Notes No. 1 on Debatalist No. 1 - Typology of Propositions

How should we call theoretical propositions about debate of distinctly different natures, and where do these different natures come from?

Foreword

Warning

This dialogue, and all Notes entries, are an unstructured and unedited collection of notes concerning a concept considered in Debatalist No. 1¹.

The content of Notes is at large exploratory, rather than exhaustive—they do not claim to define the scope of consideration for the concept and certainly warrant further inquiry (perhaps by others).

We believe certain claims here are refined. We will defend them and export them for mainline dialogues. In this dialogue, we believe these concepts are finished and broadly applicable in theoretical contexts:

• The differentiation of descriptive and prescriptive propositions.

• The differentiation of analytic and a posteriori propositions (though not the possibility of the synthetic a priori).

• The differentiation of prescriptive propositions for separate categories of debaters.

• The recognition that common invocation of separate types of prescriptive propositions (strategic: debaters would win more if they X) do not necessarily affect other distinct types (ideal evaluative: under a maximum epistemic scope, what should evaluation determine?).

• The syllogism in the analytic a priori section is unconditionally valid and sound for rational debaters adhering to categorically predictable norms.

These Notes should be considered more advanced and difficult to read than mainline Debatalist dialogues. It is not advisable for people confused about central concepts to continue reading if they cannot easily discard what they have read here.

We apologize for any semantic, syntactic, or logical errors in this dialogue.

Axioms

The same axioms as Debatalist No. 1 are imported here.

Abstract

Introduction

The types of propositions debaters can come to believe are easily definable, but often confused in common parlance. For example, confusing ideal evaluative propositions with strategic propositions leads a debater to respond to discussions about how judges should evaluate certain arguments with ‘but don’t judges believe X, and thus by extension debaters should say X?’

Let us create a typology of propositions. The first division of propositions is between the descriptive and the prescriptive.

Descriptive

A descriptive proposition says something is, was, will be, could be, or must be the case.

Prescriptive

A prescriptive proposition says something ought to be the case. There are typically different prescriptive propositions for separate classes of agents.

Various Natures of Descriptive Propositions External to Debate

A descriptive proposition can be arrived at in several distinct fashions.

An a priori proposition is justifiable before experience², and an a posteriori one is not. Thus, the a priori proposition is ascertainable by all reasoners, given that no experience of this or that person is required to determine it.

An analytic proposition is logically necessary. Here are some examples of logically necessary statements:

• P is P.

• If P, then not not P.

• Either P or not P.

• Unmarried men are unmarried.

• An X that is G and F is G.

Analytic propositions are tautologous. Their falsity would result in a true contradiction. These propositions can never be a posteriori, since a specific experience is not required to recognize a logical tautology.

Synthetic propositions are not tautologous. Claiming their falsity would not necessarily result in a true contradiction.

Analytic A Priori

One may notice that these dialogues use the term ‘a priori’ loosely and strangely. We do not believe most of the propositions we enumerate as being a priori for debaters are a priori for persons. Instead, we believe that when a debater enters a format they absolutely and universally grant some propositions presented by the administrator, and that these propositions are antecedents for conditionals that are a priori. Thus, granted that the propositions we admit are true when we debate are true, the consequent is a priori.

The Greenhill Fall Classic Invitation best demonstrates this implicit concession (emphasis ours):

Please read the invitation carefully as it contains new and important information that will affect all those attending the tournament. A common theme of this invitation, based on the language and implicit assumptions therein, is that you are a guest of Greenhill School and its coaching staff and by competing in the tournament, you are agreeing to adhere to our guidelines as a condition of participation in the Greenhill Fall Classic.³

Behold the logical form of this trickery of a prioricity:

1. If agent X agrees to adhere to a prescriptive proposition enumerating conduct for X that is permissible or impermissible, X knows what that proposition is.⁴

2. If X knows some conduct Y⁵ is prescribed by Z to be impermissible⁶, they would be culpable for that conduct Y to Z if X brought about conduct Y.

