The question of universal problems in philosophy finding a common solution is premised in observing an inherent unity through a common premise with this premise being the foundation of a further philosophy while observed both objectively and intuitively through prior philosophical movements.
The question of truth, under this unity, is less one of applying a perceived division which inherently leads to a branching of schools and the perspectives which extend from them, but rather observing a strict foundation of principles that extend not just from this unity but is the precedent for it.
This new philosophical school must not just give answers to questions about abstraction, physicality, quantity, quality, morality, ethics, religion, science, etc. but must be able to maintain them in its own rational framework while being open to extension without any fear of contradiction...and with a perceivable fear of contradiction the rationalization of contradiction as being an inherent element contained and imprisoned through the system itself.
From a unified philosophical school must come not just answers, but proceeding questions inherent within the structure which are necessary for it to maintain a progressive growth. In these respects Western Linear Relativistic and Eastern Circulatory Holism must effectively be synthesized not just for the sake of knowledge but due to the practical and abstract complication of the information age where both idea and fact is available at the push of a button.
In the age of information, opinion is the roaring ocean of chaos from which a new philosophy will be birthed.
The question of common axioms in philosophy exists through the current understanding of philosophy as an understanding of order through balance as a form of definition in itself. All definition is conducive to form and function and acts as the foundation of the boundaries of knowledge itself. Under these terms, in the pursuit of a unified philosophical system the human condition must resort to primitive axioms, the fundamentally act as prime conditions of the human experience, in order not just to understand our current state of being, but also its origins and future considering philosophy itself is conducive the entropic nature of time made evident in the multitude of philosophical and religious traditions made manifest through out the course of time and exponentiating in the 21st century.
Upon any deep research into the origin of philosophy, western thought inevitably leads to Thales and Pythagoras, whose methodology and research stems from religious traditions all over the world (embodied in the the initiation of their corresponding mysteries schools, which applies more to Pythagoras than Thales) must summating in a triad of Egyptian/Babylonian, Hebraic, and Hindu thought. The eastern schools of the Chinese, while relegated to Confucious and a variety of other teachers, may be possibility observe (emphasis on possibily) as extensions of the Egyptian tradition where research implies Chinese culture stemming from the Egyptians.
Egyptian/Babylonian Culture (and its thetical or antithetical dual of the Hebraic Tradition, depending on the origin point of measurement one wants to take) claims extension from an Atlantis type culture with Hindu culture mirroring this civilizational concept under the name Attasthali or Attatthali.
Now of course this will have to be further researched, quoted and verified through empirical evidence but it gives a vague picture of origin and the question of not just philosophy but the nature of the civilizations stemming from this origin philosophy...or rather philosophy of "origin".
But the question and answer of "origin" gives a common bond to not just all philosophy but religious tradition as well, with this "origin" being not just the foundation of the axiom but the prime axiom in itself considering all axioms are the origin of perspective as both a subjective and objective means of understanding the truth. Reverting back to ancient tradition, observed in certain religions and reflected in Pythagorean thought, "origin" acts as a seed of definition which gives structure to the nature of reality with the prime origin of being effectively the point.
The sole universal axiom of the human condition is the point, for how simple it may appear, with the axiom acting as a point in itself in the respect it not just extends to further points (in the form of linear reasoning) but inevitably circles back to itself (in the form of circular reasoning) leaving a trifold structure of axiomatic truths embodied thought the simple triadic limits of the point, line and circle that give form to reality and to us, while simultaneously observing the measuring capacity of the human condition stemming through this triad alone.
This common set of axioms reveals the axiom as a definitive means in itself where the point as origin fundamentally acts as a means of inversion where a unified axiom inverts itself to multiple axioms of both a linear and circular directive nature which gives rise to the nature of all being stemming from the nature of limit itself...with the axiomatic nature of these limits existing as connected in each other through the vary same point, linear and circular nature.
In these respects a common premise, however obvious it may be, for the future of philosophy is a quantification and qualification of reality as both 1 and Unity through "the All" where existence is accepted for what it is under the boundaries it manifests under considering the diversity of thought and religion still points to certain common underlying qualities of the point line and circle which exist dually as quantities.
Under an premise of "The All" as Constant we can observe the dualistic truth of Relativism as being an approximation of it through change and multiplicity of appearance while this dualism effectively exists as synthesis itself where the point, line and circle exist as neutral properties that simultaneous join/separate reality relative to the point of observation while existing for what they are: Limits as axioms with the axiom as the Limit.
In these respects we observe man as a both measurer and means as a reflection or image of "The All", hence divinity, and the moral questions of human dignity and value come into a clearer perspective as man can be observed as having an inherent element of Divinity with our condition through this extension of "The All" and divinity.