I’ve posted many times before on the nature of critical thinking, argumentation, and philosophical reasoning. In particular, I’ve focused on developing tools for the rational evaluation of arguments. In this post (and posts to come in the future), I aim to equip you with more tools to add to your critical thinking toolkit.
Tool 1: Seeing not versus not seeing
A critically important distinction that arises in a whole host of philosophical debates is that between not seeing (where the sight in question is the sight of the intellect, i.e. grasping or understanding some truth, phenomenon, etc) versus seeing not. To disambiguate this from perceptual sight, the distinction can also be cast in terms of not being aware of x versus being aware of not-x, or as not knowing p versus knowing not-p.
To understand why not seeing neither means nor entails seeing not, it is useful to consider concrete examples:
- Merely from the fact that you are not aware of any neutrinos passing through you, it does not follow that you are aware that no neutrinos are passing through you;
- Merely from the fact that you are not aware that your mental states are correlated with neurophysiological states, it does not follow that you are aware that your mental states are not correlated with neurophysiological states;
- Merely from the fact that you don’t see how the Goldbach conjecture is impossible, it does not follow that you see that Goldbach’s conjecture is not impossible; and
- Merely from the fact that person x is not aware that, upon seeing the Morning Star, he thereby sees the Evening Star, it does not follow that he is aware that, upon seeing the Morning Star, he does not thereby see the Evening Star.
Although it is a subtle distinction, it has far-ranging consequences. For instance, in debates surrounding the problem of evil, many argue that there exist certain (token or types of) evil states of affairs such that God could have no justifying reasons for allowing such states of affairs to obtain.
But this (often) presupposes that because we are not aware of any possible God-justifying reasons, there must actually be no such God-justifying reasons. But this does not follow: Merely from the fact that we do not see God-justifying reasons, it does not follow that we see the absence of God-justifying reasons.
In cases of the absence of sight versus sight of an absence, the inference from the former to the latter seems warranted only if the following condition is met, where P is some proposition and S is some state of affairs:
Were P to be true (or S to obtain), we would (likely) (i) be aware that P is true (or that S obtains) and (ii) recognize P (or S) qua P (or qua S)
This condition nicely accounts for the cases in which the inference from non-sight to sight-not is clearly unsuccessful.
Take, for instance, bacteria. The inference from “I am not aware of any bacteria in my room” to “thus, there (likely) are no bacteria in my room” is clearly quite poor. This is because, firstly, were there to be bacteria in your room, you would not likely be aware of them. But even if you were aware of them (say, because you have ingested some and this is giving you a stomach ache of which you are aware), you would not be aware of them qua bacteria but only qua their manifestation in a stomach ache.
For those interested, here is a small technical complication. A more accurate way to capture the noseeum inference’s reliability (that takes into account Bayesian conceptions of evidence and probabilistic updating) is as follows:
Not seeing P’s truth (or S’s obtainment) is evidence of P’s falsity (or S’s non-obtainment) only if were P to be true (or S to obtain), it is more likely that conditions (i) and (ii) are jointly met than were P to be false (or S not to obtain), where conditions (i) and (ii) are as follows:
(i) we are aware that P is true (or that S obtains), and (ii) we recognize P (or S) qua P (or qua S).
Tool 2: Misplaced modal quantifiers
Modal quantifiers, such as “possibly” and “necessarily”, quantify over a domain of objects in possible worlds (i.e. ways things could have been). Importantly, though, modal quantifiers are often misplaced, and knowing how to spot such misplacement is a crucial philosophical skill.
Consider the following claim: “X couldn’t have a cause.”
This may seem reasonably straightforward, but it is ambiguous between two possible meanings:
(1) There does not exist a C such that C possibly causes X. (Else: For all existing C, it is impossible that C causes X).
(2) It is not possible that there exists a C such that C causes X (Else: It is impossible that for any C, C causes X).
The former states that, of the actually existing things, none of them can cause X. Importantly, though, this still allows that X possibly has a cause — so long as the cause is one that could exist but does not actually exist. After all, (1) only quantifies over the actually existent things, and hence does not quantify over something that could exist but does not actually exist.
The latter, by contrast, says that it is simply impossible for anything — whether actually existent or merely possibly existent — to cause X.