3. If X intends to engage in one of Z’s proposition-exchanges, X tacitly agrees to adhere to the prescriptive propositions outlined in Z’s definition of their proposition-exchanges.

4. If X intends to agree to adhere to a prescriptive proposition, X has true belief⁷ that X will not violate that prescriptive proposition.

5. X intends to engage in one of Z’s proposition-exchanges.⁸

6. X tacitly agrees to adhere to the prescriptive propositions outlined in Z’s definition of their proposition-exchanges.⁹

7. X knows the prescriptive propositions outlined in Z’s definition of their proposition-exchanges.

8. X is culpable to Z for all conduct X brings about in violation of prescriptive propositions in Z’s definition of their proposition-exchanges.

9. If X brings about impermissible conduct in a proposition-exchange X engages in, that proposition-exchange is not one of Z’s proposition-exchanges.

10. X agrees that if X brings about impermissible conduct in a proposition-exchange X engages in, that proposition-exchange is not Z’s proposition-exchange.

11. If X intentionally brings about impermissible conduct in a proposition-exchange X engages in, then X intends that that proposition-exchange not be one of Z’s proposition-exchanges.

12. If X intentionally brings about impermissible conduct in a proposition-exchange X engages in, then X intends to engage in one of Z’s proposition-exchanges and X intends that that proposition-exchange X engages in not be one of Z’s proposition-exchanges.

13. If the proposition-exchange X engages in is not one of Z’s proposition-exchanges, then X is not engaging in one of Z’s proposition-exchanges.

14. Rational agents do not hold mutually exclusive intentions.

15. If X intends to engage in one of Z’s proposition-exchanges and X intends that that proposition-exchange X engages in not be one of Z’s proposition exchanges, then X holds mutually-exclusive intentions.

16. Debaters of Z’s format are agents that intend to engage in one of Z’s proposition-exchanges.

17. A rational debater of Z’s format does not intentionally bring about impermissible conduct as prescribed by Z’s definition of their proposition-exchanges in Z’s proposition-exchange.

The trickery is located in proposition #5.

X intends to engage in one of Z’s proposition-exchanges.

This proposition is a posteriori but unconditionally admitted by debaters of a given format. Conditionals for which #5 is the antecedent thus have a consequent that is unconditionally and universally true for debaters. This definition of a priori works out—the moment one intends to debate, proposition #5 is justifiable before experience (one knows it without observing the world since one defines onerself as a debater by engaging in the dialogue) and universal for debaters.

There are several analytic a priori propositions in this syllogism as well. The analytic proposition is tautologous—in other words, its subject is synonymous with its predicate. Take proposition #14:

Rational agents do not hold mutually exclusive intentions.

Indeed, ‘rational agent’ means an agent that does not hold mutually exclusive intentions. So the proposition is equivalent to:

Agents that do not hold mutually exclusive intentions do not hold mutually exclusive intentions.

This easily follows from axiom #1 in No. 1. Things are identical with themself.

X (an agent) that is Z (does not hold mutually exclusive intentions) is X that is Z.

X is equivalent to X. To determine if the two things are equivalent we must compare Z and Z.

Z is Z.

Seems proven to us! And—one can justify the identity axiom without experience, so it’s a priori.

Synthetic A Priori

Synthetic a priori propositions can be justified before experience, but are not logically necessary. It is hard to imagine what this sort of synthetic a priori proposition is. Kant believed in a separate definition of synthetic that the logical positivists eventually tore down. We believe the synthetic a priori still exists when analytic propositions are defined as logically necessary. For example, take a simplified form of Plantinga’s ontological argument:

1. There is a possible world where there is a being with maximal greatness.

2. A being has maximal greatness in a possible world only if it has maximal greatness in every possible world, including the actual world.

3. Therefore, there is a being with maximal greatness in the actual world.

For us, the set of possible worlds contains all worlds where the set of true propositions for those worlds are internally consistent.

Can proposition #3, the conclusion, be negated without generating a logical contradiction? Let us look at a parallel argument:

1. There is a possible world where there is no being with maximal greatness.

2. A being has maximal greatness in a possible world only if it has maximal greatness in every possible world, including the actual world.

