What is the telos of philosophy? And why exactly would PC hinder it? To investigate this question, we must probe the physis of philosophy, so to speak. In particular, its knowledge-evaluating dynamics. In this section, I shall present some arguments inspired by technical results from applied science to defend the epistemic integrity of philosophy against contentions that philosophy is or should be congenial to PC. In particular, I will briefly expose some tools originated from the field of engineering which I hold will help us understand the relationship between PC and philosophy.

Legitimate fields of inquiry, in relative contrast to stagnant pseudoscience and pseudophilosophy, other degenerate research programs and dogmatic ideologies, are; this can be informally characterized as the dual claim that their funds of knowledge tend, over time, to be populated with more and more constructs which are better attuned to the goals of the field 28 . If philosophy is a field of inquiry, it is no exception—although the advancement appears to be considerably slower than other fields of inquiry [ 118 ]. However, despite all the alleged actual and potential insurmountable mysteries, antinomies, paradoxes and theoretical dead-ends as well as unfortunate periods of wasteful degenerate philosophical research programs where the function of our philosophical knowledge loses its monotonicity, I take it that that we stand today in a more fertile ground than the one initiated by Nietzsche’s admired “Greek sages” 29 . For a candid but blunt example, the seeds of Thales have ultimately germinated in the minds of a succession of thinkers—from Aristotle, Leibniz and Boole to Gödel, Church and Turing—responsible for the formal causes of the technological marvel I am using to write this paper down 30

Following developments from contemporary epistemology which will be discussed in greater detail later in Section 5.3 , goals come in two types:and. This distinction will remain undefined and purely in the domain of intuitive appreciation; epistemic goals include standards such as wisdom, understanding, learning and, most important for our investigation,. Non-epistemic goals are a heterogeneous lot which includes economic profit, well-being, entertainment and the other primary indictee of our investigation,

Under this framework, the metaphilosophical quest for a definiendum of philosophy would typically center in the analysis of the problematics R of the field of inquiry of philosophy. I shall not venture into this hard issue. Instead, I’ll focus on other aspects I take to be both more readily scrutable and which will be sufficient for my arguments; the set of goals G and the set of values V of philosophy.

We could devise axioms for a “black box” model of the production of knowledge, where one or more professionals a , a ∈ A targeting a problem p , p ∈ R engage in a research process f ∈ B which takes as input a proper subset the fund of knowledge F and outputs a construct x , x ∈ C .

V is partitioned into proper subsets S i whose members stand under a partial order relation ≽, the different families of evaluation standards

V is a set of comparative structures, the values used by members of A to assess members of C under G

C is partitioned into proper subsets K i , each pertaining to a class of comparable constructs (rival constructs engaging with a same topic from P )

The measurement-theoretical construct of a, defined in Appendix A.1 , will be deployed many times in this section.

Genuine philosophy, alongside all of the legitimate sciences and some of the other humanities, when properly conducted as investigative pursuits (such as archaeology and history) are all taken to be examples of fields of inquiry.

My starting point is the fruitful framework designed by philosopher-scientist Mario Bunge to characterizein general and 9 ] in particular 26 . Bunge’s set-theoretical exposition of epistemic fields portrays the complex systems under which knowledge, broadly considered, is produced by human beings.

In the post-Wittgensteinian world we live in where a thriving cognitive science scrutinizes the statistical character of the contents from our most beloved concepts, we have become reluctant to accept ambitious definitions with crisp either-or membership criteria as an answer for questions with the schematic structure ’what is x?’. However, given the preliminary state of these investigations, I hold we’re warranted to explore this nebulous terrain with the aid of conceptual analysis and other formal methods conjoined with a dose of plausible empirical speculation; we must start from somewhere and diligently revise our constructs as empirical data is revealed.

