Fan of Science ; In math, we have knowledge of all sorts of things that have no empirical reference. Like the concept of infinity. That's knowledge, without any empirical basis. So, yes, knowledge can exist without any empirical basis for it.
Not all mathematics is part of the Math of the Universe, is not God’s Math.
God Math, the Mathematics involved in the Creation of the Heavens and the Earth, the Universe, the Reality of Everything that exists in the material, physical, empirical sense of the Word, is based upon a Singularity having a dual quality, 0/1 and a quantity there of, involves the addition, subtraction, the multiplication and division of a Singularity having a dual quality, 0/1.
There are no Imaginary numbers in God’s Math; the math of the Universe does however include fractals, Fractions, a Faction in which the numerator is less than or equal to the denominator is a real number, unless for whatever reason the numerator become greater than the denominator, in which case said Fractal, Fraction becomes Irrational, is no longer a real number.
If you would like I can give you a visual example of What an entity that is Infinity look like.
Take eight mirrors and form an octagon with the reflective side to the inside.
Place a dot on One of the mirrors; observe the dot from just the right angle and a series of dots will appear in the mirror, each dot becoming smaller and smaller to the point where the dot is not loner continuously visible, becomes Infinite.
The motion of a Singularity is meaningless, the existence or non-existence being Uncertain.
An Infinite entity not being readily apparent, not being measurable as to location and Momentum in Space-Time.
Paradingmer;
It was never my intent to become involved in Priori Knowledge.
I do not believe that anyone has provided the definition of Priori Knowledge, especially myself.
I have simply been stumbling around in the dark looking to attain an understanding of exactly what? Priori Knowledge is.
I would hazard a guess, that the knowledge of the Mathematics of the Universe, God Math, to be priori knowledge, of a Singularity having a dual quality. 0/1
-- Updated July 22nd, 2017, 10:15 am to add the following --
A change in my thoughts on Priori Knowledge.
The workings of the Mathematical Universe is digital;0/1.
Priori Knowledge, the Knowledge of a Reality that is not born of experience, exists a compendium of all human events, thoughts, words, emotions and intent ever to have occurred, believed by theosophists to be encoded in a non-physical plane of existence known as the etheric plane. There are anecdotal accounts but no scientific evidence for existence of the Akashic records. is the Sanskrit word for "aether" or "atmosphere". Also, in Hindi, Akash means "sky" or "heaven".
Prior knowledge is born of a Single Source, while Empirical Knowledge has many Sources, is born of somewhere far-out in left field.
The Single Source of Priori Knowledge is a omnipresent, is 'ancient.
Empirical Knowledge is born to satisfy the desires of the Flesh Body, while Priori Knowledge exists with the intent of Satisfy the Spirit, the Soul, is omnipresent and omniscient is part of the infinite Universe, the Reality of Everything that exists in the Material, Physical sense of the Word.
It could be said that Priori Knowledge is born of the mind of God, is Devine Knowledge.
IT must be understood that my thoughts on Priori Knowledge will change.
-- Updated July 28th, 2017, 12:39 pm to add the following --
Numbers simply represent a quantity of Singular objects, each having a dual quality of 0/1.
Mathematics exists as a system in which any number of objects is represented as a Number, quantity of objects.
The Universe is ruled by an orderly system of Chaos that has been brought to order by a specific system of mathematics, the Decimal System of Mathematics based upon an unspoken of quantity of a Singularities, each having a dual quality of 0/1.
Numbers as used in the Decimal system of Mathematics.
A Random Singularity having no relative, numerical value, having a numerical value Zero-0, as an affect born of displacement, was spontaneously, converted into a Singularity having relative, a numerical value of One-1.
The Universe born of a system of Chaos, had its beginning as the result of the displacement of a Random Singularity of Zero-0 being Transfigured, converted, into the First Singularity to have relative, a numerical value of One-1, the Reality of First Cause.
As the result of having been of displaced a Singularity of Zero-0 attained angular momentum, velocity of speed and direction became Readily Apparent, became measurable as to Location and momentum in what was to become Space-Time.