3. Therefore, there is no being with maximal greatness in the actual world.

Looking at the arguments, the controversy is clear. If the necessary being possibly exists, it exists, and if it possibly doesn’t, it doesn’t exist. The question is which premise is more convincing:

1. There is possibly a maximally great being.

2. There is possibly not a maximally great being.

Both these cases comply with identical modal logic except for contesting the first premise and coming to opposite conclusions. Is there a purely a priori case to believe one of these first premises over the other? Yes.

Since a possibility merely demands that the set of true propositions for that possibility be consistent, there are differing possibilities of self that indicate a massive set thereof. Even if determinism is true, it still could have been predetermined that our inner self would have neglected to decide one less or more arithmetic propositions. We know a priori only that the process of thinking is occurring, and we can a priori recognize that thinking selects to believe certain things. 5 + 7 = 12, for example, is an analytic a priori truth that this process of thought can choose to believe or not.

Thus:

1. A priori, thinking occurs that either selects to neglect, affirm, or negate propositions from a set of propositions of the form: N is a real number, where the set contains each real number.

2. There is no a priori contradiction apparent in imagining a non-contradictory way thinking could have occurred, since thinking can be irrational.

3. There are an uncountably infinite number of possible worlds.

If there is possibly a maximally great being, that maximally great being is true of every possibility. However, that does not mean all possibilities make the existence of the maximally great being (and thus, its necessity) automatically apparent.

Imagine beginning to ponder, one by one, each of the uncountably infinite number of possible worlds. Given that one’s a priori knowledge is limited to one’s ‘inner world,’ one can’t ponder actual noumenal existence. The maximally great being could always exist noumenally, but one would never be able to disprove its existence through pondering. Thus, this process could continue eternally without disproving the being.

However, the being could make its existence apparent in a possibility by some concept (perhaps arithmetic) in the inner world. Due to its maximal greatness, one’s inner world in that possibility is awed by the self-evidence of its divinity. One automatically recognizes this as the maximally great being, which also exists in the real world because one has just been inspired by divine contemplation of a mere possibility.

One can never show that a possibility does not contain the maximally great being, but one can show that it does. There are uncountably infinite possibilities to consider for this proof. The logical arguments against a maximally great being tend to either be a posteriori, to take false premises, or to assume that certain properties are maximally great that do not have to be.

Given that there are uncountably infinite possible worlds where the maximally great being could happen to be, we should consider this through three lenses:

1. The first is presumption. Somebody claiming that there is no possible world where a given thing exists has the burden of proof since they must show that the set of true propositions for that world contains a contradiction.

2. The second is simplicity. The maximally great being is likely simpliciter noncontradictory. While some raise issues with its omniscience and omnipotence, there is no reason these are qualities of the maximally great, especially if they contradict. The maximally great must maximize greatness, and by virtue of maximizing greatness maximize it in every possibility. However, a priori it is difficult to know whether the maximally great being’s properties are truly contradictory or noncontradictory. It is uncertain.

3. The third is probability. For each of the uncountably infinite worlds one ponders, there is some non-zero probability that one discovers proof of the maximally great being in one calculated from the chance that maximal greatness contains an intrinsic contradiction. Even if one is extremely suspect that maximal greatness is inherently contradictory, one’s limited cognition could not make sense of this, since the greatness is maximal. A close to zero but non-zero probability assigned here will still approach 100% over the uncountably infinite set of possible worlds. Thus, unless one is certain that the maximally great being is impossible, which one a priori should not be, one should take the probability of eventually proving the maximally great being to approach 100%.

Let us return to the same two judgments:

1. There is possibly a maximally great being.

2. There is possibly not a maximally great being.

Both of these propositions are a priori. Why? They concern possibilities other than the actual world, which must be imagined as sets of propositions in our mind. However, a posteriori observation of the actual world may elucidate one possible world: the actual one. What if the definitive proof or disproof of the maximally great being only existed in the actual world? Remember—if it does or does not exist in one world, that’s true of every world. So internally studying sets of propositions for contradictions continuously will still provide strong evidence one way or the other. If it occurred infinitely, one would discover the possibility of a world like the actual one without relying on a posteriori judgment.