Relatedly, it is utterly crucial to disambiguate between:
- Necessarily, if p then q
- If p, then necessarily q
For instance, if I know that Eli will get married tomorrow, then it logically follows that Eli will get married tomorrow. In this case, knowledge of x’s being the case entails x is the case.
But, clearly, it is not necessary that Eli gets married tomorrow. After all, Eli could come down with a high fever, postponing the wedding until next week. We therefore have, in this case:
- Necessarily, if I know that Eli will get married tomorrow, then Eli will get married tomorrow.
But this neither means nor entails that, if I know Eli will get married tomorrow, then Eli must necessarily get married tomorrow. In other words, the following is false:
- If I know that Eli will get married tomorrow, then necessarily Eli will get married tomorrow.
This becomes especially important in discussions concerning logical fatalism, free will, omniscience, open future, and so on.
In addition to the aforementioned distinction, a number of other important distinctions and points come into play. Here is a list of them:
- Just because each individual thing in a domain could fail to be, it doesn’t follow that there could be a state in which there fails to be all things in the domain (together). This is a subtle form of the quantifier shift fallacy: Just because each individual student has a counselor, it doesn’t follow that there is a counselor for all the students (together).
- This is relevant in a number of ways. Some thinkers mistakenly reason that, because there could not possibly be nothing, there must exist a necessary being. But notice that this is subtly fallacious. The impossibility of there being nothing is equivalent to the necessity of there being something. But the necessity of there being something or other does not entail that there exists some specific, particular thing that necessarily exists. Similarly, even if every individual object in reality is contingent, it does not follow that, possibly, there are zero objects in reality. This is because it could still be the case that, necessarily, there is some contingent thing or other despite the fact that, for any given particular contingent thing, that thing could fail to exist.
- Just because each individual thing in a domain is necessarily and essentially non-F, it doesn’t follow that all the things — together (as a whole) — in the domain are necessarily and essentially non-F.
- This is important with respect to principles of construction, for instance in relation to materialism and dualism. Some dualists will argue that each neural subsystem is essentially and necessarily non-conscious, in which case adding more and more subsystems together could only beget further states which lack consciousness.
- But this inference is not necessarily truth-preserving. For instance, when adding two chemicals together that are essentially and necessarily colorless, nevertheless their interactions can give rise to something with a vibrant red color.
- If two things are such that it is impossible for one to exist without the other, it does not follow that they are identical. For instance, the property having a radius cannot exist without the property having a circumference (and vice versa); nevertheless, they are clearly not identical properties.
- (Necessary) co-extension does not entail identity.
Tool 3: Intensional and extensional contexts
A linguistic context is intensional precisely when it is not extensional. An extensional context is (for our purposes) present when the following condition is met:
(1) Necessarily, inter-substituted co-referring expressions preserve truth.
Condition (1) applies to scenarios in which an object has two names, N1 and N2. In such scenarios, one can formulate a true proposition about the object using N1. When condition (1) is met, if you substitute N2 for N1 into the proposition, the proposition cannot become false. In other words, such a substitution is truth-preserving. Because the object to which each name refers is identical, the words used to denote it simply don’t matter to proposition’s truth (in extensional contexts).
But (1) is not always met, and when it isn’t, the linguistic context is intensional. In intensional contexts, co-referring expressions cannot be substituted for one another without potentially changing the proposition’s truth value. The failure of (1) in intensional contexts derives from the fact that a single object can be presented to a thinking subject under different clusters of descriptions. Under such conditions, the agent in question may be unaware that the extramental referent of such clusters of descriptions is the same in each case.
In summary, an intentional object (else: linguistic expression) construed extensionally is the intentional object’s extramental referent, whereas an intentional object construed intensionally is the mind-dependent cluster of descriptions that the thinking subject associates with an object.
This will become especially important in my upcoming series on philosophical theories of the mind.
Tool 4: The A-series and B-series
The terminology of the A-series and B-series (and the corresponding A- and B-theories of time) for characterizing time is due to John McTaggart. This is an invaluable tool in your philosophical toolkit since many arguments may implicitly presuppose the truth or falsity of one such theory of time.
The A-series is a group of succeeding temporal events that are past, present, and/or future. This series is dynamic because the tensed operators of past, present, and future are always changing depending upon what time is present. These tensed operators aren’t mere relations — they’re absolute.
