The Logical and The Empirical

The nature of knowledge creation varies across academic disciplines. I propose a differentiation into two camps: logical fields, such as mathematics and philosophy, dependent on abstract reasoning, and empirical fields, such as biology, physics, and neuroscience, dependent on observation and measurement.

It might seem difficult to reconcile these two different “sources of truth”. Could these ways of knowing ever tell us contradictory things? Does the mathematicians’ logical truth ever feel threatened by the physicists’ empirical truth? Does the neuroscientists’ empirical truth ever feel threatened by the philosophers’ logical truth? Here’s a better question: why has their reconciliation proven so easy?

The Whole World is Logical

Why do empirical results cooperate with logical preconceptions? Why, for example, do physical results fail to contradict and, instead, universally support preconceived mathematical truths?

Empirical truth itself – conceivably – doesn’t exist, but refers merely to highly complex manifestations of logical truths. “Empirical” is just the name we give to logical truths whose logical underpinnings are too intricate for us to understand. The whole world operates on logic; logic is all there is.

This is not to say that empirical truths are not instructive. Our world contains many truths, and many, unfortunately, lie beyond our ability to directly and explicitly comprehend. For these complex truths, we undertake empirical investigation.

This does explain, however, why the two realms don’t contradict. Though these two types of truth come to our attention in different fashions, they both rest on the same set of underlying principles (more precisely, one rests on the other).

There’s something more subtle happening, though. Why is logical soundness so necessary in interpreting empirical truths, even when these empirical truths are far too complex for explicit logical comprehension?

Logical Antecedes Empirical

Philosopher Peter Hacker and Neuroscientist Maxwell Bennett – together in their book Philosophical Foundations of Neuroscience (1) (2) – argue that correct understanding of philosophical underpinnings is crucial to sound methodology and interpretation in empirical research. The writers claim that knowledge is hierarchically divided: “Conceptual questions antecede matters of truth and falsehood,” they argue. “The concepts and conceptual relationships in question are presupposed by any such investigations and theorizing.” Poor philosophical underpinnings, they claim, will lead to poor empirical science. Putting neuroscientists’ philosophical houses in order, the pair seeks to pave the way towards better empirical neuroscience.

Hacker and Bennett’s fundamental argument – that, roughly, the logical antecedes the empirical – makes our picture more complex. Previously, we described a direct causal link from the logical to the (so-called) empirical. Now, however, it seems that abstract, general logical understanding can also aid our interpretation of empirical phenomena.

The Two Theories Are The Same

Perhaps logic works in recursively increasing complexity. Basic, abstract logical principles are not separate from – but ultimately derived from – complex and fine-grained ones. By understanding these principles abstractly, at a “lower resolution”, so to speak, we can receive clues about the smaller, tougher ones.

Logic, then, both produces empirical results and leads to better interpretations of these empirical results. This is because the underlying logic is pervasively identical. Logic, dictating the universe, causes particular empirical results to exist; (partially) understanding this logic, moreover, we’re more apt to properly interpret and understand these empirical results.

Philosophy, mathematics, and logic, here, have been “grouped together” as (different levels of) the universe’s basic, fundamental laws. Is this theory grandiosely speculative, or illuminating? Like Ivan Karamazov’s “quadrillion miles”, perhaps this youthful philosophizing is deeply insightful.

Alternatively, perhaps, the universe doesn’t follow predictable laws at all.

  1. Hacker, Bennett, Searle, and Dennett’s Neuroscience and Philosophy, containing key excerpts from (1) as well as rebuttals from leading philosophers.

4 comments on “The Logical and The Empirical

  1. Josh says:

    The distinction you make between logical and empirical sounds a lot like one already commonly discussed in epistemology: a priori versus a posteriori truth.

    An a priori truth is one that can be known by logic alone, such as the assertion that three is less than four. Knowledge of a posteriori truths, on the other hand, requires real-life experience. For example: the circumference of the earth is 40,075 km.