One could negate the existence of the maximally great being by establishing the possible existence of something contradictory with its existence, or by exhausting the infinite set of possible worlds in the search after infinite time has elapsed. This negation would be a priori but would not flatly result in a logical contradiction.

However, they are not analytic in the sense of either Kant or the logical positivists.

For Kant, their subject is not synonymous with their predicate. Let us substitute the whole of their meaning:

1. A maximally great being who if existent is necessary is possible.

2. A maximally great being who if existent is necessary is not necessary.

And for the logical positivists, negating either does not flatly result in a logical contradiction. Thus, premise #1 of Platinga’s ontological argument, the conclusion, and the same propositions from the parallel argument are synthetic a priori propositions. If the first two are true, the last two are false, and vice versa. Ergo there are some true synthetic a priori propositions.

Given the context of No. 1, the above speculation on the synthetic a priori is rather unnecessary, since agency and objective value as epistemic wagers both are a priori arguments for an ought concerning conduct per some belief that neither results from the synonymity of the subject and predicate nor have a negation that results in logical contradiction.

Moreover, we are not committed to the existence of the true synthetic a priori proposition and its falsity does not negate our theory at large.

Synthetic A Posteriori

A synthetic a posteriori proposition bases itself on observation of the outside world. There is not much to be said about the synthetic a posteriori here.

Practical

Descriptions

A priori descriptions are categorical propositions. They identify some facts true for all debaters as a category when they are instantiated and conditionals are granted absoluteness of their antecedent.

Analytic a priori descriptions are definitional propositions. They identify some intrinsic, logically necessary facet of their subject.

Synthetic a priori descriptions are systematic propositions. They a priori construct a full system of descriptions and consequent prescriptions for debaters.

Synthetic a posteriori descriptions are contingent propositions. They identify some empirical fact that merely happens to be true.

Prescriptions Ethical and Prudential

Ethical prescriptions say that there is some true metaethic that an agent objectively ought to act following.

Prudential prescriptions say that there is some conduct an agent should undergo either for their self-interest or some other significant subjective goal.

Administrators

Nomothetic

A nomothetic proposition is an ethically prescriptive proposition true for an administrating debater. It is directly imported from the true metaethic and imposed upon debate contexts—for example, the administrator must consider that other debaters should act per their will, and thus act per the metaethical right insofar as it’s true. The term ‘nomothetic’ was selected for its similarity to the fashion in which the administrator ‘lays down’ the law and its uncommon usage.

Operative

An operative proposition is a prudentially prescriptive proposition true for an administrating debater. It suggests what is in the best self-interest of the administrator. Operative propositions are usually political and often evoke liberal concepts of the common welfare since the administrating agent is a network of agents with one agency at the top. Nomothetic propositions objectively trump operative ones.

Proposition-Evaluators

Evaluative

An evaluative proposition is an ethically prescriptive proposition true for a proposition-evaluator. Its scope is confined to the roles laid out for the proposition-evaluator by the administrator since any moral action insofar as agents engage with debate must be performed per the administrator’s will. It is called evaluative because the chief role of the proposition-evaluator is to evaluate propositions.

Ideal Evaluative

The ideal evaluative proposition is a subset of the evaluative one. It asks “Given a maximal epistemic scope, how should I evaluate X?” While normal evaluative propositions consider only the propositions presented in the round, abstract out-of-round theorization often ponders how arguments line up all else being equal and truth being considered. Often, some phrase the ideal evaluative inquiry as ‘debated evenly, which argument wins?’

A precise definition is here:

The ideal evaluative proposition prescribes how the proposition-evaluator should credit or discredit certain propositions given that they know all other relevant propositions.

Derelict

A derelict proposition is a prudentially prescriptive proposition true for a proposition-evaluator. It suggests what is in the best self-interest of the proposition-evaluator. Derelict propositions are devoid of any duty or morality except perhaps basic care for children in the activity. A proposition-evaluator following derelict prescriptions might arrive only to deliver an affirmative output unconditionally and liberally utilize the amenities in the judge’s lounge.