The B-series is an extended group of temporal events that stand in the relations of earlier than, later than, or simultaneous with. This series is static because the tenseless operators previously articulated are unchanging: when x is earlier than y, x is always earlier than y and cannot transition to becoming later than y.
Roughly, A-theories of time hold that:
- The A-series is the fundamental characterization of time
- Tensed operators pick out objective features of reality
- Reality is dynamic and changing — temporal becoming is a real and objective feature of reality
- Not all times are equally actual
- Past, present, and future are absolute and objective determinations, not relative to reference frame, observer, perspective, other times, and so on
B-theories stand in opposition to A-theories in that B-theories hold (roughly) that:
- The B-series is the fundamental characterization of time
- Tensed operators do not pick out objective features of reality
- Reality is static and temporally unchanging — temporal becoming and temporal passage are neither real nor objective features of reality
- All times are equally actual
- Past, present, and future are neither absolute nor objective determinations
Some important arguments thinkers have leveled in favor of A-theory:
- The argument from our phenomenological experience of temporal becoming
- Our experiences (both perceptual and phenomenological) are pervasively infused with objective, dynamic flow and temporal passage
- The argument from the inadequacy of B-theoretic accounts of change
- Change involves the actualization of things which are not-yet existent, i.e. potentially existent — in which case, if all of temporal reality were equally actual, there would be no change within temporal reality (which is absurd)
- The argument from the ineliminability of tense
- If B-theory is true, then there must be adequate translations of tensed language into tenseless language; but no such adequate translations could exist
Some important arguments thinkers have leveled in favor of B-theory:
- Special and general relativity indicate that (i) there cannot be absolute simultaneity, (ii) time is relative to frame of reference, and (iii) space is inextricably bound up with time — time and space form a single four-dimensional spacetime block
- As one frame of reference approaches the speed of light relative to another frame of reference, time in the former frame of reference passes much more slowly
- The argument from successful reference to past and future times
- We successfully refer to things in the past and future; but one cannot successfully refer to x unless x actually exists
- The argument from time-indexed truthmakers
- There are truths about the past and future; but truths require actually existent states of affairs serving as truth-makers; and the only possible truth-makers for time-indexed propositions are the time-indexed states of affairs themselves
- The argument from the indeterminacy of experience between the truth of A and B theories
- The order and intrinsic character of events in the A-series and B-series are identical, in which case the causal order between the two series is identical, in which case (since experience of x requires a causal connection to x) experience would be identical in either the A-series or B-series
- The argument from causation
- Past temporal states stand in the relation of causation to present things; but only actually existent things can serve as causes; hence, past temporal states must actually exist
- The argument from existence-entailing relations
- The past and future stand in all sorts of relations to the present; but x and y can only stand in a relation if x and y actually exist; hence, the past and future actually exist
Tool 5: Different types of possibility and necessity
It is crucial to disambiguate what we mean when we say that x is possible or not possible. Here are various ways to disambiguate it:
(1) Conceptually possible
- Something’s being conceptually possible means that it, as a concept in itself, has no internal contradiction of incoherencies
- So, arguably Plato’s Realm of Forms is conceptually possible, since there seems to be nothing utterly incoherent about the concept of a non-spatiotemporal, acausal reality in which abstracta exist.
(2) Logically possible
- Something’s being logically possible means that its negation cannot be derived from (i.e. is not entailed by) the true logical axioms.
- For instance, arguably logical axioms alone do not entail that “the number 32 cannot produce a badminton player”, in which case 32’s producing a badminton player may be logically possible even though it is not metaphysically possible.
- This example illustrates that, when we talk about whether a claim is logically possible, we consider only the logical features of the sentence and not the nature of the objects or properties to which the claim refers.
