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Open Future and Fixed Past

How open is our future and why is our past fixed?

Open Future and Fixed Past


I wrote this essay when I was 18. I was lucky enough to have won the 2nd Prize globally in Cambridge Trinity College Philosophy Prize 2018 as an autodidact: I had never studied philosophy formally (until at Oxford).

The original essay question set by the competition was 'How open is our future and why is our past fixed?'

As with other things in my life (see: my work), I wanted to beat others at their own games. So I taught myself 1) formal philosophy, 2) philosophical landscape of metaphysics, and 3) philosophy of time

I shall caveat that:

  • this essay is most updated til 2018
  • the scope of the essay was limited to 4000 words; hence,
  • the essay was exploratory and secondary, rather than ground-breaking

In line with academic essay formatting, the reference list is at the end.

ToC: please ignore page number 


We all feel that we have the ability to make choices in the future, but not to have changed our past. Indeed, the idea of an ‘open future’, coupled with the passage of time, is best summarised by the cosmologist George Ellis:

Things could have been different, but second by second, one specific evolutionary history out of all the possibilities is chosen, takes place, and gets cast in stone. (Ellis, 2006,1812-3)

It is evident that ‘things could have been different’ refers to the openness of future; ‘second by second’ indicates the passage of time; ‘gets cast in stone’ links to the notion of a ‘fixed past’. Horwich (1992) commented in his work, Asymmetries in Time, that time itself is asymmetric and anisotropic—a significant lack of symmetry between the two directions of the temporal continuum, namely past and future. Consider this view a contrast with our attitude towards space, directions are numerically distinct from one another but essentially similar—isotropic. To further investigate the seemingly intuitive experience of ‘open future' and ‘fixed past', it is essential to divide the issue into the following sub-questions:

  • Question 1. What is 'openness'?
  • Question 2: On what grounds is our future open?
  • Question 3: Is a single determinate future compatible with 'open future' ?
  • Question 4. Why is our past ‘fixed’?
  • Question 5: Is our past necessarily fixed?

This essay has two sections: Part I investigates ‘open future'; Part II discusses the seemingly indisputable concept of ‘fixed past’. In Part I, with reference to Barnes and Cameron (2009, 2011) and Torres (2011), I introduce their arguments with regards to the question of to what extent open future is compatible with a single determinate future. Then, I evaluate their arguments and their criticisms, offering my own objections and extensions, particularly of Barnes and Cameron’s interesting notion of ‘metaphysical indeterminacy’. In Part II, I explain in detail and with cross-reference to Part I, how a ‘fixed past’ is justified by an ‘open future’. I conclude the essay by examining the counter-intuitive position Markosian (1995) took: an ‘open future’ entails a ‘fixed past’.

Part I: Open future

Criteria for Openness

Barnes and Cameron (2009) identified the following three criteria of openness that align with our intuition. Evaluation of whether the following three premises are reasonable follows. Both Cameron (2009) and Torre (2011) thought that they are unreasonable and unnecessary premises of an open future. Their counter-arguments and evaluations will be incorporated in the following paragraphs. Even though I believe that there are overwhelming arguments against OF-compatibilism and that perhaps OF-incompatibilism provides the wider picture because it can accommodate eternalism, growing-block theory, branching theory, and presentism, there is much value in recognizing and understanding OF-compatibilism's core premises and core arguments first.

(i) Non-bivalence

The principle of bivalence does not hold unrestrictedly in the past, the present, and the future—in other words, simpliciter. Future contingents are, thus, neither true nor false. The principle of bivalence is enshrined in the following fatalist argument:

(1) It is true that either there will be a sea battle tomorrow or there will not be a sea battle tomorrow (by the Principle of Bivalence)

(2) It is true now, then, that either there will be a sea battle tomorrow or there will not be a sea battle tomorrow

(3) Whatever will happen tomorrow is inevitable because true future propositions already exist and are determined

(4) The future is in all respects settled already  

If the above argument is sound, then an open future is impossible to exist because of the principle of bivalence. Indeed, some philosophers such as Markosian (1995) even defined open future as a failure to apply the principle of bivalence:

