The Role of Critical Path in Logic, Systems and Science

It is the essence of critical thinking. A critical path is the ordered chain of incremental events or logic which produces the most elegant pathway to a reasonably constrained objective. While an aspect of critical thinking however, its application is more related to actual discovery and accomplishment than it is to the more common, cynical martial art of denial. Pop critical thinking is more about explaining the reasons why, what is right is right. Critical path inside of science is about applying intelligence to discover the pathway to what is right. Fearing being not informative, even more than merely being wrong.

It is the most effective (not efficient) path of progress which cuts through the bullshit in order to get to an objective. If you are a regular reader of The Ethical Skeptic, you will hear me speak often of critical path. The ability to discern it, is one of the skills which allows a sincere researcher to spot the agenda faker. It is the same reason why a whitetail buck deer will reliably traverse a path following the ridgeline through a chain of mountains, avoiding the gorges and ravines to either side. Critical logic is the inverse of the condition involving ingoratio elenchi (a misdirection in argument) or ingens vanitatum (a great deal of irrelevance). Modern versions of ‘critical thinking’ taught by today’s social skeptics are usually entropic in their application; producing misinformation, irrelevance and conformity. Energy sucking gorges and ravines of distraction and misdirection. This amateur teaching by activist numpties results in an array of enforced, conforming and simplest answers (see The Art of the Professional Lie). A critical path is in many regards, the opposite of this pseudo-skeptical process. Critical thinking may produce the same conclusion as critical path logic, but in the case of ‘critical thinking’ this is simply an accident in outcome. It is the critical path of logic which is the process of science, and not ‘critical thinking’. Just because someone might virtue signal around promoting the right answer inside a scientific question, does not serve to legitimize the process, path or method they employed to get there.

You will not find critical path logic defined in most scientific or philosophical handbooks and guides. Believe me I have over 40 of such guides in my personal library. In guides to science, you will most likely find the scientific method1† – which is in its essence a process involving a critical path discipline; incomplete though it may be in constituting actual science. In books of philosophy, sadly, rather than finding tenets on logical calculus and the development of knowledge, one finds a list of previous philosophers and their work, also bereft of critical path elemental exposé.

†Please note that Wikipedia has removed its older definition of ‘scientific method’ which began with ‘Define a Question’ as the first step (see the old definition extracted April 1, 2014 in The Scientific Method is Not Simply The Experimental Method), and has replaced it with ethical skepticism’s – ‘Conduct Observation’ now instead!  This is a major breakthrough, and while a remote stretch to imply that The Ethical Skeptic provided contribution to this change; nonetheless, it has taken time and activism on the part of real researchers just like us to supersede the false version of the scientific method, formerly taught by social skeptics over the last 6 decades. They have yet to add in the steps of ‘Frame Intelligence’ and ‘Establish Necessity’ (Ockham’s Razor), before asking a question – but this is a step in the right direction. The Ethical Skeptic is very pleased with this. This evolution is part of the contribution to the dismantling of the social skepticism movement currently underway.

An exception to such paucity on the topic may be found (below quote) in physics and computational scientist Stephen Wolfram’s ‘Completion Theory’, inside of his work, A New Kind of Science, (p. 1037).2 In this critical development of the philosophy of science, Wolfram outlines a set of approaches and principles used in converting conditions of non-confluence in a model structure, into one of confluence or even, unifinality (note, not monofinality). These modeling paradigms outline the benefit of reducing probative insight questions into elements of critical pair testing (highly constrained Bayesian model segments) which force two divergent analogues into one single conclusion, artificially. This approach is forcing rationalization to Bayesian reduction in its ethic of course, but more importantly outlines that – pairing of critical elements must be done iteratively and in the right succession, in order to produce a single, non-entropic answer. This is the essence of a critical path of logic, reducing an argument into single steps of validity which can be used to underpin a larger more comprehensive conjecture.

If one has a multiway system that terminates but is not confluent then it turns out often to be possible to make it confluent by adding a finite set of new rules. Given a string p which gets transformed to either q or r by the original rules, one can always imagine adding a new rule q → r or r → q that makes the paths from p immediately converge. To do this explicitly for all possible p that can occur would however entail having infinitely many new rules. But as noted by Donald Knuth and Peter Bendix in 1970, it turns out often to be sufficient just iteratively to add new rules only for each so-called critical pair q, r that is obtained from strings p that represent minimal overlaps in the left-hand side of the rules one has.