But what truth are we talking about? Modern mathematical logic has a built-in formal theory of logical truth as model-satisfiability which has been famously advanced as an interpretation of the “classical” (correspondence) conception of truth. I shall not assume this particular schematic structure of truth. Instead, in the spirit of maximizing generality and neutrality, I characterize a bland conception of truth for fields of inquiry which should be compatible with many different theories of truth. Truth, being a goal, will be represented as a bounded comparative structure 〈 T , ≽ 〉 with a pair of real numbers setting a lower bound (absolute falsity) and an upper bound (absolute truth). For convenience reasons, we can use the well-known interval [ 0 , 1 ] . The relata of the ordering relation ≽ are constructs x 1 and x 2 being compared with respect to truth. If one holds that philosophical truth is strictly bivalent, one may replace a continuous comparative structure for a discrete one so that the image of the function of truth τ ( x ) only has two values, such as {0,1}. However, I believe the analysis is more fruitful if we concede orders of truth for philosophical representata . For instance, assuming that the following examples are rival positions and thus members of the same class K 1 , for a philosopher to hold that x 1 (neutral monism) is truer than x 2 (materialism) and to hold that materialism is truer than x 3 (substance dualism) is to assign as the image for the function of truth τ ( x ) of these constructs three real numbers y 1 , y 2 , y 3 so that 0 ≤ y 1 ≤ y 2 ≤ y 3 ≤ 1 .

Up to this level of analysis, the postulated features of truth-seekingness and cognitive progress not only underspecify philosophy but makes it indistinguishable from basic (as opposed to applied ) science. This is not an accident, but probably comes from shared inheritance for basic science is historically an offshoot of philosophy. It is also not a demerit for the arguments I shall deploy in support of a radical separation of philosophy from political correctness will be just as effective if applied to basic science.

This metaphilosophical position may no longer be as fashionable, but I contend that it is hard to make sense of philosophy which does not take truth as an epistemic goal. If one holds that philosophy has nothing to do with the pursuit of truth, I take it as a conversation stopper and a performative contradiction. For if metaphilosophy is philosophy, the disagreement with the metaphilosophical inquiry of what philosophy isis a disagreement on theof what philosophy is for. If one wishes to follow the road of doing philosophy that rejects these basic constraints of rationality, one is at the risk of, to paraphrase philosopher Daniel Dennett, to engage in nothing more than “verbal ballet” [ 123 ] or to play “intellectual tennis without a net” [ 124 32 . Philosophies so unrestrained are mere belief systems,fields of inquiry. The question of the possibility of philosophy being able to thrive as both a truth-oriented activity and a vehicle for social justice—both understand the world and to save the world—will be answered negatively in the next sections.

What are the goals of philosophy? I accept that the gist of this issue has been successfully captured by one of the oldest (if not the oldest) metaphilosophical accounts; out of the Pythagorean, we extract that philosophy is, first and foremost, aenterprise [ 121 ]. Even if there exists contentious disagreement on both the domain of truths philosophy seeks (not to mention the nature of truth itself!),of some persuasion remains the supremeof philosophy 31

I posit that sound philosophical and scientific inquiry is often constrained by a shared set of regulatory ideals, i.e., for an arbitrary family of evaluation standards from a basic scienceand another from philosophy,, we should expect that. For instance, one of these which I hold follows naturally from the character of philosophy as a truth-seeking field of inquiry is the epistemic value of; philosophy ought to be consistent with the truths revealed by other epistemic fields at least as epistemically secure as itself, the natural sciences being a prominent example 36 . If your descriptive metaphysics is inconsistent with the most established developments of quantum mechanics and general relativity, then your system loses epistemic value. If your normative ethics is inconsistent with the most solid results of behavioral genetics and moral psychology, then this is also a serious defect of your theory. And so on.

This last definition is stimulated by intuitions on the existence of possible hierarchies of alethic epistemic values in which some are more “basic” than others and the possibility of there being alethic epistemic values that are, performing idle work. For instance, elegance 35 may be tracking simplicity, in which case it would be aepistemic value. However, in scientific practice, proxy variables are often indispensable, particularly when the relevant variable researchers aim to track is non-observable.

is a dummy alethic epistemic value if and only if there exists another alethic epistemic value

An alethic epistemic value 〈 E , ≽ 〉 is a dummy alethic epistemic value if and only if there exists another alethic epistemic value 〈 E ′ , ≽ 〉 and the values of the function ϵ ( x ) are proxy variables of ϵ ′ ( x ) , that is , ϵ ′ ( x ) is better correlated with τ ( x ) than ϵ ( x ) .

is a politically correct value if and only if the function of social justice

For a certain field of inquiry F with the non-epistemic goal of social justice, 〈 J , ≽ 〉 ∈ G , a value 〈 P , ≽ 〉 ∈ V is a politically correct value if and only if the function of social justice σ ( x ) is positively correlated with the function of the value ρ ( x ) .