(3) Metaphysically possible
- Metaphysical possibility is a subset of logical possibility and is more stringent than logical possibility
- Something’s being metaphysically possible means that it exists in at least one possible world, where a possible world is just a complete way our actual world could be (else: could have been)
- That in virtue of which worlds are (metaphysically) possible depends on the correct modal metaphysics
- According to Aristotelian metaphysical accounts of modality, x is possible provided that x is either actual or potential, where x is potential provided that there is some actual thing with the causal power to initiate a causal chain leading to x’s actuality
- According to Platonic accounts, x is possible in virtue of being a member of a maximal consistent (else: compossible) set or collection of propositions
- Leibnizian accounts hold that possible worlds are maximal self-consistent ideas or concepts in the divine mind
- According to Lewisian (extreme modal realist) accounts, x is possible in virtue of being true in an actually existent, spatiotemporally related concrete world, where actuality is indexical; all possible worlds genuinely exist and are on ontological par with one another in having the same modal status
- Metaphysical possibilities have to be consistent not only with the logical landscape, but also with (i) the necessary truths of reason and reality (e.g. if container C1 contains a container, C2, then C1 contains whatever C1 contains), and (ii) the nature of the substances, events, properties, and so on to which the proposition refers
- Examples of metaphysical impossibilities include:
- Something can’t be red and green all over.
- Solely in terms of logical features this sentence is perfectly consistent: “It’s impossible for something to have property R and property G on all its color-reflective parts.” Hence, if the proposition is true, it has something to due with the nature of color properties
- The mind is identical to the brain (else: the mind is not identical to the brain)
- Something can’t be red and green all over.
(4) Epistemically possible
- Something’s being epistemically possible means that, for all we know (or justifiably accept), x could be true; x is not known to be false or impossible
- For instance, it is epistemically possible that Goldbach’s conjecture is true, but it is also epistemically possible that Goldbach’s conjecture is false. Nevertheless, apart from our justified acceptances, it is either necessarily true or necessarily false
- Currently, I do not know whether it is raining in London or not. So, epistemically, it is possible (given my justified acceptances) that it rains in London, and it is possible that it does not.
(5) Temporally possible
- Something’s being temporally possible is essentially a matter of time-indexed metaphysical possibility
- In other words, something is temporally possible provided it is metaphysically possible when indexed or specified at a particular time (or collection of times) t
- It is essentially tensed metaphysical possibility (i.e. it includes reference to one or more times)
- Some examples of temporal modality
- X necessarily holds at the next temporal state of reality
- X eventually cannot fail to hold (somewhere on the subsequent temporal path of reality)
- X cannot fail to hold on the entirety of a potential subsequent temporal path of reality
- X cannot fail to hold on the entirety of every single potential subsequent temporal path of reality
- X cannot fail to hold at all times
- There exists at least one temporal path reality could take starting from the present moment where X holds
- Possibly (or necessarily), it will sometimes be the case that X
- Possibly (or necessarily), it will always be the case that X
- Possibly (or necessarily), it was sometime the case that X
- Possibly (or necessarily), it has always been the case that X
- One may claim that everything that is (a) past relative to t, and (b) true, is thereby metaphysically necessarily true at t
(6) Physically possible
- Something’s being physically possible means that it is consistent with the actual laws of physics
- Traveling faster than the speed of light is physically impossible, whereas having 20 children is physically possible
Tool 6: Putting the grounded before the ground
Putting the grounded before the ground is a version of putting the cart before the horse. More specifically, it consists in mistakenly thinking that X is grounded in Y, whereas Y is, in fact, grounded in X.
For instance, even if it’s already true that, say, tomorrow I will eat chicken for lunch, it’s not in virtue of this proposition’s truth that I eat the chicken. Rather, the proposition is true in virtue of my eating chicken. So, although I may not “change” the truth value of the proposition (which may give the illusion of my not grounding it), we still have counterfactual dependence: had I chosen instead to eat fish, the proposition would have been false, and it is presumably my eating chicken (or at least the fact that I will eat chicken) that makes it be the case that the proposition is true.
Another example concerns the argument that B-series entails the absence of free will. But arguably this puts the grounded before the ground. My decision to phi in the future in the B-series is not grounded or true in virtue of its being “already actual” in the future; rather, it’s the other way around. My decision to phi in the future is actual precisely in virtue of my choice to phi. The event is actual in virtue of my choosing it to be actual; I don’t choose it to be actual in virtue of its actuality. We must avoid putting the cart before the horse.
So, even if the future is already actual, it doesn’t follow that I cannot do otherwise, since the actual status of the future event is grounded in my choice rather than vice versa. The future would have different actual features had I chosen non-phi, meaning that the future could have been different even if it is already actual.