Similarly, German polymath Gottfried Wilhelm (von) Leibniz’s devices for the evaluation of the validity of given theses (ars iudicandi) and for finding new truths on the basis of given truths (ars inveniendi) outline principles which show that scientific logical reduction is nigh unto the art of mathematical reduction – itself the most pure form of critical path in logic.3 The Stanford Encyclopedia of Philosophy summarizes critical path logic thusly, in its series on foundational philosophy of logic:4

Leibniz stresses in the “Nouveaux essais” that syllogistic is part of a sort of universal mathematics, an art of infallibility (art d’infaillibilité). This art is not restricted to syllogisms, but concerns all kinds of formal proofs, i.e. all reasoning in which inferences are executed by virtue of their form.

What is Critical Path? Driving a Dark Highway at Night to an Unknown Destination

Critical path logic is simply a deployment of true critical thinking itself. Critical thinking has nothing whatsoever to do with ‘Stanovich goal enabling behaviors and cognitive dispositions’5 – as that is nothing but compliance and the ability to spot how to comply. This is the definition of critical thinking, and it has nothing to do with what you currently know – or pressure you receive from your peers, to conform to ‘rationality‘:

Critical Thinking

/philosophy : skepticism : science/ : the ability to assemble an incremental, parsimonious and probative series of questions, in the right sequence, which can address or answer a persistent mystery – along with an aversion to wallowing in or sustaining the mystery for personal or club gain. Critical thinking is the ability to understand, along with the skill in ability to deploy for benefit (value, clarity, risk and suffering alleviation), critical path logic and methodology. A process of methodically and objectively evaluating a claim to verity, through seeking new observations/questions which can be creatively and intelligently framed to challenge elements of fiat knowledge which underpin the claim, regardless of how compulsive, reasonable, justified and accepted that knowledge might be promoted or perceived.

There are several species of critical path logic application most commonly employed inside business, law, warfare and science today (I have been extensively and professionally involved in all of these):

  • Legal Prosecution – the critical sequence of evidences and questions which serve to convict or acquit a defendant.
  • Operations Research – the critical sequence of task and work content analytics which serve to attain a specific goal in the most objective/constraint effective method.
  • Science – the critical/sound basis from which to ask each next incremental question under the scientific method, which will serve to most completely and confidently answer a single query into the unknown.
  • Patent Prosecution – the critical set of disclosures, prior art, framings, constraints and claims, which inexorably lead to a non-obvious, teachable and novel invention, use or application.
  • Target Prosecution – in the Navy, when hunting a sub, the sub’s position is unknown at first. However, it can be eventually derived through a deductive process of critical path called Target Motion Analysis. This is a logical and incremental series of questions which, once answered, reveal a set of, or even one single possible instance of, a sub’s location, depth, speed and heading.

Therefore it has become clear over the last 200 years of the development of the philosophy of scientific logic (albeit more of late as opposed to of former), that, inference itself is drawn from three things which act in concert to clarify (reverse entropy) knowledge inside a horizon of unknown:

  • Develop a mathematical pathway of logical reduction – which evolves flexibly by novel outcomes rather than deterministically (as does maths),
  • Constrain in order to iteratively and convergently test critical pairs of modus ponens conjecture (the novelty), and
  • Sequence testing in such a fashion as to maximize probative potential and either an intelligence structure or unifinality (reduce entropy of knowledge).

For instance, let us compare two natural questions, an orphan question and a scientific question (bearing features of critical path):

Did a consciousness craft the universe?   <— This is a probative question, but it is not critical path.  It bears no underlying sound premise, is not parsimonious, incremental nor sequitur inside any particular argument bearing a logical calculus.  This is an orphan question. Even if we obtained the answer from some certified divine revelation, we would not know what to do with it next. It is next to useless, as both a question and an answer. Being right or wrong is inconsequential, as it is not informative.

Can a signal indicating observer effect on one particle, between a particle and its anti-particle carry information about that observation to the complimentary particle, faster than c (speed of light)?   <— Bears premise, is parsimonious and testable, incremental and sequitur – and finally, is highly probative; that is, it bears informative potential which can be crafted into intelligence, which further allows us to craft and constrain a further series of related probative questions.  This is the essence of critical path. It is a turning on, of the headlights of science, while it drives down a dark highway at night. But not only that, it also eventually selects the most effective route to the destination – or even the destination itself.