For instance, if we have good reasons to think that when a philosophical construct fares well in semantic definiteness and formal rigor, its truth is being enhanced, then these are candidates for being alethic epistemic values. If scoring well in ad hocness and unwarranted aprioricity has the opposite effect, we have the opposite conclusion.

is an alethic epistemic value if and only if the function of truth

For a certain field of inquiry F with the epistemic goal of truth , 〈 T , ≽ 〉 ∈ G , a value 〈 E , ≽ 〉 ∈ V is an alethic epistemic value if and only if the function of truth τ ( x ) is positively correlated with the function of the value ϵ ( x ) .

The sole epistemic goal we will be interested in isand the only epistemic values I’ll be interested in I’ll call, those that are truth-enhancing. Other possible epistemic goals (such as understanding or curiosity satisfaction) do not necessarily converge with truth. For instance, educators teaching basic arithmetic with positive integers to small children, in an attempt to make the subject more intelligible, (that is, to attain the epistemic goal of) often utter verbal heuristic devices such as “you can’t take a bigger number from a smaller number” which are strict mathematical, either decreasing or neutralize the goal of truth [ 130 ].

Let us taketo be accomplishable by constructs bearing the appropriate epistemic values and the converse happening with. For instance, applied science, such as the several branches of engineering, differs from basic science by having additionalnon-epistemic goals which supply further normative requirements [ 129 ]. As an example, the field of inquiry of aerospace engineering has an overarchingofand, the construction of machines that transit the atmosphere and beyond. These crafts, in turn, must efficiently carry on a variety of specialized supplementary practical duties depending on the role—from belligerent air supremacy to peaceful civilian transportation. Thus, the epistemic appraisal of an x (such as the computational model of an aircraft) must also be guided by the relevant non-epistemic or contextual values such as safety, resilience, acquisition cost, payload capacity, and firepower. Aerospace engineers naturally also want their fluid dynamics to be approximately true 34 or else their aircraft may not kick off the ground (much less reach escape velocity).

To formally characterize this relationship, we turn to a vibrant discussion in the contemporary epistemology of science onor 33 values (such as empirical adequacy, predictive accuracy, and external consistency; a finer-grained typology in the context of the epistemic field of science is found at [ 128 ]). These epistemic values are contrasted withorvalues (such as safety, social equality, and racial diversity). Fields of inquiry may employ both, in variable configurations according to their set of goals.

What must the relationship between a bearer of content x and a particular goalbe for it to be successful? A received philosophical view I’ll assume is that we are justified to hold x as being on the road to achieve a certain-goal if x “embodies” the appropriate. In the words of epistemologist and philosopher of science Stephen E. Grimm, “a belief earns positive marks (counts as justified, rational, virtuous, etc.), from an epistemic point of view, just in case it does well with respect to the things with intrinsic epistemic value (i.e., helps to promote them or bring them about). Likewise, a belief earns negative marks just in case it does poorly with respect to the things with intrinsic epistemic value” [ 126 ].

This kind of problem has been entertained by both philosophers of science dealing withandand epistemologists dealing with, which we may generalize as the problem of(for a contemporary overview, see [ 125 ]).

How do the members of an epistemic field legitimately evaluate a given construct as successfully attaining a particular goal of the field? And what if the field has multiple goals or worse, multiple conflicting goals?

We may now draw several semantic equivalences that will allow us to frame the problem of epistemic appraisal using the terms of fields of inquiry. Table 2 summarizes these correspondences:

These frameworks are commensurable. For instance, the criteria functions from MCDA just are the objective functions from MOO. Researchers often engage with the two types of problem at different stages of a same project 37

For each function ϕ i ( d ) , ϕ i ( d ) is to be either maximized or minimized

I shall make a very brief exposition of MCDA and MOO problems and draw some lessons for our project. Some understanding of vector algebra will be assumed for this section. Vectors are referenced in, conforming to a standard notation. First, let us check the structure of an MDCA problem (adapted from [ 134 ] (p. 10)):

The actors A intend to select a decision variant x , x ∈ X 0 for which μ ( x ) is the most preferred multiple criteria valuation

When one does not know in advance the alternatives of a problem involving multiple goals but has a working mathematical model to represent it, one has a design problem and may attempt to find solutions through multiobjective optimization (MOO, also called multicriteria optimization and multiobjective programming ).

From OR, we have two types of problem of interest; roughly, when an agent knows in advance a finite set of alternatives with variable performance in such and such criteria and needs to pick the best, one has an, and one does(MCDA, also calledor). The relevance of MCDA methods on the problem of theory choice in the philosophy of science has been explored in recent years [ 132 133 ].

