The Gauntlet

Arguments against the false equivalence

For too long, the Standard Argument (SA) against free will has relied on a false premise; that indeterminism equals randomness. Libertarians (event causal, agent causal and non causal) have developed coherent and robust theories and conceptions, by themselves, that should have been sufficient to have shown that you can have non random indeterministic choices and actions in an indeterministic world.

However, to avoid any potential risk of begging the question, it is crucial to show that the logical possibility of non-random indeterminism exists independently of libertarian premises. In this respect, the propensity theory of probability (PTP), established by Charles S. Peirce (1910/1978), then separately developed by Karl R. Popper (1959), offers an independent paradigmatic example. This theory has also been interpreted more recently by numerous philosophers of science, including J.H. Fetzer (1981), D.A. Gillies (1973/2010), and D. Miller (1995). According to this approach, probability is not merely an observed frequency or a degree of subjective belief, but an objective physical disposition, an inherent tendency or propensity within a given system or experimental setup. This propensity characterizes the tendency of that system to produce a certain type of outcome, considered as a real property of the generating conditions themselves. The very existence of this theory, developed entirely outside the philosophical debate on free will, guarantees that non-random indeterminism is an independent conceptual possibility, which definitively dispels any suspicion of circularity in our argument.

To crystallize this foundational point with logical precision, the argument for the conceptual coherence of non-arbitrary indeterminism, drawing upon the independently established Propensity Theory, can be stated as follows:

Challenge 0 : A Rough Start

This argument establishes that indeterminism does not necessarily equate to mere arbitrary randomness. It proposes the coherence of indeterministic outcomes being guided by stable, inherent factors.

Core Definitions:

• Indeterminism: In an indeterministic world, the same event could have had a different outcome. (this definition is defended later on in Challenge 2) 
• Propensity Theory of Probability (PTP): Views probability as an objective, single-case disposition (a “propensity”) of a specific generating system to produce a particular outcome. These propensities can be indeterministic (i.e., their values lie between 0 and 1).
• Arbitrary Randomness (AR): Refers to indeterministic outcomes that occur without any specific guiding principle, stable tendency, or reason beyond chance itself; they are haphazard or chaotic.
• Non-Random Indeterministic Disposition (NRID): An objective propensity (as per PTP) for an outcome that, while indeterministic (not strictly determined), is specifically guided by stable, inherent factors or structures within the generating system, rather than being arbitrary.

The Argument:

1. P1) The Conceivability of Guided Indeterministic Propensities. It is conceptually coherent, within the framework of the Propensity Theory of Probability (PTP), to posit the existence of Non-Random Indeterministic Dispositions (NRIDs).
   
   • Illustration: Consider an agent’s decision-making mechanism that is Reason-Responsive (RR)—sensitive to reasons. If this mechanism operates indeterministically, it could manifest an NRID. For example, the agent might have a 60% propensity to choose action A (and 40% for action B) due to a stable set of reasons. This propensity is indeterministic (the outcome isn’t guaranteed) but guided by the agent’s reasons, not arbitrary.
2. P2) Essential Distinction from Arbitrary Randomness. If an outcome arises from a Non-Random Indeterministic Disposition (NRID)—meaning it is indeterministic yet specifically guided by stable, inherent factors—then this mode of occurrence is, by definition, distinct from Arbitrary Randomness (AR), which lacks such guidance.
   
3. C) Indeterminism Need Not Be Arbitrary. Therefore, since the concept of Non-Random Indeterministic Dispositions (NRIDs) is coherent (as illustrated by combining PTP with concepts like RR), indeterminism is not necessarily equivalent to Arbitrary Randomness.

To get a grip on what really are objective probabilities in PTP, let’s start easy :  

Introductory Challenge (0.5) : Laying down the groundwork

Preamble: Challenge 0 established the conceptual coherence of Non-Random Indeterministic Dispositions (NRIDs) within the Propensity Theory of Probability (PTP). This current challenge now explores how PTP applies to different mechanisms when evaluating their capacity to account for a fundamental characteristic of agency: Intentional Action Control (IAC). IAC denotes the ability to intentionally initiate an action or sequence of actions, sustain and repeat them based on ongoing intentions, and voluntarily cease them according to the agent’s reasons and goals, all within a potentially indeterministic world. We use “Task A”—an agent, for example, choosing to repeatedly press a button a certain number of times and then voluntarily stopping—as a clear illustration of IAC.