Let us agree on some terminology. To say, with regard to some time, t, that the future is open at t is to say that there are some propositions about the future relative to t that is, at t, neither true nor false. To say that the future is closed at t is to deny this i.e. to say that every proposition about the future relative to t is, at t, either true or else false. (Markosian, 1995,96)

Since we are attempting to philosophically analyze the intuition that the future is ‘open’ and the past is ‘fixed’, it is counter-productive for us to reject the principle of bivalence at first sight. Many philosophers indeed claim that an open future is compatible with the principle of bivalence. It is perhaps best for us to assume, at the outset, that openness does not only entail the lack of truth-value, and that we should accept the principle of bivalence until we have found no better way of accommodating the openness asymmetry unless we do the otherwise.

(ii) Indeterminism

The laws of nature are indeterministic. And thus, the future is indeterministic. That is, the certain state of affairs of a world at time t does not necessitate nomologically its state at future time t’.

Even if our world turned out to be deterministic, we would maintain that there is an asymmetry in openness between the past and the future, because of ontological asymmetry and causal asymmetry. Furthermore, if the laws in our world are indeterministic, our world is compatible with multiple futures. However, given indeterminism, however strong or weak, the current state of affairs and laws are also compatible with multiple pasts. So indeterminacy alone cannot explain the asymmetry in openness between the past and the future, and even suggests the counter-intuitive position of an ‘open past’, as Markosian (1995) suggested.

(iii) Non-existence of future

The future does not exist and any events in the future do not exist ontologically simpliciter.

If the future exists out there already, then the future is closed, intuitively. Contrarily, if the future does not exist at this moment simpliciter, then the future is open. But eternalists defend that the existence of the future can still accommodate an ‘open’ future.

Do we need to discard all three intuitive premises of an open future? Barnes and Cameron (2009) argued that none of the above three premises are true implications of the open future thesis. They showed that an open future theorist needs not to accept them and is not committed to them. Any one, or all,of the premises may be false. Yet the open future thesis may still stand. We will discuss the implications of this later in the essay.

Ontological asymmetry

Does the future exist ontologically? A natural response is to say that the future did not exist before, does not exist now, but will exist. The presentist maintains the position that only present objects and events exist simpliciter. Future objects and events do not even exist in the most unrestricted existential quantifier—an analogy would be asking God for an inventory of everything that exists in the universe. The Growing Block Theorists will agree with the presentist in denying the existence of future objects and events. However, they assert that dinosaurs and the incumbent President of the United States both exist. According to Growing Block Theorists, the universe is like a block-universe that extends its length with the passage of time. What exists is the sum of reality from the past to the present, which is also the surface of the block.

On the other hand, eternalists (who are also called as block-universe theorists) and branch theorists will answer ‘yes' to the question about whether future objects and events exist ontologically. However, they will disagree with regards to whether a single event such as the sea battle exists in a single future or in multiple futures. Eternalists posit one single timeline that describes the history of the universe from the beginning of time until the end (if there is any).

Future contingents and future ontology

Does a single determinate future exist in the domain of our unrestricted existential quantifier? Presentists and growing-block theorists can maintain that there is one determinate way that the future will go without being ontologically committed to future objects and events. To have determinate truth-values for future contingent propositions, it is not necessary for the future to exist. They could easily defend that future contingent propositions have determinate truth-values in spite of their non-existence. Since eternalists assert the existence of past, present, and future events, it entails that they must also support a single determinate future.

Figure 1: Branching Model

Two different versions of the branch theory will give two different sets of answers to the question of the existence of a single determinate future. One version maintains that all future branches are ontologically on par. A future branch with a sea battle tomorrow is ontologically the same as another future branch without a sea battle tomorrow. Truth in this version then is in terms of a supervaluationist semantics. A future contingent statement is true at time t if and only if the statement is also true in all the branches at time t; conversely, a future contingent statement is false at time t if and only if the statement is also false in all the branches at time t If there are some branches in which there is no sea battle, and there are some branches in which there is sea battle, the statement, ‘there will be a sea battle tomorrow’ is neither true nor false. Thus, a branch theorist can either point to the ambiguous referent of ‘tomorrow’ as having an indeterminate reference. Alternatively, the proposition may be assumed to be a unique proposition, but still it has an indeterminate truth-value. Regardless of what responses a branch theorist chooses to respond to, it is more reasonable for a branch theorist to completely deny that all future contingent propositions have a determinate truth value.  