Proposition-Exchangers

Competitive

A competitive proposition is an ethically prescriptive proposition true for a proposition-exchanger. Its scope is confined to the roles laid out for the proposition-exhanger by the administrator since any moral action insofar as agents engage with debate must be performed per the administrator’s will. It is called competitive because the chief role of the proposition-exchanger is to compete in the proposition-exchange.

Delinquent

A delinquent proposition is a prudentially prescriptive proposition true for a proposition-exchanger. It suggests what is in the best self-interest of the proposition-exchanger. Delinquent propositions grant instructions for whatever a debater wants to do. We’ll argue later in an anthropological commentary that these delinquent propositions explain the basis of debatability and contingent predictability. These can include lying, stealing prep, stealing and submitting the ballot oneself, and physically harming one’s opponent or proposition-evaluator.

Strategic

A strategic proposition is a subset of the delinquent proposition that is strange in that it occasionally overlaps with the competitive proposition. The strategic proposition asks in all cases how to maximize outputs in one’s favor submitted by the proposition-evaluator, or modified by the administrator. It was originally believed that all delinquent propositions were strategic, but Aryan Prabhakar disproves the idea that true prudential propositions must always be a strategic judgment. Prabhakar has a self-interest that directly contradicts winning debates.¹⁰

Interlopers

Docile

A docile proposition is an ethically prescriptive proposition true for an interloper. The docile propositions are likely determined, as benign interloping defined in No. 1 is permissible, and malicious interloping is impermissible.

Obtrusive

An obtrusive proposition is a prudentially prescriptive proposition true for an interloper. It suggests what is in the best self-interest of the interloper.

Short, Exportable Guide

Descriptive Propositions

Categorical Propositions

These are a priori descriptions. These identify a fact that is admitted as an unconditional truth for all debaters

Definitional Propositions

These are analytic a priori descriptions. They identify some logically necessary facet of their subject—they define some concept.

Systematic Propositions

These are synthetic a priori descriptions. They identify intersections between other categorical propositions.

Contingent Propositions

These are synthetic a posteriori descriptions. These identify some facts that are merely true of happenstance.

Prescriptive Propositions

Administrator Prescriptions

These prescribe something for the administrator.

Nomothetic Propositions

These are ethically prescriptive for how the format ought to be organized. These typically follow directly from the metaethic and the definition of competitive two-sided debate.

Operative Propositions

These are prudentially prescriptive, and serve the self-interest of the administrator.

Proposition-Evaluator Prescriptions

These prescribe something for proposition-evaluators.

Evaluative Propositions

These are ethically prescriptive, based on what the administrator lays down.

Ideal Evaluative Propositions

This type of evaluative proposition claims how much credibility¹¹ a proposition should be evaluated with when all relevant propositions are known, a.k.a. 'evenly debated...'

Derelict Propositions

These are prudentially prescriptive, and serve the self-interest of the proposition-evaluator.

Proposition-Exchanger Prescriptions

These prescribe something for proposition-exchangers.

Competitive Propositions

These are ethically prescriptive, and based on what the administrator lays down

Delinquent Propositions

These are prudentially prescriptive, and serve the self-interest of the proposition-exchanger.

Strategic Propositions

This type of delinquent proposition prescribes conduct for strategic success (i.e. output from the proposition-evaluator and administrative modifications thereof in one’s favor).

There are possibly two further subsets of the strategic proposition—a perfect strategic, which aims to win by acting as if the proposition-evaluators are always acting per the true evaluative propositions, and the honest strategic, which aims solely to garner successful output from the proposition-evaluator as is.

Interloper Prescriptions

These prescribe something for interlopers.

Docile Propositions

These are ethically prescriptive for an interloper. These statements, when true, permit benign interloping and bar malicious interloping as defined in No. 1.

Obtrusive Propositions

These are prudentially prescriptive, and serve the self-interest of the interloper.

Notes on This Arrangement

• Nomothetic propositions are typically based chiefly on contingent propositions.