Dealing with herculean projects which aim at the simultaneous satisfaction of multiple clashing objectives, often in the light of information that is partial and even inconsistent, is what many engineers, computer scientists, and economists working in the interdisciplinary field of inquiry of operations research (OR) do for a living. In the spirit of consilience among epistemic fields, I suggest that the general problem of epistemic appraisal in philosophy and other fields of inquiry can be represented using the formal skeletons of types of problems managed in OR and that we may tentatively draw some lessons from the decades of human ingenuity accrued by research in this field on the prognosis of politically correct philosophy.

5.5. Modelling Epistemic Appraisal

ordinal varieties of MOO and MCDA. In this move, we potentially lose several technical options but still capture what is more essential. As a team of control engineers puts it, “order [of objective functions] is much more robust against noise than ’value”’ [ Further qualifications are warranted. In the name of formal rigor and structural conservativeness, we strive to deal, if possible, solely withvarieties of MOO and MCDA. In this move, we potentially lose several technical options but still capture what is more essential. As a team of control engineers puts it, “order [of objective functions] is much more robust against noise than ’value”’ [ 137 ] (p. 13). Getting the order right is what’s most crucial.

simplicity of constructs [ Sometimes it is assumed that the values involved in epistemic appraisal can be readily given a cardinal interpretation. For instance, in the context of the epistemic appraisal of scientific theories and the demarcation problem, Martin Mahner proposes such an account of scientificity [ 138 ]. It is true that several such characterizations have been proposed for particular alethic epistemic values. Most notably, ways to quantify different senses of theof constructs [ 139 140 ]. Such polysemies in alethic epistemic values are probably the norm, making the problem even harder. The concept of simplicity in the context of epistemic appraisal, for instance, appears to be a mongrel concept that designates different syntactical, semantical, epistemological, practical and aesthetic properties of constructs [ 141 142 ]. Unfortunately, most philosophical theories (and other philosophical constructs) are informal and are yet to be expressed in the regimented languages required for such computations. This fact gives more credence to the proposal that presently, epistemic appraisal in philosophy (and science) should be a strictly ordinal endeavor.

〈 A i , ≽ 〉 . In MCDA and MOO, engineers regularly defy the measurement-theoretical doctrine of permissible transformations by treating ordinal variables as if they were interval or ratio-scalable (for instance, by extracting arithmetic means of arbitrary data and assuming that the different levels of Likert-type scales 38 are equally spaced magnitudes). In the absence of evidence that the variable at hand satisfies the axioms for linear structures or any kind of structure where an operation of concatenation isomorphic to arithmetic addition can be defined, one should be conservative and assume that it just meets the simpler and less demanding family of comparative structures

Postulate 19 (Non-Optimality). I suppose that, in general, for a given multi-objective optimization problem M O , there exists no solution x ∈ S that simultaneously attains the desired outcomes of objective functions f (i.e., maximizations and minimizations) under constraints h and g . Now, for an exposition of some of the results from these fields of inquiry:

The rule of thumb is that multiple objectives will conflict with each other. MOO is an art of negotiation and compromise; the quest for a Platonic ideal aircraft, traffic system, or automated factory is irremediably tragic—the optimal solution in the sense of scalar or single-objective optimization is generally impossible, and one must be content to one of their possible efficient worldly realizations.

Pareto efficiency (also called Pareto “optimality”). Consider the following definition of Pareto-efficiency (adapted from [ Definition 8 (Pareto Efficiency). For a MOO problem M O where the vector of objective functions f = { ϕ 1 ( x ) , … , ϕ m ( x ) } T is to be maximized , x ∈ S , a decision vector x ′ is Pareto-efficient if and only if there does not exist another x so that ϕ i ( x ) ≥ ϕ i ( x ′ ) for all i = 1 , … , n . A Pareto-efficient decision vector is strictly Pareto-efficient if and only if ϕ j ( x ) > ϕ j ( x ′ ) for at least one index j . Otherwise, it is weakly Pareto-efficient There are many types and hierarchies of efficient solutions; below the crown of scalar optimality [ 143 ] (Chapter 2), what rules more firmly is the notion of(also called Pareto “optimality”). Consider the following definition of Pareto-efficiency (adapted from [ 135 143 ]):

We call a set of Pareto-efficient solutions a Pareto frontier . Although these are often not computable, we may strive for solutions which approximate the Pareto frontier. We say that all Pareto-efficient solutions dominate over the rest of the solutions in the feasible region space.