Social Skeptics will make scientific arguments of denial, which sound like they are principles of science, but in reality bear no more critical path value, than does the orphan question above. Anecdote and eyewitness testimony are to be ignored, complex ideas are wrong, conspiracy theories are wrong, pseudosciences are false topics, question the facts, examine every alternative you can think of.  These are orphan conjectures in science; crafted and disguised so as to not look like religious statements. But they are religious tenets and tools, nonetheless.

If something is false, it should eventually falsify itself through accrued intelligence. And in being found wrong, become highly informative in the process. If we choose instead to pre-certify it as wrong and then choose to block further research through use of apothegms, no informative critical path development (intelligence) can ever be undertaken from that point.  Wrong and seeing, is a world better state than is correct and blind.

This is the essence of a critical path in logic, science and systems. Most people, including many prominent skeptics and scientists, do not get this. It is a discipline of methodically focusing on what is important – and making the inquiry outcome even more rewarding in the process. Walt Whitman laments in “Thoughts”, inside his work Leaves of Grass, about the inability to cut through bullshit and focus on the path of the salient, incremental and sequitur, as such:6

OF persons arrived at high positions, ceremonies,
wealth, scholarships, and the like;
To me, all that those persons have arrived at, sinks
away from them, except as it results to their
Bodies and Souls,
So that often to me they appear gaunt and naked;
And often, to me, each one mocks the others, and
mocks himself or herself,
And of each one, the core of life, namely happiness,
is full of the rotten excrement of maggots,
And often, to me, those men and women pass unwit-
tingly the true realities of life, and go toward
false realities,
And often, to me, they are alive after what custom has
served them, but nothing more,
And often, to me, they are sad, hasty, unwaked son-
nambules, walking the dusk.

In fact, Whitman’s lament stands as metaphor to the elegance of an effective scientific process – it is satisfying and honing in skill, every bit as much as it is illuminating. As head of a materials lab, as CEO of a markets research and intelligence company, as a Director in Intelligence, as a philosopher and as a systems engineer planning over $600 billion in trade throughout my career (all $5 million to $100 million income companies), I have applied extensively, all three forms of professional critical path variant: science, logic and systems. My firms have been in premium demand for this role for over 3 decades; brought in to solve scientific, business and national infrastructure challenges which daunt classic organizations. In my experience, less than 1% of the population grasps the role of critical path in argument, planning and scientific reduction. Whitman’s unwaked sonnambules. Lawyers and mathematicians often do, and scientists sometimes do grasp critical logic. But diagnosticians, technicians, the dilettante and abduction/induction specialists rarely exhibit the skills honed under experience in handling critical path disciplines (see Diagnostician’s Error and The Three Types of Reason). This is why it is important to sense what type of mind you are dealing with early on inside a discussion.  One seldom can accompany a numpty across a path of critical logic or progression, as they do not bear the background nor skill set to assimilate such things. They only know the talking points by means of which they were trained.

Anecdote – BAD! Complex Alternative – BAD! Pseudosciences – BAD! Eyewitness Testimony – BAD! Conspiracy Theory – BAD!

A critical path involves several components of defining feature, which are similar in nature to, however much more than simply engineering critical path method:7 (note: In engineering critical path planning, ostensibly one knows all the tasks, work content, slack, drag and interconnections in advance, and is simply arranging them into a duration minimized framework. In science and in logic, one must apply the intelligence of early steps, in order to improve the clarity, structure and efficacy of the latter steps. There is fog on that horizon – one must adopt a pair of fog lights. See below.)

Critical Path (of systems, science or logic)

/philosophy : skepticism : science : critical thought/ : a preselected and interdependently ordered chain of incremental tasks, experiments or arguments which produce the most elegant pathway of progress to a reasonably constrained goal or answer. Elegance being defined as resource efficiency, plenary completeness and expediency, employed in ethical balance. Each step in a critical path relies upon a foundation of its previous steps/logic, yet adds in one incremental goal, test or claim which is being examined for validity or is sought for accomplishment (incrementalism).  In science, a critical path constitutes a series of tests or analyses crafted in such a succession hierarchy so as to produce a constrained and deductive incremental answer.  In the philosophy of logic, a critical path is the assembly of prior art foundational modus ponens or tolens arguments of logical calculus, which lead to sound basis for a greater incremental truth conjecture.  Finally in systems engineering, a critical path is the chain of interdependency of necessary and sufficient tasks, arranged in their most elegant progression, which leads to accomplishment of an incremental process step or overall planned goal.