• Prudential prescriptions are largely based chiefly on contingent propositions.

• Non-nomothetic ethical prescriptions are chiefly based on categorical propositions.

• Most of the existing debate theories solely consider competitive, strategic, evaluative, and ideal evaluative propositions.

Final Note on Debatalist No. 1

Some criticized No. 1 because it lacked several traits of dialogue they’d consider ‘easy’ to read, such as style or comprehensibility. We understand and sympathize¹² with this perspective, but it is ultimately a sickness of current debate for which our lack of style and specificity is the best medicine.

These dialogues exist to argue for certain ideal evaluative propositions. One of the largest problems in debates is the inability of debaters to grasp distinctions between distinct concepts. For instance, debaters often attempt to leverage strategic truths to disprove an ideal evaluative one, which is never a valid argument. Perhaps another example serves better here—in response to the predictability standard on 2AC framework, sometimes the kritikal debater will say their argument is ‘common,’ and is thus predictable. Policy debaters would do the same for agent counterplans, so this is not a flaw of only the kritikal debater.

Once one has realized this is true, one should easily recognize that the aforementioned ‘comprehensibility’ problem is a sickness of being a debater inundated by the current state of high-level debates. The obsession with texts that are easy to read, characterized by style, and less meticulous certainly leads readers to Nietzsche over Kierkegaard and Kierkegaard over Kant. However, that ease of reading Nietzsche led to his perennial abuse. Even Kant, for his ambiguities, has been mired in interpretative disputes. It follows that the clearest text minimizes semantic and syntactic ambiguities, for all the ambiguities of texts prior suffer unto death of the lack of clarity.

We specify what a concept means and then use it brutishly, in conjunction with precisely defined logical and metaphysical concepts and other concepts we have packaged. This meticulosity is unceasing because it is in every case necessary. To construct an exportable and clear general theory of debate, that theory must be meticulous and perhaps difficult to understand. It requires attention.

There is always a tradeoff between specificity (ensuring that the text is read closer to the intended way) and ease of comprehension (the ability of the reader to comprehend the text the way they’d like to). We have unequivocally chosen specificity. No quarter will be given to the sickness of anti-intellectualism’s grasp over debate.

1. (Chinmay Khaladkar, Adam Humphrey, & Adhi Thirumala, 8-21-2024, “Debatalist No. 1 - General Constructive,” The Debatalist Papers, https://substack.com/home/post/p-147730271, accessed 8-21-2024)

2. (N.A., 5-6-2020, “A Priori Justification and Knowledge,” Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/apriori/, accessed 8-22-2024)

3. (N.A., 2024, “2024 Fall Classic Invitation,” Greenhill Debate, https://docs.google.com/document/d/1c1amwviBXgADKBOLq2sxPUt7UTYJXctKk9XhoJ4pRAc/, accessed 8-21-2024)

4. This is less problematic than it appears. To agree to something, one must comprehend it—otherwise, one is not agreeing to it. Most agreements include that the signatory understands the guidelines for redundancy, and to clarify this point.

5. Failing to perform mandatory conduct is impermissible conduct.

6. Impermissible here can exist in any context—it could mean ethically impermissible, prudentially impermissible, or impermissible as per the command of another agent.

7. This does not necessarily demand knowledge. X must believe that they will conduct themselves per the agreement, or the agreement is false. X must conduct themselves per the agreement, or they accidentally fail it.

8. Debatalist No. 1 demonstrates how this must be unconditionally accepted as a precondition for a dialogue on how to debate better.

9. This is implicitly contained in X’s becoming a debater of Z’s format. Because X intends to be a debater of Z’s format, they intend that their proposition-exchanges be a member of the set of Z’s proposition-exchanges.

10. This is detailed further in the forthcoming The Non-Black Hero of Black Debate: A Critique of 'Becoming Transracial'.

11. A forthcoming dialogue will detail the nature of dialogues, credence, minimal evidence, maximal evidence, and the flow.

12. Some forthcoming dialogues will be non-Debatalist anthropological discourses that contain style, brevity, and clarity.