A different version of the branch theory completely denies that all future branches are ontologically on par. In this version, one of the branches is privileged in the sense that it is as if it were marked out by a ‘thin red line’, as Belnap and Green (1994) proposed—In Figure 1, a red branch is marked from Event A to Event B1 at t1 to Event E2 at t2. Thus, a future contingent proposition is true at time t if and only if the proposition is true in the branch marked in red at time t. A future contingent proposition is false at time t if and only if the proposition is false in the branch market in red at time t. This version of branch theory allows determinate future while claiming the openness of future.

The following question lies at the heart of the debate over the open future: is an open future compatible with the fact that there is a single determinate future? ‘OF-compatibilists’ would answer yes— the openness of future is compatible with the fact that all future contingent propositions have a determinate truth-value (growing block theorists/supervaluationist semantics branching theory); ‘OF-incompatibilists’ maintain that if all future contingent propositions have a determinate truth-value, the future is closed.

I owe much credit to Torre (2011) for conducting a rigorous literature review and clarifying and reformulating the question of open future

OF-Compatibilism: Counterfactual asymmetry

It is perhaps intuitive to us to favor OF-incompatibilism. After all, if there is a single determinate future, how can the future be genuinely open? If there are determinate truths about future propositions, do we not fall to the fatalist’s argument that whatever will happen is inevitable and that there is nothing we can do about it? Later I will argue that OF-compatibilism is an indeed unfavorable position and that there is no necessity for us to adopt this position because OF-incompatibilism and Cameron's solution to the problem—Openness as Metaphysical Indeterminacy— encompasses most of the ontological positions in the philosophy of time. Nonetheless, it is crucial to review how OF-compatibilists respond to these objections.  

A logical defense is to say that openness of the future is compatible with future propositions now having a determinate truth-value because it does not follow that the proposition is inevitable, inexorable, fixed, or necessary to happen in the future. David Lewis, a block-theorist (a B-theorist and an advocate of the block-universe ontology) links temporal asymmetry to counterfactual dependence between the past and the future. Lewis (1987) wrote that:  

I suggest that the mysterious asymmetry between open future and fixed past is nothing else than the asymmetry of counterfactual dependence. The forking paths into the future—the actual one and all the rest—are the many alternative futures that would come about under various counterfactual suppositions about the present. The one actual, fixed past is the one past that would remain actual under this same range of suppositions

Lewis explains that the way the future is depends counterfactually on the way the present is. Had the present been different, the future would be different; the present depends counterfactually on the past too. In general, the future counterfactually depends on its present and past. What is central to Lewis’ explanation of the openness asymmetry is that the future depends counterfactually on the present in a way in which the past does not depend on the future. Hence, the future is open in virtue of its counterfactual dependence but not its determinacy of truth-value.

Criticisms against OF-Compatibilism

Two of the most notable objections are raised against OF-Compatibilism by John MacFarlane (2003). First he objected to the thin-red-line branching theory. By positing a red line, it amounts to directly giving up the openness of future because objectively speaking, the non-red branches are not genuine possibilities; they are only possible in the epistemic sense. Second, he objected against Lewis’ metaphysical framework of a divergent world, namely that present events only spatiotemporally correlate to one future. However, there are other worlds that are unrelated to the actual world but qualitative duplicates of the actual world until present time t. Thus, their future diverges from our future in the sense that they differ qualitatively. MacFarlane objected on similar grounds with the previous objection he has made: the future contains possibilities only in the epistemic sense—it does not amount to genuine openness. Diekemper (2007) similarly argued that ‘the possibility of an alternate history containing an alternate future is not a possibility for me’.

What I think critics are missing here, is that we need to point out exactly are the differences between epistemically possible worlds, ersatz, and actually possible worlds. In other words, what metaphysical property/account is required in order for a world to be genuinely possible, and to be counted as part of a genuinely open future?