The Universe born of a system of Chaos as it was slowly brought to order by way of the Decimal System,
No Chaos no order, order only existing amongst the Chaos, as the Universe is brought to order.
The order of the decimal system resulting in the collation of the Universe as a Whole.
The System of Chaos being born of the transfiguration of a Singularity of Zero-0, a Singularity of Zero-0 being reborn a Singularity of One-1, resulting in the birth of Decimal System of Mathematics, 0/1.
A Singularity of Zero-0 alone in the Emptiness of Infinite Time and Space being meaningless simply because a Singularity Zero-0 is motionless, exists without displacement, without angular momentum, without velocity of Speed and Direction, is dead in the water, is simply not readily apparent, is not measurable as to location and momentum within the Infinite Nature of either Time or Space each existing as a Singularity within the Nothingness that existed prior to the creation of the Reality of First Cause.
First Cause being the First Singularity of Zero-0 to attain a relative value, to be converted into a Singularity to have relative a Numerical value of One-1.
-- Updated July 28th, 2017, 12:44 pm to add the following --
Numbers simply represent a quantity of Singular objects, each having a dual quality of 0/1.
Mathematics exists as a system in which any number of objects is represented as a Number, quantity of objects.
The Universe is ruled by an orderly system of Chaos that has been brought to order by a specific system of mathematics, the Decimal System of Mathematics based upon an unspoken of quantity of a Singularities, each having a dual quality of 0/1.
Numbers as used in the Decimal system of Mathematics.
A Random Singularity having no relative, numerical value, having a numerical value Zero-0, as an affect born of displacement, was spontaneously, converted into a Singularity having relative, a numerical value of One-1.
The Universe born of a system of Chaos, had its beginning as the result of the displacement of a Random Singularity of Zero-0 being Transfigured, converted, into the First Singularity to have relative, a numerical value of One-1, the Reality of First Cause.
As the result of having been of displaced a Singularity of Zero-0 attained angular momentum, velocity of speed and direction became Readily Apparent, became measurable as to Location and momentum in what was to become Space-Time.
The Universe born of a system of Chaos as it was slowly brought to order by way of the Decimal System,
No Chaos no order, order only existing amongst the Chaos, as the Universe is brought to order.
The order of the decimal system resulting in the collation of the Universe as a Whole.
The System of Chaos being born of the transfiguration of a Singularity of Zero-0, a Singularity of Zero-0 being reborn a Singularity of One-1, resulting in the birth of Decimal System of Mathematics, 0/1.
A Singularity of Zero-0 alone in the Emptiness of Infinite Time and Space being meaningless simply because a Singularity Zero-0 is motionless, exists without displacement, without angular momentum, without velocity of Speed and Direction, is dead in the water, is simply not readily apparent, is not measurable as to location and momentum within the Infinite Nature of either Time or Space as they each exist within the Emptiness, the Nothingness, a Great Void, that existed prior to the creation of the Reality of First Cause.
First Cause being the First Singularity of Zero-0 to attain a relative value, to be converted into a Singularity to have relative a Numerical value of One-1.
-- Updated July 28th, 2017, 2:56 pm to add the following --
Paradigmer I do not argue against the Reality of unisonal interactions.
The only point begin is that before the beginning moment of Creation, Singularity only had the potential of having a dual quality, having unisonal interaction.
A singularity alone in the Emptiness of the Great Void, the Nothingness, existed as a Singularity having no relative, numerical value,
having a numerical value of nada, zip, zilch, nothing, Zero-0.
-- Updated July 29th, 2017, 10:27 am to add the following --
The Unisonal evolution mechanism, "The System of Chaos", came into existence as the result of metamorphic change, the rebirth, the Transfiguration in the priori singularity of Nothingness, Zero-0.
The Priori Knowledge of an Infinite Singularity that had no relative, numerical value, that had a numerical value of "Zero-0", that had no mass, a Singularity of Zero-0 as the result of displacenent was transfigured, converted into a Singularity of One-1, as an affect, was converted into the Reality of First Cause.