P1) Foundational PTP Applicability. The Propensity Theory of Probability (PTP) provides a framework for understanding objective probabilities inherent in various systems operating within an indeterministic world:

• a) Pseudo-Random Number Generators (PRNGs): In a PTP context, given a fixed starting seed, their subsequent outputs can be described by propensities of 1 (for the next determined output) or 0 (for any other output).
• b) Quantum Random Number Generators (QRNGs): The quantum events these devices utilize (e.g., photonic behavior, radioactive decay) are characterized by objective physical propensities (e.g., a 0.5 propensity for a specific bit outcome from an ideal quantum coin flip).
• c) Reason-Responsiveness (RR) Mechanisms: An agent’s choices emerging from an RR mechanism, operating indeterministically, can manifest as objective propensities (NRIDs) that are shaped and guided by their deliberative framework of reasons, values, and intentions.

P2) Evaluating Mechanisms against the Standard of Intentional Action Control (IAC). While PTP can describe underlying probabilistic elements in these mechanisms, their capacities to exhibit IAC (exemplified by performing Task A) differ critically:

• a) PRNGs and IAC: PRNGs can produce repetitive outputs if so programmed. However, they lack the capacity for IAC; they cannot voluntarily initiate Task A based on a current intention, flexibly sustain it while being open to altering course, or intentionally decide to cease the task based on an internal goal or reason. Their operations are fixed by their algorithm and initial seed.
• b) QRNGs and IAC: Although QRNGs are based on PTP-describable quantum propensities, they are designed to produce statistically random sequences. They possess no intrinsic mechanism for forming intentions, pursuing goals through sustained action like Task A, or exercising voluntary control over the initiation, continuation, or cessation of such a task. Replicating the controlled execution of Task A via a QRNG would be an outcome of extraordinary chance, not an exercise of capacity.
• c) RR Mechanisms and IAC: RR mechanisms, when understood as NRIDs within a PTP framework, are uniquely suited to explain IAC. An agent’s stable reasons and intentions can ground robust propensities to initiate and continue Task A. Simultaneously, their responsiveness to reasons provides the capacity for ongoing guidance, re-evaluation, and the voluntary cessation of Task A when their intentions or reasons shift (e.g., the intended number of repetitions is reached, a new, overriding reason emerges). This demonstrates controlled, guided indeterminism in action.

P3) The Explanatory Mandate for Models of Agency. A comprehensive model of agency, particularly within an indeterministic framework compatible with PTP, must be able to account for evident agentive capacities such as Intentional Action Control.

Conclusion (C): Therefore, while PTP offers a fundamental language for describing objective probabilities across various systems (PRNGs, QRNGs, and RR mechanisms), it is only when PTP is integrated with Reason-Responsiveness (conceptualized as NRIDs) that we find an adequate explanation for Intentional Action Control (as seen in Task A) within an indeterministic world. This reveals a crucial distinction: RR mechanisms demonstrate a PTP-compatible capacity for guided and controlled indeterminism that is essential for agency. Models that attempt to reduce indeterministic choice merely to the determinism of PRNGs or the unguided statistical randomness associated with QRNGs are therefore insufficient to capture this fundamental aspect of agentive behavior.

Challenge 1 : Hostile Grounds

• P1) In an indeterministic world, the propensity theory of probability (PTP) is a relevant interpretation. “[P]ropensity interpretations regard probabilities as objective properties of entities in the real world. Probability is thought of as a physical propensity, or disposition, or tendency of a given type of physical situation to yield an outcome of a certain kind, or to yield a long run relative frequency of such an outcome.” [2]
  
• P2) Intrinsically, all dispositions, including the propensities defined by PTP, are never random as properties themselves.
  