The features of a critical path of logic involve the following:

  • a preselected and interdependently ordered chain of incremental tasks, experiments or arguments
  • an elegant pathway of progress, being defined as resource efficiency, plenary completeness and expediency, employed in ethical balance
  • a reliance upon prior art, a foundation of previous steps/logics which imbues soundness
  • is incremental in the nature of each critical step
  • employs a mathematical pathway of logical reduction
  • constrains in order to iteratively and convergently test critical pairs of modus ponens conjecture
  • tests in such a fashion as to maximize probative potential and either an unfolding intelligence structure or unifinality
  • employs feedback from intelligence selected early testing, to modify downline testing steps
  • is deductive in as much as is possible, versus other forms of inference
  • and does not wander aimlessly in testing, rather employs necessity and intelligence to strike a more elegant path to unifinality.

My Example

Of course this does not equate exactly to a logical critical path example, but it does combine systems planning and science into one discipline of critical logic. To the right is an example drawn from a classified lab I managed in the past – the specifics of which are unimportant, save to say that we were comparing the compatibility of various Transition metals as to their lattice substitution tolerance. In an effort to circumvent testing 9 different metals, under three different parameters, with 3 settings to each parameter (just to start off), which would involve 81 peer parallel experiments and take 8 months of costly and valuable reactor time, we decided to shortcut this by focusing instead on comparatives along one indice. In theory, if we did not find probative advantage early on, we could end up having to pursue all 81 orthogonal study permutations. But by focusing on 1 indice, running testing based on that 1 input and 1 setting in order to hone in on our most probable candidate, we were able to develop intelligence around the performance of various materials – which would accelerate our prosecution of the broader question (Q3301). The 3301 testing series related to the compatibility of niobium diboride in this role, as compared to a variety of other materials. Previous testing had shown niobium to bear significant advantage in both substitution and even some issues of interstitial phase displacement. We used this intelligence to our elegance advantage, if you will – by focusing on the most critical components of the broader question, 3301.

Before we simply shotgun tested every parameter and combination, we did some quick up front comparatives with our most promising element, which allowed us to focus on the core issues, and cut out 85% of the 81 permutations of test necessary in answering this one question alone.  This because, there were a series of at least 35 more questions necessary to answer before we could approach this material as a technology, not just a science.

The essence of this approach was to establish a path of testing which was focused on a guess (constraint), and then employ early results to modify the number of downline tests necessary (intelligence). Wolfram’s path convergence.

In other words, we pursued a relational dynamic between converging the schedule of events inside our testing, to become congruent with the unfolding of the critical logic inside the discovery. This is the process of developing and using intelligence – wherein our method made for our guesses getting better and better, very fast. Some scientists even bristled over this. We pursued what was probative as a priority, not simply what was methodically reliable.

We were not afraid to be wrong – we feared being not informative, even more.

Now this is but simply one version of a critical path – those of simply scheduling and logic may differ in structure, but not really in ethic. They all focus on what is important, and critical in attaining the goal, based upon advanced observations and only that information necessary in getting to the objective. Nothing more. This is the essence of a critical path.

The faking skeptic will toss out every manner of ignoratio elenchi and ingens vanitatum. They want to look the part, and enjoy being praised as science. They have no tolerance for wrongness, because being informative is not their primary goal. Be wise to this.

The Ethical Skeptic, “The Role of Critical Path in Logic, Systems and Science” The Ethical Skeptic, WordPress, 25 March 2018, Web;

  1. Wikipedia: Scientific method; extracted 25 Mar 2018;
  2. Wolfram, Stephen; A New Kind of Science; Wolfram Media, Inc., Champaign, IL; 2002; p. 1037
  3. Leibniz, G. W., Sämtliche Schriften und Briefe, ser. 6: Philosophische Schriften, vol. 6: Nouveaux Essais, A. Robinet/H. Schepers (eds.), Akademie Verlag, Berlin, Germany, 1962.
  4. Peckhaus, Volker, “Leibniz’s Influence on 19th Century Logic”, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.), URL = <;.
  5. Stanovich, K. et. al.; Heuristics and biases as measures of critical thinking: Associations with cognitive ability and thinking dispositions;
  6. Whitman, Walt. Leaves of Grass. Philadelphia: David McKay, [c1900];, 1999.
  7. Wikipedia: Critical path method; extracted 25 March 2018;
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Looks like «Define a question» is back again at in the winning position.


I am grateful that you made a window out of Walt Whitman’s poem, for those of us who are babes in the woods in matters and norms of logic, but sense in “critical path” something of electric value and use! : )