As discussed above, OF-compatibilism does not seem to be a convincing position. On the other hand, MacFarlane endorses the branching theory instead. In this view of the branching theory, openness means that there exist future branches in which a sea battle takes place tomorrow, and there also exist future branches in which no sea battle takes place tomorrow. All branches are ontologically on par with each other, as mentioned in the previous section. The openness asymmetry inherent in the temporal continuum is an ontological asymmetry: a single ‘tree-trunk' past and a multitude of ‘tree-branches' future.

With regards to the branching theory, Torre (2011) posed two questions that he thought worth considering when we attempt to accommodate the open future by positing this model of reality. Firstly, is such an account required in order to accommodate open future intuitions? If the open future can be accommodated by positing a single, non-branching, future? If a single, non-branching, future can accommodate the openness of future, by the principle of Occam’s Razor, there will not be any internal or external motivations considering this multi-branch theory. Secondly, does multiple branching futures succeed in capturing our intuition of the open future? Torre referred to David Lewis’ objection that multiple branching futures make nonsense out of our ordinary beliefs (1986)—that if there are two equally valid and possible futures, it is ‘nonsense to wonder which way it will be as it will be both ways, yet I do wonder’.

Figure 2: The Branching Model Revisited

In fact, neither Torre nor Lewis successfully challenged the crux of branch theory. As shown in Figure 2, there are different probabilities that lead one event to another e.g. P(A -> B1)= 0.7. The fact that there is one event with an overwhelming probability may indicate the possibility of a single determinate future. What critics of branching theory should challenge is the ontological grounding of the theory: Given that different events have different probabilities, do they all exist? If so, what really differentiates the ontology of merely multiple possibilities and multiverse? These are the questions that branching theorists truly have to answer.

Reconciling Open Future with determinism: Openness as Metaphysical Indeterminacy

According to Barnes and Cameron (2009), 'truth is one thing and determinate truth another' (298). They uphold criteria (i) bivalence for future contingents. They do admit that the proposition that there will be a sea battle tomorrow is either true or false, as ‘they are the only two options’ (294). However, they deny that all future contingent propositions are determinately true or determinately false. Extrapolating from this claim, they argue that the nature of future is metaphysically indeterminate. Metaphysical indeterminacy is distinctive from semantic indeterminacy and epistemic indeterminacy in the following ways: it is not linguistic indeterminate nor is it rooted in our ignorance or failure to obtain knowledge about the world.

Consider the following statement:

P:Ralph is bald

Barnes and Cameron explained that semantic indeterminacy rules that the predicate ‘is bald’ lacks precise definition and conditions. Statement P is semantically indeterminate because of the existence of borderline cases. Epistemically, there are conditions for the predicate ‘is bald’ to be indeterminate but we are unaware of those conditions. Hence, we are ignorant of the truth-value of P. Metaphysically, P is indeterminate since the world is unsettled with respect to Ralph’s baldness. Although it is true, and it must be granted as true by the principle of bivalence which Cameron accepted, namely that P is either true or false, it is metaphysically indeterminate whether P is true or false.

Openness as indeterminacy

Hence, Barnes and Cameron (2009) summarized their position in the following paragraph:

The future is open with respect to some future contingent sentence S at t if and only if (1) S at t expresses a proposition that is, at t, metaphysically indeterminate in truth-value and (2) either it will be the case that, determinately, S was true, or it will be the case that, determinately, S was false. The future is open simpliciter if and only if there is some future contingent S such that the future is open with respect to S.

Using this framework of indeterminacy, they explained the intuitive asymmetry in openness between the past and the future.

Barnes and Cameron’s Radical Desideraturms

Barnes and Cameron (2011) further considered the following desideratum to fulfill their tenet of ‘openness’

Open Future refers to the proposition that there are multiple possible ways our future might go

Desideratum 1: ‘might’ cannot be merely epistemic, but has to be genuine ontological openness in how things turn out. Open Future must be a metaphysical claim about the future in and of itself

Desideratum 2: a model claim is not just about multiple metaphysically possible ways that the complete history of the world could have been; not just about multiple metaphysically possible ways that the complete history of the world could have been given the actual history of our world so far.

