itself from nothing, but how exactly? Stephen Hawking says in his latest book The Grand Design that,

Because there is a law such as gravity, the universe can and will create itself from nothing.

Is it not circular logic? I mean, how can gravity exist if there is no universe? And if there is no gravity, how can it be the reason for the creation of universe? 
Also, if the universe doesn't exist, how can it create itself? The very sentence doesn't make sense to me. It seems so absurd and illogical that I've never heard such sentences even in philosophy. On what grounds does Stephen Hawking claim this?
 A: At face value, I interpret the statement as follows:
Quantum mechanical fluctuations may  generate from the vacuum ( nothing) enough energy for a universe. Because gravity exists for any ensemble that has energy, then the big bang will go on its usual development in time.
One has to presuppose that the mathematical formulations exist,( a mathematical theory of everything including quantum mechanics and gravity), irrespective of the existence of matter/energy. A kind of platonic ideal.
A: Unfortunately I don't have a copy of "The Grand Design", so can't be 100% sure of the context, however, from the terminology, it sounds like this may be a reference to Hartle and Hawking's no-boundary proposal.
In this scheme, they propose a method for computing what they refer to as the "wavefunction of the universe".  This wavefunction uses Feynman's path integral to assign probability amplitudes to three-metrics on a three-surface $\Sigma$ bounding a Euclidean spacetime M.  By analytic continuation, the wavefunction can be continued to a function representing a Lorentzian signature spacetime.
This approach is explained in Hawking's publicly available lecture.  There he describes an explicit example where $\Sigma$ is a three-sphere and the Euclidean manifold M is a four-ball.  "On the other side" of the bounding three-sphere $\Sigma$ is Lorentzian de Sitter space.  This model is proposed as a model for a spontaneously created de Sitter universe, and he makes the statement 

Unlike the black hole pair creation, one couldn't say that the de Sitter universe was created out of field energy in a preexisting space.  Instead, it would quite literally be created out of nothing: not just out of the vacuum, but out of absolutely nothing at all, because there is nothing outside the universe.

A: The flaw in the argument is the assumption of causality, and that it's linear. Nothing doesn't exist, which makes saying a given entity is nothing empty.
A: If the input to cosmology is trivial in the sense that the initial conditions have to be trivial, then creation itself was trivial, and needs no explanation. It's the output which needs to be explained, not the input.
There's no need for even the laws of physics to be included in the input because eternal inflation and the multiverse of the string theory landscape leads to an ensemble of all possible laws.
A: Stephen Hawkings is a physicist and he needs to put any idea of God outside of the domain of physics. (a)
Georges LeMaitre was (WP Hubble-Law) a belgian priest and the BBT leaves intact the divine intervention as a justification to the act of the creation of the universe/matter, and it  appraises to the Catholic Church and other religious positions.
If you beleive in ONE single BB then you are a priviledged observer of something that begs the question: And before? and why?
(gravity in the sentence is not about gravity but only: there is a law...)
The sentence:

the universe can and will create itself from nothing.

Is a circular reasoning as you say, even worst: create itself (like god!); from nothing? (a free lunch!). From 'nothing' we can not get 'something'.  
I think that Spinosa's view is more adequate to a physicist:
The Universe was, is and will be ALL with no start nor end. The event of matter creation, we use to call it BB, is a repeatable event. 
This way I do not need to call for any entity exterior to the universe.   
(a) - if God exists, or not, is a different question, and is outside of the domain of this site.
In Physics we can not invoke any transcendental entity to be 'a cause'. 