• C) Therefore, in an indeterministic world where PTP applies, propensities (objective probabilities) are intrinsically not random.
  

[2] Hájek, Alan, “Interpretations of Probability”, The Stanford Encyclopedia of Philosophy (Winter 2023 Edition), Edward
N. Zalta & Uri Nodelman (eds.),
URL = https://plato.stanford.edu/archives/win2023/entries/probability-interpret/.

Challenge 2 : A Stronger Definition

• P1): There are two standard definitions (SD) in contention regarding indeterminism:
  ○ SD(a): In an indeterministic world, the same event could have had a different outcome.
  ○ SD(b): An indeterministic world is a world where ontologically random events can occur.
• P2): SD(a) is compatible with all known forms of indeterminism: Libertarian approaches to free will (LFW), probabilistic approaches such as PTP, and approaches of ontological randomness such as in quantum mechanics (QM).
• P3): Ontological randomness (as defined in SDb) is incompatible with LFW and Propensity Theory of Probability approaches.
• P4): The criterion of extensional adequacy for a definition states: “A definition is extensionally adequate iff there are no actual counterexamples to it.”
• P5): SD(a) has no actual counterexamples.
• P6): SD(b) has actual counterexamples (notably, if LFW and TPP approaches represent valid forms of indeterminism, they would constitute such counterexamples because they do not involve ontological randomness according to P3).
• C): Therefore, SD(a) is the only definition [of the two presented] that is extensionally adequate.

Challenge 3 : The Final Blow

• P1): The standard argument against libertarian free will rests on a dilemma opposing determinism and “randomness”, presupposing an equivalence between indeterminism and randomness.
  
• P2): The Premise of Exclusivity (PE): The Standard Argument (SA) against free will must be considered as implicitly resting on the Commonplace Thesis (CT) [or an equivalent intuition or PE], because its rigid dichotomous structure (determined vs. random-uncontrolled) ignores or excludes outright the possibility of alternative models of structured indeterminism, such as those proposed by Propensity Theories of Probability (TPP) where the agent could act via objective dispositions and probabilities; however, this exclusion is logically founded only if one presupposes, like CT, that any form of non-determination (chance/randomness) necessarily equates to randomness incompatible with agentive control.
  
• P3): Moreover, the Commonplace Thesis is itself also anchored in strong common intuition and tradition.
  
• P4): The Premise of Exclusivity is anchored in CT, which in turn is anchored in strong intuition and tradition.
  
• C) Consequently, the Standard Argument is incapable of conclusively refuting libertarian free will. By relying on a Premise of Exclusivity (PE/CT) that is intuitive but undemonstrated, and which excludes a priori models of structured indeterminism (PTP or LFW), the SA commits a petitio principii (begging the question) or, at best, rests on an incomplete basis. The burden of proof is thus reversed: defenders of the standard argument must justify this exclusion, while logical space is reopened to explore libertarian models based on PTP that could reconcile indeterminism and agentive control.

Consequent Challenge 3.1: A brutal wake-up The Petitio Principii of the Standard Objection

• P1) The preceding arguments (1-3) establish the conceptual coherence and relevance of structured indeterminism models (e.g., PTP, LFW) that are distinct from simple randomness/arbitrariness (as encapsulated notably in P3 of Argument 2, which denies the universal applicability of SDb). Let us denote this position P, which implies Not (Indeterminism ⇒ Simple Randomness/Arbitrariness).
  
• P2) The Standard Objection (SO) against libertarianism fundamentally uses the inference chain: Indeterminism ⇒ Simple Randomness/Arbitrariness ⇒ Lack of Control/Explanation. The SO therefore crucially presupposes the equivalence or implication : Indeterminism ⇒ Simple Randomness/Arbitrariness. This is exemplified by Randolph Clarke’s description (2003) :

An undetermined action, it is said, would be random or arbitrary. It could not be rational or rationally explicable. The agent would lack control over her behavior. At best, indeterminism in the processes leading to our actions would be superfluous, adding nothing of value even if it did not detract from what we want. (p.1)

• P3) Attempting to refute a position (P) using an argument (SO) whose essential premise (Indeterminism ⇒ Simple Randomness/Arbitrariness) is equivalent to (or directly presupposes) the negation of the main thesis of that position (Not (Indeterminism ⇒ Simple Randomness/Arbitrariness)) constitutes a petitio principii (begging the question).
  
