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As a result, the fundamental JOI renders the hallowed method of inquiry just another doctrine among others, equal in its manner of justification, its final appeal, and its ultimate justice to every other belief system.  But this is not the criticism that finally condemns it.  Being just the same as other systems of belief is not the fatal flaw.  That only makes all systems of belief equal under the law, if no longer a law of inquiry but a law of compromising positions and convenient resolutions.  Still, there would not necessarily have been anything wrong with this, if it were not for the self-imposed burden that inquiry brings down on itself via the dishonesty or the self-deception of promising something else.

As a result, the fundamental JOI renders the hallowed method of inquiry just another doctrine among others, equal in its manner of justification, its final appeal, and its ultimate justice to every other belief system.  But this is not the criticism that finally condemns it.  Being just the same as other systems of belief is not the fatal flaw.  That only makes all systems of belief equal under the law, if no longer a law of inquiry but a law of compromising positions and convenient resolutions.  Still, there would not necessarily have been anything wrong with this, if it were not for the self-imposed burden that inquiry brings down on itself via the dishonesty or the self-deception of promising something else.

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Could great men thunder

 

As Jove himself does, Jove would never be quiet,

For every pelting petty officer

| colspan="2" | Could great men thunder

Would use his heaven for thunder, nothing but thunder.

Merciful heaven,

| colspan="2" | As Jove himself does, Jove would never be quiet,

Thou rather with thy sharp and sulphurous bolt

Split'st the unwedgeable and gnarled oak

| colspan="2" | For every pelting petty officer

Than the soft myrtle.  But man, proud man,

Dressed in a little brief authority,

| colspan="2" | Would use his heaven for thunder, nothing but thunder.

Most ignorant of what he's most assured,

His glassy essence, like an angry ape

| colspan="2" | Merciful heaven,

Plays such fantastic tricks before high heaven

As makes the angels weep, who, with our spleens,

| colspan="2" | Thou rather with thy sharp and sulphurous bolt

Would all themselves laugh mortal.

Measure for Measure:  Isabella—2.2.113-126

| colspan="2" | Split'st the unwedgeable and gnarled oak

| colspan="2" | Than the soft myrtle.  But man, proud man,

| colspan="2" | Dressed in a little brief authority,

| colspan="2" | Most ignorant of what he's most assured,

| colspan="2" | His glassy essence, like an angry ape

| colspan="2" | Plays such fantastic tricks before high heaven

| colspan="2" | As makes the angels weep, who, with our spleens,

| colspan="2" | Would all themselves laugh mortal.

| ''Measure for Measure'', 2.2.113&ndash;126

 

It is probably wise to stress this point.  It is not being claimed that an authority based system of belief, simply by building itself on traditional foundations, is necessarily hypocritical or inconsistent in its own right.  It can be as accurate, authentic, and honest in what it says and tries to say as any other belief system or knowledge base.  In fact, a modicum of reliance on one source of authority or another is not only prudent but most likely to be found inescapable.  Authority based systems, in form so analogous to axiom systems, if not in the context of their use, simply have the specific properties and the generic limitations that they can be observed to have.

It is probably wise to stress this point.  It is not being claimed that an authority based system of belief, simply by building itself on traditional foundations, is necessarily hypocritical or inconsistent in its own right.  It can be as accurate, authentic, and honest in what it says and tries to say as any other belief system or knowledge base.  In fact, a modicum of reliance on one source of authority or another is not only prudent but most likely to be found inescapable.  Authority based systems, in form so analogous to axiom systems, if not in the context of their use, simply have the specific properties and the generic limitations that they can be observed to have.

At this point, let authority based systems and axiom systems be lumped together into the same class, at least temporarily, on the basis of the forms of derivation that they allow, and without regard for the different ways that they are initially brought to light or subsequently put to use.  Further, let this whole class be described as "founded systems", for the moment ignoring the distinction between informal and formal systems, or regarding all prospectively, in anticipation of their formalizations.

At this point, let authority based systems and axiom systems be lumped together into the same class, at least temporarily, on the basis of the forms of derivation that they allow, and without regard for the different ways that they are initially brought to light or subsequently put to use.  Further, let this whole class be described as ''founded systems'', for the moment ignoring the distinction between informal and formal systems, or regarding all prospectively, in anticipation of their formalizations.

Every project of a founded system voluntarily risks certain limitations.  But there is one limitation that appears to be a genuine defect from the standpoint of this inquiry, amounting to the chief source of worry that this inquiry has about the whole class of founded systems.  This is the fact that whatever acuteness of reverence or accuracy of reference to their objects they do in fact achieve is a matter of grace or luck, and not something that can be subjected to change, criticism, or correction.  This puts it outside the sphere of inquiry, as I understand it, even if its formulations are suggested by data within the sphere of experience.