    Regarding the distinction you pose, it seems that all logical truths are a priori and that all empirical truths are a posteriori. According to your argument, then: as all empirical truths could ultimately be reduced to logic, all a posteriori truths may well be described as a priori.

    Now, though, we might run into some trouble. Would you really claim that, given perfect information and complete understanding of the universe’s logical rules, you could predict the circumference of the earth? Perhaps you could claim this. If anything, though, this claim would point to the uselessness of deeming empirical truths a priori. Perhaps all truths could be reduced to the rules of logic, but that doesn’t mean that logic will be replacing empiricism any time soon.

    That said, I do agree with the argument that logic can help formulate an empirical claim even if the precise logical foundation of that empirical claim isn’t known.

  2. Jonathan Anomaly says:

    Your first hypothesis: Empirical truth itself – conceivably – doesn’t exist, but refers merely to highly complex manifestations of logical truths.

    You rightly suggest that logic helps us make sense of empirical observations – it requires that we reason in accordance with certain inferential rules, that we discipline our observations by rendering them consistent, etc. Good reasoning even presupposes the kinds of inferential rules that comprise the core of what philosophers call deductive logic (on this, see Lewis Carroll’s essay about the Tortoise and Achilles).

    But here’s a simple insight I had many years ago while teaching logic to high school kids. Most interesting or instructive deductive arguments rely upon at least one inductively established premise (a premise that is established by reasoning from a set of empirical observations). For example, Fyodor is a person, people are mortal, so Fyodor is mortal. The conclusion deductively – or “logically” – follows from the premises. But the justification for our assumption that people are mortal is based on experience and observation in the broadest sense, and maybe some principles from biology like the Hayflick limit.

    This suggests to me that empirical truths cannot be collapsed into logical truths, and are not mere manifestations of them either. Instead, we’re dealing with two kinds of reasoning, which are mutually supportive, and constraining.

    Your conjecture that the two “realms” (or, as I prefer, kinds of reasoning) don’t conflict seems plausible, but it’s not because they are identical, or because one can be reduced to the other.

  3. Wilson says:

    About this notion that “physical results fail to contradict and, instead, universally support preconceived mathematical truths.” I’m not sure this is true. Our simple mechanical physics described a world in which quantum and relativistic effects do not occur. But then, observation contradicted the conclusions of “preconceived mathematical truths.” Those truths were based on the axiom that T=T; relativity shows that T=T/sqrt(1-v^2/c^2). So ultimately math is a human-constructed system to explain what we perceive from the empirical phenomena. Now, mathematical reasoning can lead to some awesome inferences; for instance, most of the subatomic particles were theorized mathematically before they were discovered empirically. But it does not follow that math is prior to empirical reasoning: math is constructed with recourse to empirical observations. This isn’t to say that there is nothing that can be known a priori; it at least SEEMS (and I think very likely is) that the number line, the Cartesian plane, and the fundamental theorem of calculus can all be deduced a priori. (Though perhaps notions of space and time are not intuitive! Now there’s a question.) But there is no way of knowing the extent to which these have power to explain the real world without empirical observation. This is the distinction between mathematics and physics.

    This all kind of goes to the question; is logic a construct used to explain empirical phenomena, or is the notion of empiricism a logically constructed one? This post seems to insist upon the latter interpretation. But I think it’s clear there’s some kind of give-and-take (to use what is no doubt the wrong word) here. We start, like Descartes, with some a priori principle that leads us to develop a theory of knowledge and come up with what constitutes empirical evidence. Then we observe. Then we come back to logic for mathematical tools to explain what we see.