Since the frameworks of MOO and MCDA are commensurable, each decision vector x may correspond to a decision variant x .

Let us contemplate some simple examples of evaluation problems in epistemic appraisal for philosophy. Consider a hypothetical metaethicist comparing three constructs, the thesis of moral cognitivism, the thesis of moral noncognitivism and a hybrid theory of both. He holds that four alethic epistemic values are relevant for his evaluation and posits ordinal values under a bounded interval [0, 10]. Table 3 summarizes this scenario:

Starting from very instinctive standards of rationality, it is a no-brainer that our model metaethicist should choose moral non-cognitivism over the others for it is either better or equivalent to the alternative positions in every respect. x 2 is the only Pareto-efficient solution of this set of decision variants, and it thus dominates the others.

Now, consider a philosopher of mind evaluating theories of personal identity also under four criteria. Table 4 depicts this scenario:

In this example, there is no decision variant dominating. All three options are Pareto-efficient. How does one choose? There exists no transcendental procedure, no single general algorithm that takes a set of efficient decision variants and outputs the most preferred one. Instead, there are several. Engineers may often find themselves in the paradoxical situation of having a second-order MCDA problem when choosing which method to use to solve a particular MCDA problem [ 144 ].

generalized concordance rules [ In the ordinal MCDA case, although the vast majority of algorithms involve aggregation procedures employing addition and multiplication at some point, there are fortunately some purely “qualitative” strategies. For instance, the approach of 145 ], which does not assume the additivity of typical “compare and aggregate” approaches in multicriteria decision-making.

How MCDA may model evaluation problems in fields of inquiry should be easy to see. What about design problems ? Here things get more complicated. I intend to use the framework of MOO to represent an ideal hunt for constructs that efficiently carry out the goals of the field through the maximization of the associated values.

stochastic optimization , so-called “ordinal optimization” procedures exist as an antecedent backstage to eschew computational burden for run-of-the-mill cardinal optimization [ empirical interpretation, (i.e., are not meaningful heuristic or pragmatic grounds and be positively informative. It is not clear if purely ordinal cases of MOO are feasible. Over the literature, in the context of, so-called “ordinal optimization” procedures exist as an antecedent backstage to eschew computational burden for run-of-the-mill cardinal optimization [ 137 ]. Some decision theorists (such as [ 134 ] (p. 58), in the context of scalarization techniques) have argued that even though some mathematical manipulations in certain procedures have nointerpretation, (i.e., are not 39 in a measurement-theoretic sense) they can be justified onorgrounds and be positively informative.

Postulate 20 (Epistemic Effectiveness of a Field of Inquiry). The epistemic effectiveness of field of inquiry F is a function of its power to produce quality constructs in C . I shall now add another informal companion for Postulate 19 meant to express something on the standards of success of fields of inquiry:

A received hierarchy of quality of constructs in the context of evaluation and design problems is thus:

Scalar Optimality, for problems with m = 1 functions

Strict Pareto Efficiency, for problems with m ≥ 2 conflicting functions

Weak Pareto Efficiency, for problems with m ≥ 2 conflicting functions

Approximations of Pareto Efficient solutions, for problems with m ≥ 2 functions

effective one. This leads us to the following consequence: Postulate 21 (The Curse of Multiple Goals). In general, for a field of inquiry F , the more goals in G it has, the more ineffective it is at the development of constructs in C which are efficient . Given this crude characterization, a field of inquiry that consistently produces more efficient constructs relative to the problems it entertains is a moreone. This leads us to the following consequence:

This conjecture emerges from considerations of Section 5.3 where each goal is associated which a cluster of values which have, as elaborated in Table 2 , a direct correspondence with objective functions of a MOO problem.

not linear ; it increases dramatically fast as m rises. This is partially due to an assortment of formal phenomena dubbed “the curse of dimensionality” (first exposed by [ This claim may look like a trivial truism; of course it is expected that the more targets a field aims to secure, the harder it is to secure them. But the point I’d like to emphasize is that the growth of difficulty is generally; it increases dramatically fast asrises. This is partially due to an assortment of formal phenomena dubbed “the curse of dimensionality” (first exposed by [ 147 ], in the context of dynamic programming) that take place with mathematical optimization as the number of objective functions increases.