• C) Consequently, using the Standard Objection (SO) to directly refute the coherence of structured indeterminism (P, supported by Arguments 1-3 and affirmed by P3 of Arg2) begs the question and is therefore dialectically invalid in this specific context. The SO is thus neutralized as a tool for direct refutation of this position.

Consequent Challenge 3.2 : Caught on the Horns

• P1: Influential models of Event-Causal Libertarianism (ECL) largely share their structure (reasons-causation, rationality, non-coercion, etc.) with standard Compatibilist models, differing primarily by adding a requirement of indeterminism in the causal pathway to action. This structural similarity is noted by key authors. [3]
  
• P2: As established in Argument 4 (Challenge 1.1), using the Standard Objection (Indeterminism = Randomness = Incoherence) to directly attack the indeterminism requirement of these ECL models commits a petitio principii against the possibility (defended in Arguments 1-3) of structured (non-R/A) indeterminism.
  
• P3: A critique aiming to show these specific ECL models (described in P1) are incoherent due solely to their distinctive feature (indeterminism) must logically target either: (a) the features shared with compatibilism, or (b) the indeterministic feature itself.
  
• P4: Targeting the shared features (Horn 1 / P3a) is dialectically problematic: it likely undermines widely accepted compatibilist positions and, more importantly, fails to engage with the distinctive indeterministic element of the ECL models in question.
  
• P5: Targeting the indeterministic feature itself (Horn 2 / P3b) faces significant hurdles: (a) Employing the Standard Objection based on ‘Indeterminism = Randomness = Incoherence’ is question-begging (per P2). (b) Demonstrating that non-random indeterminism (whose coherence Arguments 1-3 defend) specifically generates incoherence or loss of control within the otherwise compatibilist-like structure requires a novel and detailed argument, shifting the burden of proof to the critic. (c) Arguing that indeterminism/PAP (Principle of Alternative Possibilities) (even if coherent and non-random) is irrelevant or insufficient for moral responsibility shifts the debate away from the coherence of the ECL model itself and onto the conditions for MR (e.g., via Frankfurt-style arguments).
  
• C: Therefore, critics wishing to reject these specific ECL models based solely on their incorporation of indeterminism are caught in a difficult dilemma: Horn 1 is off-target or self-undermining; Horn 2 either begs the question (2a), requires discharging a significant new burden of proof (2b), or changes the subject from coherence to relevance for moral responsibility (2c). The standard, simple objection based on ‘Indeterminism = Randomness = Incoherence’ is thus shown to be insufficient against these ECL models.
  

[3] Examples of two models :

Let us start with a sketch of a rather simple view of this type. It employs an event-causal theory of action. And it imposes, for free action, the very same requirements as do many good compatibilist accounts (for compatibilist accounts, at least in recent times, do not typically require determinism). It differs from compatibilist views primarily just by also requiring, in order for an action to be directly free, that certain agent-involving events (such as the agent’s having certain beliefs and desires and a certain intention) that cause the action must nondeterministically cause it. (Randolph Clarke, 2003, p. 29)

Directly Free Action as Action Indeterministically and Non-deviantly Caused by Reasons of the Agent’s Own: A decision or other act is directly free just in case it is caused non-deviantly and inderministically by reasons of the agent’s — such as convictions, desires, values, beliefs and preferences — and other reasonable compatibilist conditions on free action are met, including that the act is not compelled and is not the result of (non-self-arranged) manipulation or coercion. An agent’s performing a directly free act requires that it be open to her at the time not to perform that action, either by performing an alternative act right then or by not performing any action at all right then. (Laura Ekstrom, 2016, p.137)