Hence Cameron wrote that one of the advantages of Openness as Indeterminacy is that it explains how our world will turn out to be, but not what it could have been. Facts about our world are now unsettled but will be resolved as time passes. We are describing what our history is, but not merely describing alternatives to it—satisfying the second desideratum.

Implications of Cameron's Metaphysical Indeterminacy

Barnes and Cameron (2009) concluded their work by claiming that they have argued that ‘the thesis that the future is open does not entail either the denial of bivalence, the denial of determinism or the non-existence of future ontology’. The significance of their argument is that contrary to the intuitive positions as stated in the Section ‘Criteria for Openness’, anyone who supports open future does not have to commit to any one of the three criteria. Perhaps it means that the open future thesis is, surprisingly, compatible with (i) bivalence (ii) determinism (iii) eternalism. As convincing as their arguments might sound, I dispute that the open future thesis is compatible with (ii) determinism and agrees with (iii) eternalism albeit through a different explanatory lens.  

It is important to make clear what they meant by the indeterminacy of future: there are determinately ways that the future is going to be; there is NO way for the future to determinately go in ONE particular way. Cameron phrased it rather nicely: “ ‘Determinately, there is some way the future will be’ is fine but ‘there is some way the future will determinately be’ is indeed fatalistic and we reject it”.  

Assume determinism is compatible with open future. If we reject some ways that the future will potentially be (because of strong determinism), then how does our concept of ‘open future’ accommodate Desideratum 2? A single determinate future is incompatible with an open future. Alternative views might shed a light here: both the branching model and the multi-verse model fulfill Desideratum 2. The problem with Cameron’s (2009, P.303) reasoning is that he begs the question when he claims ‘both theses (strong and weak determinism) are compatible with the open future thesis even if it is fully determinate what laws obtain’. It is beyond doubt that determinism gives rise to a determinate future. With that being said, how can open future be compatible with determinism?

With regards to the compatibility of (iii) eternalism, I would like to take the argument further: a single indeterminate future is compatible with an open future. Metaphysical indeterminacy is indeed compatible with a single future. Whether the future exists simpliciter or not is not the issue. What is at stake is whether or not the future is settled simpliciter. I would argue that it is definitely consistent to claim that there are future entities, but that it is not settled which future entities there are. Similarly, I foresee an objection against my argument above that determinism only determines the existence of future entities, but it is still not settled which future entities there are. I think this line of thought might be promising but due to the limited scope of this essay, I could not have entertained this counter-argument.

Part II: Fixed Past

Arrow of Time and Backward Causation

Our inability to affect the past perhaps arises from temporal asymmetry: time flows from past to present. Backward causation, hence, is improbable because of the following:

(i) Ontological asymmetry, as discussed above the fundamental structural difference between the past and the present

(ii) physical asymmetry, as Sklar (1981) argued that just as how spatial directions can be reduced to the gravitational potential gradient, the temporal arrow might be reduced to the thermodynamic arrow which obeys the Second Law of Thermodynamics—Law of Increasing Entropy

(iii) counterfactual dependence, as Lewis (1979) asserted that future counterfactually depends on the present; past does not counterfactually depend on the past

Does an Open Future entail an Open Past?

Markosian (1995) argued in his article, the Open Past, that if some laws of nature are both indeterministic with regards to future, and time-symmetrical, then equally, those laws are indeterministic with regards to the past. In parallel, he claimed that if there are good arguments that extend indeterminism to the future, then there should be analogous and equally valid indeterminist arguments with regards to the past. As he himself noted, his assumption is that the only plausible and non-question-begging defense available against fatalist's attack on open future is to appeal to indeterminist laws of nature. It is a heavy cost committing to his counter-intuitive position so how we should respond, is not to accept that an open future entails open past, at least not at the outset; but to investigate if there are any other non-question-begging defenses of open future. Perhaps the answer lies in the Open-Future-Compatibilism debate in Section I.


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