    So ultimately it’s this conflation of “philosophy” and “logic” and “mathematics” that seems to be getting us into trouble here. This article seems to assume that of these two “kinds of knowledge,” one must encapsulate – one whole corpus of knowledge must be more fundamental than – the other. That, indeed, is the suggestion of the question I posed in the last paragraph. But now let me suggest that we discard that assumption. Some kinds of theoretical knowledge, I think, must constitute “first principles” because they are necessary for what is perceived to be known – they are necessary to establish the relevance of perception in the first place. (And if that sounds trivial, think about issues of empiricism vs. religious doctrine – these questions matter!). But I also think it is clear that many kinds of theoretical knowledge are not derived empirically.

    Lastly, we should note that our list of disciplines at the beginning totally omitted the social sciences and the non-philosophy humanities. But I believe those fields – the social sciences in particular – address this same question, and help us see it with more clarity. History requires us to begin with reasoning regarding what should and shouldn’t constitute evidence, and how evidence should be interpreted: we like unbiased primary sources, we don’t like biased secondary sources; we like archaelogical evidence (and that field’s scientific conclusions regarding good and bad evidence apply as well). This is not to say, of course, that the discipline of history could not have begun before these ideas were settled, or that they have been settled, or that they ever even could be settled. But the point is that to begin an analysis of history one must have some conception of what does constitute evidence about the past, and why, and how, and how much. Then, the historian proceeds to actually examine history. And then our historian – if he iIS a historian, and is not merely an archaeologist in disguise – will come up with some theory to explain it. So there are three things: first principles, evidence, and then theories which explain the evidence. The analogues in the the study physics are metaphysics, empirical observation, and then physical models. Mathematics may exist prior to empirical observation, but it lacks explanatory power unless it is constructed to explain an observed phenomenon.

  4. Ben says:

    A comment here could hopefully resolve some confusion.

    The epistemic a priori vs. a posteriori distinction concerns how a truth is known. Can we know it through abstract reasoning (a priori), or must we learn it through empirical measurement (a posteriori)? This, loosely, is the distinction I attempted to draw.

    Within this distinction, though, we might divide further. We could ask whether we’re concerned with how things in practice typically come to be known, or how things theoretically could ever be known.

    My original piece, unfortunately, was quite unclear. I intended to explore the landscape generated by the “theoretical” distinction. In “The Whole World Is Logical”, this intent is apparent. In “Logical Antecedes Empirical”, though, my argument looks like it more closely concerns the “practical” question. Furthermore, and perhaps worst of all, Hacker and Bennett’s original arguments rests on a still-different distinction, unrelated to epistemology altogether.

    Hacker and Bennett would agree that the academic disciplines which I’ve described as logical and the academic disciplines which I’ve described as empirical are fundamentally different. They’d underpin the difference, though, not on how they’re known, but on the role that they play. “Conceptual truths delineate the logical space within which facts are located… An empirical proposition is a description of how things stand.” What’s at stake is not how these claims are known, but whether they’re “normative” or “descriptive”.

    It’s true, then, that abstract logical truths help us interpret empirical truths. The reason, though, is perhaps subtle. Conceptual truths (which tend to be epistemically a priori) establish the preconditions for understanding of descriptive truths (which tend to be epistemically a posteriori). (I refer to the “practical” distinction here.) That’s how things now seem to be, at least.

    The above distinction between “theoretical” and “practical” epistemology — and my assurance that the former was my intention — should reassure Josh.

    Wilson, the “preconceived mathematical truths” you describe are no such thing. They are mathematical models intended to describe physics. When the physical world proves to be more complex, the models are shown ineffective. But math (understood as a set of conceptual truths) hasn’t been contradicted in any way. Hacker and Bennett elucidate the distinction: “It would be mistaken to suppose that the theorems of the differential calculus were confirmed holistically by the predictive success of Newtonian mechanics and might have been infirmed by its failure and rejection. They were confirmed by mathematical proofs.”

    As for Anomaly: This is true, I concede. Your argument, though, might perhaps be weakened to require not just any empirical truth, but one particular, extremely fundamental one — say, perhaps, the state of the universe at the time of the big bang. This could be the one and only empirical “ingredient” for subsequent logical deduction.

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