Every project of a founded system voluntarily risks certain limitations.  But there is one limitation that appears to be a genuine defect from the standpoint of this inquiry, amounting to the chief source of worry that this inquiry has about the whole class of founded systems.  This is the fact that whatever acuteness of reverence or accuracy of reference to their objects they do in fact achieve is a matter of grace or luck, and not something that can be subjected to change, criticism, or correction.  This puts it outside the sphere of inquiry, as I understand it, even if its formulations are suggested by data within the sphere of experience.

In effect, there is no amplification of intelligence, no leverage of reason, in short, no instrumental gain or "mechanical advantage" to be acquired from the use of a founded system.  It can transmit the force of reason, in a conservative way at best, from premisses to conclusions, but the effective output of the system achieves no greater level of certainty as it bears on any question than the level of authority it can grant itself on input or justly claim for itself at the outset.  If I can continue to use the image of a lever, while delaying the examination of its exactness until a later point of this work, it is as if the lack of leverage in a founded system can be traced back to one of several defects:

In effect, there is no amplification of intelligence, no leverage of reason, in short, no instrumental gain or &ldquo;mechanical advantage&rdquo; to be acquired from the use of a founded system.  It can transmit the force of reason, in a conservative way at best, from premisses to conclusions, but the effective output of the system achieves no greater level of certainty as it bears on any question than the level of authority it can grant itself on input or justly claim for itself at the outset.  If I can continue to use the image of a lever, while delaying the examination of its exactness until a later point of this work, it is as if the lack of leverage in a founded system can be traced back to one of several defects:

1. The "fulcrum" of a founded system, the fixed point of its critique, is the "examen" of its critical powers, the tongue of its balance, and this has to be placed so evenly between the objective domain, whereof its ignorance is writ so large, and the fund of applied information, wherein its share of accumulated knowledge resides, that no gain in the effective intelligence of the actions thus founded can be derived.

# The ''fulcrum'' of a founded system, the fixed point of its critique, is the ''examen'' of its critical powers, the tongue of its balance, and this has to be placed so evenly between the objective domain, whereof its ignorance is writ so large, and the fund of applied information, wherein its share of accumulated knowledge resides, that no gain in the effective intelligence of the actions thus founded can be derived.

 

# A founded system is forced to be a ''grounded system'', that is, one that requires a moderately strong emplacement on grounds already settled and a preponderance of certainty on the side of the applied intelligence.

2. A founded system is forced to be a "grounded system", that is, one that requires a moderately strong emplacement on grounds already settled and a preponderance of certainty on the side of the applied intelligence.

# In effect, a ''founded or grounded'' (FOG) system requires absolute certainty with respect to some of its points, the points on which it is said to rest.  It is as if these fixed points put it in contact with an infinite source of knowledge or connect it to an infinite sink for uncertainties.  Of course, a FOG system that casts itself as a beacon of enlightenment and sells itself under the label of &ldquo;science&rdquo; can never admit to seeing itself in this image, since the very act of making the claim explicit already puts its grant in jeopardy.  But that is what it amounts to, nevertheless.

 

3. In effect, "founded or grounded" (FOG) systems require absolute certainty with respect to some of their points, the points on which they are said to rest.  It is as if these fixed points put them in contact with an infinite source of knowledge or connect them to an infinite sink for uncertainties.  Of course, a FOG system that casts itself as a beacon of enlightenment and sells itself under the label of "science" can never admit to seeing itself in this image, since the very act of making the claim explicit already puts its grant in jeopardy.  But that is what it amounts to, nevertheless.

Another way to see the over constrained nature of these FOG conditions, for the certainty of foundations, is by expressing them in terms of the "boundary conditions" that a given system of belief is assumed to have.  In this regard, it helps to make the following definition.  An "open" system of belief is one that has each of its points "mediated" by the system itself, in other words, surrounded by, apprehended within, and evidentially or argumentatively justified by a neighborhood of similar points that falls entirely within the system in question.

Another way to see the over constrained nature of these FOG conditions, for the certainty of foundations, is by expressing them in terms of the "boundary conditions" that a given system of belief is assumed to have.  In this regard, it helps to make the following definition.  An "open" system of belief is one that has each of its points "mediated" by the system itself, in other words, surrounded by, apprehended within, and evidentially or argumentatively justified by a neighborhood of similar points that falls entirely within the system in question.