Strategy development is a process for achieving an organization's purpose. Strategizing involves finding solutions to wicked problems, complicated issues without a clear problem definition and without a fixed set of remedies.
Strategy paradoxes[1] are opposite demands placed on the organization that seem to be contradictory at a certain level, but can be combined in innovative ways.
Viewing a strategy tension as a paradox challenges the strategist to find a way to get the best of both worlds.
Strategy synthesis is an effort to meet opposite demands simultaneously. A synthesis is a hybrid solution to a strategic problem that combines elements from opposing strategy perspectives. The process of synthesizing requires a rich understanding of both perspectives and dialogue about the qualities of the two extremes.[2]

In their publication Strategy Synthesis: Resolving Strategy Paradoxes to Create Competitive Advantage (2010), Bob de Wit and Ron Meyer have defined the most common strategy paradoxes.

[1] Wikipedia: A paradox is a statement that, despite apparently valid reasoning from true premises, leads to an apparently-self-contradictory or logically unacceptable conclusion. A paradox involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. Some logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking.

[2] The triad thesis, antithesis, synthesis originated with Johann Fichte. The scheme present a certain type of argumentation about two seemingly contradictory propositions. The contradiction is abrogated when the proposition synthesis has been reached.

10 strategic paradoxes
Strategic Thinking:            Logic versus Creativity
Strategy Formation:          Deliberateness versus Emergence
Strategic Change:              Revolution versus Evolution
Business Level Strategy:   Markets versus Resources
Corporate Level Strategy: Synergy versus Responsiveness
Network Level Strategy:   Competition versus Cooperation
Industry Context:             Choice versus Compliance
Organisational Context:    Control versus Chaos
International Context       Globalization versus Localization
Organisational Purpose:   Profitability versus Responsibility

De Wit & Meyer have defined a number of strategic paradoxes in their publications.
The little booklet from Ron Meyer's website describes 10 such dilemmas.

Click on the picture for the link to this booklet.