N P -hard” decision problems where the computational resources required to reach a sufficiently strong solution may grow exponentially. Many families of algorithms effective at attaining or bordering the Pareto front in MOO with a small number of objectives do not scale well with a greater number of objectives. For instance, many evolutionary algorithms struggle to find Pareto-efficient solutions when m ≥ 3 [ hypervolume indicator , has a # P -hard (“Sharp-P”) complexity class, being as hard to solve as its associated NP decision problem [ These complex problems are a breeding ground for the infamous “-hard” decision problems where the computational resources required to reach a sufficiently strong solution may grow exponentially. Many families of algorithms effective at attaining or bordering the Pareto front in MOO with a small number of objectives do not scale well with a greater number of objectives. For instance, many evolutionary algorithms struggle to find Pareto-efficient solutions when 148 ]. Also, one of the most used procedures to test for the quality of two Pareto-efficient sets, the, has a-hard (“Sharp-P”) complexity class, beingto solve as its associated NP decision problem [ 149 ].

Up until this point, many criticisms are possible. I’ll briefly consider two of them. First, by taking as relevant these results from theoretical computer science in the context of mathematical optimization, we are implicitly representing the production of knowledge in an arbitrary field of inquiry F as a classical computational process, a program implementable in a Turing machine. Black box model for black model, it could be argued that professional experts are best modeled as more powerful computational systems (such as oracle machines) and thus, being able to circumvent the imposed difficulties in the formal framework I’m grounding my analysis in, rendering them irrelevant.

Second, it can also be questioned that since approximate solutions at a small distance from the Pareto frontier scanned by much faster heuristic algorithms are often good enough and attainable with fewer resources, by analogy the activities of professional philsophers may be modeled by much more realistic heuristic algorithms.

a priori expert knowledge compacting expectations of what a good solution looks like can be incorporated in the model, relieving burdens (for example, in the context of an evolutionary optimization [ The first line of argument is congruent with standard practice in operations research. In design problems,expert knowledge compacting expectations of what a good solution looks like can be incorporated in the model, relieving burdens (for example, in the context of an evolutionary optimization [ 150 ]). In evaluation problems, this is even more obvious as experts are consulted to place decision variants under preference relations, and this feedback is used to build decision-making procedures. Under a formal decision setting, experts can indeed be modeled as oracles of a sort.

very skeptical of the powers of their professional experts to find even “good enough” solutions in the feasibility space—much less efficient solutions (for instance, political psychologist Philip E. Tetlock has documented the underwhelming predictive accuracy of social scientists over even general economic and political trends [ However, I claim that, particularly for the less methodologically robust fields of inquiry (such as philosophy and the social sciences), we should beof the powers of their professional experts to find even “good enough” solutions in the feasibility space—much less efficient solutions (for instance, political psychologist Philip E. Tetlock has documented the underwhelming predictive accuracy of social scientists over even general economic and political trends [ 151 ]). Philosophy, in particular, may be the field of inquiry most pessimistic of the status of its cognitive achievements [ 120 152 ]. Also, as already acknowledged in Section 3.1 , existing empirical evidence on expertise effects behind properly philosophical inquiry (such as epistemology and ethics) is not consistent with philosophers having particularly special epistemic powers.

Under this framework, I posit that the main reason why philosophy, in contrast to science, is more ineffective is due to lack of robust standards under which contradictory efficient decision variants are to be evaluated. Science arguably has the “tribunal of experience” as the primary, if not overriding, standard of excellence, up until the point it faces empirical underdetermination.

Is philosophy doomed? If each goal deploys a portfolio with a myriad of values whose structure we know little about, we appear to be hostages of the curse of dimensionality. Postulate 21 may seem to undermine optimality in truth-seeking pursuits. Or does it? There are two basic routes when engaging with a MOO problem; either one treats it as a MOO problem in its own right and incurs in any computational burdens involved or one attempts to transform it into a much more tractable single-objective optimization problem (SOO) through a particular process of scalarization . ’Scalarization’ names families of different algorithms that transforms a vector of multiple objectives f = { f 1 ( x ) , … , f n ( x ) } T into a scalar { f ( x ) } .

Postulate 22 (Scalarization of Vectors With the Same Type of Goal). For a vector of functions f = { ϕ 1 , … , ϕ n } associated with the portfolio of Ω - values from a goal 〈 Ω , ≽ 〉 , it is assumed that f can be scalarized into f = { ϕ } without significant loss of information . In the name of optimism, I thus deploy the following bold conjecture: