Most philosophers have at least a vague awareness of this. For instance, they know from standard textbooks that traditional and modern logic differ in their interpretation of categorical propositions, the repercussions this has for their understanding of the square of opposition, and so forth. They know that there has been much debate in contemporary philosophy over the status of modal logic, not to mention even more exotic systems like quantum logic. They may be at least dimly aware that systems of logic were developed in the history of Indian philosophy that differ from those familiar to Western thinkers. And so on.

All the
same, contemporary philosophers tend unreflectively to utilize the formal
methods they learned in graduate school, treating (b) as if it were for all
practical purposes the same as (a). In
particular, they seldom consider that these methods might assume, or at least
suggest, challengeable metaphysical presuppositions.

When you
think about it, it would be surprising if it were* *not so. As I have argued
many times (e.g. in this
recent post and in greater depth in *Aristotle’s
Revenge*), the mathematical abstractions of modern physics, for
all their undeniable utility and power, can distort our conception of concrete
physical reality if we are not careful. For
mathematical representations of their very nature both leave out aspects of the
concrete reality they represent, and can also introduce features that are not
part of that reality but rather merely reflect the mode of representation
itself.

But formal
logic can do the same. For one thing,
qua formal, its aim is precisely to abstract from the specific nature of the
subject matter being reasoned about.
(What is traditionally called *material
logic*, by contrast, aims to reflect rather than abstract from that specific
nature.) At the same time, modern
symbolic logic was developed precisely in a manner that would facilitate the
expression of one particular subject matter, namely mathematics. It would hardly be surprising, then, if the
way that propositions concerning some other subject matter are expressed in
modern formal logic might be potentially metaphysically misleading.

For example,
John Bigelow has
suggested that modern physics’ mathematical representations of local
motion over time, *together with* the
apparatus of modern predicate logic, tend to insinuate an eternalist rather
than presentist conception of time. For when
we formulate the propositions of physical theory using predicate logic, we need
to quantify over not only present events but also *past and future* events. And
if the existential quantifier asserts the existence of a thing, then physical
theory is thereby made to seem to assert the existence of past and future
events no less than present ones.

Now, this
fact does not by itself actually show that past and future events really do
exist just as present events do. For all
we know just from what has been said so far, the result in question may
reflect, not objective reality *itself*,
but merely modern formal logic’s mode of *representing*
objective reality. To show that the
eternalist conclusion really follows, and does not merely falsely appear to do
so, would require independent metaphysical argumentation. But in that case it is precisely this
independent metaphysical argumentation itself, and not the system of formal
logic, that is really doing the work. (I
would suggest that the “truthmaker” objection to presentism – which, as I
have argued several times, is greatly overrated – may reflect this
fallacy of reading off metaphysical conclusions from what is really nothing
more than predicate logic’s mode of representation.)

*Humean logic?*

Rani Lill
Anjum and Stephen Mumford, in chapter 5 of their book *What
Tends to Be: The Philosophy of Dispositional Modality* (which
earlier appeared as a separate paper),
argue that modern formal logic reflects a metaphysical bias in favor of a
Humean conception of the world and against an Aristotelian conception. In particular, it is well suited to express
causal propositions understood, as Hume would, as describing merely contingent
relationships holding between “loose and separate” existents. It is poorly suited to express causal
propositions understood the way Aristotelians understand them, as describing
necessary connections between intrinsically related existents.

Now, among
the crucial features of modern logic in this connection are that it is *extensional* and *truth-functional*. In the
context of predicate logic, extensionality has to do with the fact that
co-referring terms can be substituted for one another without changing the
truth value of a statement. For example,
since the statement that *Spider-Man
fights crime* is true, and Spider-Man = Peter Parker, then it will also be
true that *Peter Parker fights crime*. (Statements involving propositional attitudes
don’t fit this pattern, however. They
are famously *intensional* rather than
extensional. For example, if it is true
that *Aunt May believes that Spider-Man
fights crime*, then even though Spider-Man = Peter Parker, it does not
follow that *Aunt May believes that Peter
Parker fights crime*. For if she does
not know that Spider-Man = Peter Parker, the second statement might not be true
even though the first is.)

In the
context of propositional logic, extensionality has to do with the fact that a
proposition that is a component of a compound proposition can be replaced by
one having the same truth value without changing the truth value of the
compound proposition. For example, if it
is true that *water is wet and grass is
green*, and we replace the second of the component propositions with the
true proposition that *the sky is blue*,
then the resulting proposition that *water
is wet and the sky is blue* will also be true.

Truth-functionality
has to do with the fact that in propositional logic, the truth or falsity of a
compound statement is a function solely of the truth or falsity of its
component parts. For example, if it is
true that *the sky is blue* and it is
also true that *I am drinking coffee*,
then the conjunctive statement that *the
sky is blue and I am drinking coffee* will also be true.

Now, where
these features have especially interesting implications – and implications
relevant to Anjum and Mumford’s point – is with respect to *material conditionals*, statements of the form *p* É *q* or “If *p*, then *q*.” In propositional logic,
the only case where a statement of this form is false is when the antecedent *p* is true and the consequent *q* is false. In every other case the conditional will be
true. This has some notoriously odd
results (known as the “paradoxes of material implication”). For example, the statement that *if the sky is green, then robots rule the
earth* is true. The antecedent and
consequent are, of course, both false, but the statement as a whole still comes
out true, as anyone knows who has worked through the relevant truth table. Also true are the statement that *if the sky is green, then 1 + 1 = 2*
(since the consequent is true even though the antecedent is false) and the
statement that *if the sky is blue, then 1
+ 1 = 2* (since both antecedent and consequent are true even though they have
nothing to do with one another).

Now, suppose
you agree with Hume that there are no necessary connections between any things
or events in the world. Everything is,
as Hume puts it, “loose and separate,” and in theory any effect or none might
follow upon any cause – striking a match may cause it to turn into a cat,
planting an acorn might cause a Volkswagen to grow out of the earth, and so
on. We don’t seriously believe such
things will ever happen, but that has nothing to do with the natures of these
things themselves. It has instead to do
only with psychological expectations on our part based on past experience, or
at most with whatever laws of nature happen contingently to associate an event
of one type with events of another type (where what a “law of nature” is on a
Humean view is *itself* a problematic
issue).

In that
case, say Anjum and Mumford, modern formal logic is well suited to convey any
causal claim you want to make. Weird
conditionals like the examples given above are not prima facie suspect. (True, there may be no *law* connecting, say, the sky’s being green with robots ruling the
earth, and for that reason a contemporary Humean wouldn’t take the conditional
in question to express a true *causal*
claim. But that would have nothing to do
with anything *intrinsic* to the sky’s
being green – nothing to do with there being no objective necessary connection
between the sky’s color and robots ruling the earth. Again, for the Humean there *are no* intrinsic or necessary
connections between things in the first place.)

But suppose instead
that you take the Aristotelian view that natural substances have inherent *dispositions* or *powers* by which they necessarily tend to generate effects of a
certain specific kind. Then, weird examples
of conditionals like the ones in question *are*
suspect. They show that the connections
between things that are captured by the material conditional are simply too
weak to correspond to the strong connections posited by the Aristotelian
metaphysics of causal powers. You’re not
going to be able to capture the truth of a causal statement like “Striking a
match generates flame and heat” or “A planted acorn will grow into an oak tree”
via the material conditional. Indeed, attempts
to capture such claims in terms of conditionals, or even in terms of
counterfactuals, face notorious difficulties.
(See pp. 53-63 of *Scholastic
Metaphysics* for an overview of the main arguments.)

Now, Anjum
and Mumford note that adding predicate logic to propositional logic does not
solve the problem, because predicate logic builds on propositional logic’s
account of the material conditional. But
even adding modal operators, as modal logic does, does not solve the problem either,
because the truth-functional character of propositional logic is preserved. You’ll still get weird results (known as the
“paradoxes of strict implication”), and in particular results that are going to
be suspect from an Aristotelian point of view.
For example, you get the result that anything strictly implies a
necessary statement:

□ *q* ® (*p*
® *q*)

For instance,
“If it is necessary that water is H_{2}O, then this strictly implies
that the fact that tomorrow is Taco Tuesday strictly implies that water is H_{2}O.” That weird sort of modal statement hardly
captures the *kind* of necessary
connections in nature that Aristotelians posit when they affirm the reality of
causal powers.

Now, David
Lewis famously held that every possible world is as real as the actual
world. And as Anjum and Mumford point
out, this provides a way to read even statements in modal logic in a Humean
manner that denies any intrinsic causal connections between things. The truth of the statement that *necessarily, if p then q* requires only
that in every possible world where *p*
is true, *q* is also true. It does not require that there be anything *intrinsic to* the states of affairs
described by *p *and *q* (such as causal powers that follow
upon the essence of a thing) that ties them together. Of course, most people wouldn’t agree with
Lewis’s view about possible worlds, but the point is that the mere possibility
of interpreting modal logic in Lewis’s terms shows that it doesn’t capture the *kinds* of necessary connections that
Aristotelians attribute to the natural order.

There is
also the fact that on the Aristotelian account, causal powers *tend toward* generating certain outcomes,
but still may not *in fact* generate
them, because the manifestation of a power can be blocked. Given the nature of the sulfur in the head of
a match, it *tends* toward generating
flame and heat when struck (as opposed to frost and coldness, or turning into a
snake, or what have you). But that
doesn’t entail that flame and heat will always follow, because that tendency
can be frustrated (for example, if the match gets wet).

So, things
are not “loose and separate” in the manner Hume supposes (e.g. it just isn’t
true that striking a match might in principle bring about any old effect at
all). But at the same time there are not
going to be exceptionless correlations between events (because the operation of
a power can be frustrated, so that the event of striking a match might in some
cases not be followed by the event of flame and heat being generated). Anjum and Mumford propose positing a
“dispositional modality” of *tending
toward* that lies in between mere possibility on the one hand and
necessitation on the other. More
traditional Aristotelians would speak of *potencies*
that are distinct from actualities but are nevertheless really there in things
themselves even if they are never actualized.
But however we describe the metaphysical details, Anjum and Mumford’s
point is that they are not going to be captured in standard extensional and
truth-functional formal systems.

You might
say “So much the worse for the Aristotelian,” but the point is that such a
judgment *would have nothing to do with formal
logic* *itself*. Rather, it has to do with independent
metaphysical assumptions that might lead one to *favor *a certain formal system.
A formal system may be useful for certain purposes and not so useful for
others. Our metaphysical predilections
might lead us to judge that there is nothing more to the world than what the
formal system captures, or they may lead us to judge that it leaves important
things out. Either way, the
characteristics of the formal system *itself*
don’t settle anything. As Anjum and
Mumford write:

*Metaphysics is First Philosophy,
prior even to logic. And from that it
would follow that one should first choose one’s metaphysics and then choose
one’s logic, rather than the other way around*. (p. 86)

I would
qualify this by saying that metaphysics is prior to logic if “logic” is
understood *in sense (b) *described
above, though not if understood in sense (a).
Naturally, we have to presuppose certain canons of reasoning when
reasoning about anything, including metaphysics. But it doesn’t follow that we have to
presuppose the codification enshrined in some particular formal system – such
as, for example, modern propositional and predicate logic rather than
traditional Aristotelian logic, or rather than some system that tries to
capture the best of both worlds (such as that
of Fred Sommers).

Again, at
some level most philosophers realize this, but it can be easy to forget if you
and your colleagues all routinely learn and utilize a certain formal system,
and questions about its underlying philosophical assumptions are considered only
by the small minority of philosophers who specialize in such things. Anjum and Mumford speculate that, despite his
famous disagreement with Mill on matters of the philosophy of mathematics,
Frege picked up a set of essentially Humean empiricist prejudices about logic
from Mill’s *A System of Logic*. These were then passed down from Frege to
Carnap, then from Carnap to Quine, and then from Quine to Lewis and
contemporary philosophers in general.
(Naturally, Russell and Whitehead played a major role too.) Whatever one thinks of this hypothesis, it is
certainly true that a dogmatic conventional wisdom can take root on matters of
logic no less than it can with respect to any other area of intellectual
interest.

*What-logic versus relating-logic*

Aristotelian
complaints about the metaphysical prejudices enshrined in modern formal logic
are not new. Over fifty years ago, Henry
Veatch addressed the issue at length in his book *Two Logics: The Conflict between Classical and Neo-Analytic Philosophy*
(which was recently
reprinted by Editiones Scholasticae).

Veatch notes
that we can distinguish *what a thing is*
from *the relations it bears to other
things*. Now, Aristotelians are
essentialists, who hold that there are facts of the matter about what things
are and that we can at least to some extent discover those facts. Logic, as understood in the Aristotelian
tradition, is a tool for helping us to discover and express what things
are. A humble categorical proposition
like “All whales are mammals” does precisely that, however little such a
statement tells us all by itself.

However,
Veatch argues, statements formulated in terms of the formal logic hammered out
in works like Russell and Whitehead’s *Principia
Mathematica* do not and indeed *cannot*,
strictly speaking, tell us what a thing is.
They can express only relations. Now,
one of the advantages of modern predicate logic is precisely that it can
represent relations in a way that Aristotelian categorical logic cannot. It does so using multi-place predicates. For example, the relation “___ loves ___”
would be represented by the two-place predicate L ___, ___ where the spaces
would be filled by lower-case letters naming individuals. Hence “Harry loves Sally” would be
represented as: Lhs.

But even
one-place predicates, Veatch notes, are treated as representing relations, viz.
relations between a thing and a property.
For instance, “Fred is bald” or Bf would represent the relationship
between Fred and the property *baldness*. One-place predicates are essentially treated
as a *limiting case* of relational
predicates.

For this
reason, Veatch argues, modern formal logic can really only ever express the *relations* between things, and not *what a thing is*. Before you judge that that cannot be right,
it would be a good idea to keep in mind that Russell himself held that even
modern physics, when formulated in the language of modern logic, gives us
knowledge only of relations and not of the intrinsic natures of anything. (I discuss Russell’s views a length in *Aristotle’s Revenge*.) One could, however, take this to show, not
how little physics tells us, but rather how little formal logic tells us.

As Veatch
also points out, the analysis of ordinary statements into statements of
predicate logic tends to suggest an ontology of *bare particulars* and *universals*. For instance, the statement “There’s a
Ferrari parked outside” comes out as something like: ($x) (Fx • Px). Any concrete attributes that might
characterize the thing being described get analyzed as predicates, leaving just
a bare *something* of which the
universals named by the predicates (*being
a Ferrari*, *being parked outside*) are
predicated.

Now, the
notion of a bare particular is metaphysically dubious (cf. David Oderberg’s
essay “Predicate
Logic and Bare Particulars”), as is the notion of a world of which we can know
only relations. Of course, someone might
nevertheless want to defend such philosophical exotica. The point, however, is that even if the
utility of predicate logic might *suggest*
such views, it does not actually by itself give evidential *support* for them. Again, if
some apparent aspect of reality is difficult to describe using the apparatus of
a system of formal logic, that may indicate merely the expressive limitations
of the system, rather than the absence of those aspects from objective reality. We cannot read a metaphysics *out of* formal logic without first reading
one *into* it. Metaphysics, as Anjum and Mumford insist, is
in this sense prior to logic.

*Faux rigor*

Such
considerations lend additional force to a point I have made before, which is that
the use of formal methods in philosophical analysis and argumentation by no
means guarantees that the results are more rigorously established, and indeed in
some cases can even make them less so.

For example,
when analyzing an argument like Aquinas’s Third Way, some commentators like to reformulate
it using the formal apparatus familiar from contemporary modal logic. The reader easily impressed by such things
thinks: “Wow, this is so much more rigorous than a less formal treatment!” But in fact, such an analysis will simply
change the subject, because the distinctively Aristotelian way in which Aquinas
understands the relevant modal concepts cannot (as Anjum and Mumford point out)
be captured in that formal language. And
an analysis that simply fails to capture what Aquinas is talking about is
hardly rigorous.

In a
post from a decade ago I discussed Robert Nozick’s treatment in *Philosophical
Explanations* of the question why there is something rather than
nothing, and noted that it affords another example of how semi-formal methods can
obfuscate rather than illuminate. Nozick
speaks of various possible “states N [that] are natural or privileged” (one of
which might be “nothingness” itself), of various “forces of type F” (one of
which might be a “nothingness force”), of an “amount” there might be of such a
force, and so on, and then proceeds to consider what relations may hold between
N and various quantities of F, etc. Because
the discussion is couched in terms of symbols and variables, it gives the
appearance of rigor. But it is not
prefaced with any treatment of the more fundamental and indeed crucial
philosophical question of whether the proposed states and forces referred to
are plausible (or indeed even coherent) in the first place. Hence the apparent rigor is bogus.

None of this is intended to suggest that formal methods have no value, or to deny that sometimes they are even necessary. The point is rather that their utility can be oversold and their neutrality overestimated.

Ed, do you know if there is a parallel between these different types of logic (one of which prioritizes relations) and the notion in the "trinitarian" theologies of Zizioulas and others who reject a substance ontology in favor of a relation ontology?

ReplyDeleteTim Finlay

Interesting question, Tim. I don't think there is any direct connection, since theologians of the kind you're referring to seem primarily motivated by what they take to be the nature of relations of the

Deleteinterpersonalkind, specifically, whereas writers like Russell are concerned with relations of a much more abstract sort. But I suppose the former group could deploy the work of those of the latter group in the service of their own ends.This is extremely important to know since it is sometimes very difficult to understand the implications related to formal logic and even more difficult to see some fallacies in some arguments. Thank you for that, Ed! May God bless you!

ReplyDeleteSo does this mean that logic is an abstraction of the same particular system of metaphysics that it's meant to serve?

ReplyDeleteGreat Spider-Man analogy by the way.

It's endlessly amusing how you make it seem like comic books and their content were invented by philosophers to express and teach philosophy.

TEACHER: You see boys and girls, Stan Lee -like Nostradamus- was the greatest visionary of his time.

But, the world was not ready; so he too had to cloak his wisdom in common mediums of the time where only those with wisdom could recognize them.

Can someone recommend a good book which gives a treatment of “ the rules that determine the difference between good and bad reasoning”? Want to have something for my kids before they hit late high-school or college.

ReplyDeleteI have Peter Kreeft's "Socratic Logic". It is touted as the best introduction to Aristotelian style logic in circulation.

DeleteAs with all of Kreeft's work it is very readable and not dry at all! It is also designed for high school use and includes lots of practice questions and the text itself includes answers to odd-numbered questions (I think you can email Kreeft for the even answers). It is hardcover, in-depth (but not too much). It will cost you a bit, being in the $40-50, but worth it.Good luck!

https://www.amazon.com/Socratic-Logic-Questions-Aristotelian-Principles/dp/1587318083/ref=sr_1_1?dchild=1&keywords=Socratic+Logic&qid=1626211637&sr=8-1

Yeah it even gives logical examples from Winnie the Pooh!

DeleteLogic as a Human Instrument by Parker & Veatch and Logic: The Art of Defining and Reasoning by Oesterle

DeleteMemoria Press's Traditional Logic I and II are good for high school students. So is their Material Logic. Might as well get the Rhetoric while you're at it.

DeleteW. Stanley Jevons' Elementary Lessons in Logic is very readable and was the most popular logic text in the English speaking world for decades from late Victorian times well into the 20th century.

DeleteIf you need a hard-copy it's available on Amazon in several editions.

Jevons was responsible for modifying Boole's original system into what we recognize today as boolean algebra (Boole's system was more complex and used ordinary high school algebra). His method is outlined in a chapter of the book. It's my favourite logical 'system' because it's so easy to use and is based very directly on Aristotle's three laws of thought, and the only inference rule is substitution of equals for equals.

I also highly recommend his Magnum Opus - The Principles of Science.

And if you're ever in Oxford, you should check out his 'Logic Piano' in the Museum of the History of Science.

There's a formal system that ameliorates at least some of the problems listed here, called "case-intensional logic", by allowing (and indeed requiring in some circumstances) intensional predication rather than merely extensional predication, and making it clear that the "existential" quantifier isn't ontologically committing. I've found it to be the most intuitive way of combining modal and predicate logic:

ReplyDeletehttp://philsci-archive.pitt.edu/9375/

Thank you for this post! I need to make reading time for Logic... after I finish the books on my list for Ethics.

ReplyDeleteHi Ed,

ReplyDeleteThere is some justice in the Aristotelian-Thomistic complaint that modern predicate logic fails to capture the way we normally talk about dispositions, causal relations and necessary connections. But in that case, the obvious question is: why don't Aristotelians develop their own calculus, for the modern world? (It is universally acknowledged that Aristotle's 2,300-year-old logic is inadequate: for example, it is unable to demonstrate, from the fact that a horse is an animal, that the head of a horse is the head of an animal.) Do you know any Aristotelians who have attempted this task? Rob Koons, perhaps?

Check out Fred Sommers's work.

DeleteVincent,

DeleteThis is a short helpful blog that answers that question.

https://www.google.com/amp/s/vexingquestions.wordpress.com/2014/08/08/the-horse-head-argument/amp/

Mr. Vecchio offers a particular syllogism:

Every horse is an animal in virtue of being a horse.

Every horse is that which has a head.

Therefore: Some of those which have heads are animals, in virtue of being horses.

Vincent,

DeleteI don't quite get how what you're saying makes sense. Take the following syllogism.

All horses are animals.

Each horsehead belongs to a horse.

Each horsehead belongs to an animal.

Is this not a valid syllogism?

I find Sommer's plus-minus calculus rather confusing, but his major insight was to recognize that the old Dictum de Omni et Nullo of traditional logic is applicable not only to simple 3 term syllogisms, but also to relations and multiply general sentences, such as 'Some boy loves every girl'. The dictum is a rule of substitution, and applying it to the horses head argument (using plain English) :

DeleteH : horses

A : animals

h : heads

1. All H are A

2. All h of H are h of H (tautology)

Now, by the dictum we can substitute A in premise 1 into the H in the predicate of premise 2, which gives :

All h of H are h of A

@ Mister Geocon, strictly speaking, it isn't a valid categorical syllogism because there are too many terms. But it uses the dictum in a more general way, a la Sommers, and is actually easier to read than my solution because it hasn't pulled a tautology seemingly out of a hat.

DeleteJoe,

DeleteThere are only three terms: horses, animals, horseheads. How is this too many terms?

Well, I count 5 terms : horses, animals, horseheads, 'a thing which belongs to a horse' and 'a thing which belongs to an animal'.

DeleteThere are only 3 terms if the copula is 'belongs to', but you haven't used it in the first premise; you used 'is'. To be valid, you would have to use 'belongs to' as the copula consistently throughout. But 'All horses belong to animals' doesn't seem right.

Actually, Aristotle's original formulation of categorical propositions did use 'belongs to' as the copula. The form was

A does/doesn't belong to all/some B.

But 'belongs to' in your argument doesn't convey the same meaning (that of subsumption). There, it's taken to mean 'a part of' or 'has', ie, a portion of a natural object.

Joe,

Delete'A thing which belongs to a horse' and 'a thing which belongs to an animal' aren't actual terms. To show why, let's reformulate the syllogism.

Horses are a kind of animal.

Horseheads are heads that belong to a horse.

Horseheads are heads that belong to an animal.

This says precisely the same thing as the other syllogism, except now, everything uses 'is.'

Mister Geocon,

DeleteThere are still 5 terms in your argument. So although not a valid categorical syllogism (which must have exactly 3 terms), it is valid.

It contains an implicit substitution though. Let's make it explicit. The terms of your argument are:

1. H = horses

2. A = animals

3. hh = horseheads

4. hbH = heads that belong to a horse

5. hbA = heads that belong to an animal

Do you agree?

The premises are :

1. All H are A

2. All hh are hbH

Now, by deriving the conclusion

3. All hh are hbA

you have substituted 'A' in premise 1 into the 'H' in the predicate of premise 2. But this assumes that hbH can be interpreted as 'heads that belong to x', which isn't the kind of term allowed in standard categorical logic; it's more like a predicate in the predicate calculus, something like Bhx, where B = 'Belongs to', h = heads, and x is a variable.

Your argument is an example of what traditional logicians called 'immediate inference by added determinants', except that the second premise is superfluous: you can go from :

1. All H are A

directly to

2. All heads of H are heads of A

But you have to be careful that the added determinant ('heads', in this case) doesn't qualify the predicate in a way which makes the conclusion fallacious. e.g. An invalid example would be :

1. All elephants are animals

2. therefore, 'All small elephants are small animals'.

Actually there *is* a standard categorical syllogism which fits the bill :

1. All [horses] are [animals]

2. All [horses] are [that which have heads]

3. => some [animals] (namely,horses) are [that which have heads]

This is AAI, figure 3.

Sorry, I meant to start my 2nd sentence with 'BUT although not a categorical syllogism...'

DeleteFeser: "For when we formulate the propositions of physical theory using predicate logic, we need to quantify over not only present events but also past and future events. And if the existential quantifier asserts the existence of a thing, then physical theory is thereby made to seem to assert the existence of past and future events no less than present ones."

ReplyDeleteAn example here would be nice. I don't entirely follow.

It seems rather like taking seriously the idea that to assert "unicorns don't exist" implies that unicorns exist, because nothing can be true about something (including unicorns) unless that something exists -- and furthermore claiming that this is a "metaphysical presupposition" of ordinary language. Quine takes this so seriously (or pretends to?) that he thinks we have to resort to the logic (in the narrow sense) of Russellian paraphrases to avoid the problem. Anyway, I do think "metaphysical predispositions of formal logic" would have been a better title here. Gyula Klima has a very nice paper on "Ontological Alternatives vs. Alternative Semantics in Mediaeval Philosophy" which I think treats the issue well. It think it puts more emphasis on the fact that metaphysics (ontology) doesn't really follow from logic (semantics).

I wonder how Aristotelianism would analyse indeterministic forms of causality in terms of the tendencies of things? Quantum mechanics is often cited as an example, but another one is a six-sided die which lands on any particular side in a non-deterministic stochastic fashion.

ReplyDeleteIn this case, the indeterministic die has a well-defined set of final causes (landing on 1, 2, 3, 4, 5, 6) and has a clear form. Its indeterminism may also be explained by its formal cause since it's like that by its very nature. The die landing on any particular number also has efficient causes - whatever threw the die, and maybe the die itself which lands on a number. Yet though the die has the tendency to generate a specific set of outcomes, and there are probabilities attached to each outcome, the way the outcomes are caused isn't deterministic.

If the die were thrown and landed on 4, the fact it's indeterministic means that if you reversed time and played the event all over again, the die could also have landed on any other number instead. So no one particular outcome always follows - but not for reasons of interference of powers being frustrated.

The fact that the outcomes are indeterministic and may not have a contrastive rather-than explanation is something intrinsic to the nature of the die because indeterminism is intrinsic to it.

How would Aristotelianism view this type of causality, where any particular outcome doesn't always manifest, but not because of intereference - rather because of indeterminism?

Does Aristotelianism even have better metaphysical tools for dealing with indeterministic causes than formal logic, since it avoids both there being no tendencies, but also those tendencies strictly always manifesting?

Yet in thi

There aren't an infinite number of potentials for any given real object. Take the six-sided die. If you rewound time and threw the die again and again, you'd get a number between one and six, but however many times you rewound time and threw the die, you wouldn't get a number other than those six, nor would the die explode or turn into a live chicken. It's within the nature of the die to land on one of its six sides when thrown.

DeleteThose aren't the only potentials of a die. A die can land here, or it can land there, or it can be melted down a certain way, or... In the absence of gravity, it doesn't land.

DeleteWhen I took an intro to Logic class in college our teacher went to some lengths to point out that we were studying whether arguments had a valid *form*, but validity on its own said nothing about the truth of the arguments. It was also great that the formal logic section was followed by one on "informal" logic, introducing us to many of the more common fallacies, such as post hoc ergo hoc.

ReplyDeleteIsn't all this a reflection of the fact that merely asserting p -> q or □ p -> q doesn't tell us anything about WHY it is true (it may be explainable because of what p is, or, on the other hand, have nothing to do with the nature of p)? And can't these kind of relations also be incorporated into predicate logic? Something like □ (Np & ~Oq) -> (p -> q) where Np is the nature of p, and Oq is some other obstacle preventing q?

ReplyDeleteAny thoughts on "George Englebretsen - Robust Reality, An Essay in Formal Ontology (2012)"?

ReplyDeleteThese are good points about the limitations of formal logic, Dr. Feser, but I have a different perspective on the limitations of formal logic. It isn't that they have an implicit metaphysics, but that, like any formal system, they have limited scope.

ReplyDeleteIn mathematics, 2+3=5 is only useful if 2 and 3 are the numbers of disjoints sets. If the sets overlap, then the answer is bogus. In probability, p(A&B)=p(A)p(B), but only if A and B are independent. Similar limitations apply to all forms of formal logic: they have constraints on how they can be used; for example, the law of the excluded middle is only true if you don't allow sentences like the Liar, and the predicate calculus only works for systems that have been idealized into something like bare particulars and universals (I don't care for that specific characterization, but it will do for purposes of discussion).

However, this does not mean that predicate logic has a metaphysics; it only means that predicate logic has a restricted application.

"predicate calculus only works for systems that have been idealized into something like bare particulars and universals."

DeleteIs that right? I'd have said that the things have to be expressed in terms that might be amenable to an interpretation along the line of bare particulars and universals; but that doesn't seem the same as the requirement of actually idealizing them into something like that. If it did, then the claim wouldn't be true, that "this does not mean that predicate logic has a metaphysics." Again, you say, "it only means that predicate logic has a restricted application." But why does it mean that? Why must it have just this restricted application, where it only 'works' on the supposition of a particular (seemingly metaphysical) idealization of the elements in its domain?

Spot on. Before logic and ratiocination can get to work, PERCEPTION must first take place. And, to do that accurately and adequately is truly an art that is difficult to attain. Athanasius, Augustine, and, more recently, Chesterton, Lewis, Balthasar, and DC Schindler come immediately to mind.

ReplyDeleteGreat post. I can't help thinking that it was prompted by the recent exchanges with Joe Schmid?

ReplyDeleteIt's something I've thought about writing up for quite a long time, actually, but the red herrings that came up in that recent exchange did indeed serve as an immediate inspiration.

DeleteI think Joe would be pleased knowing he had inspired you. ��

DeleteThis was a great post on an interesting subject. What is Feser's favorite formal logical system? Aristotelian/syllogistic logic? I always found the case-by-case enumeration of validity strange in that system. That is, looking at each syllogism form and determining whether it is valid or invalid, rather than positing more general rules.

ReplyDelete"David Lewis famously held that every possible world is as real as the actual world."

ReplyDeleteIsn't that just an assertion of what the definition of "real" is?

Or it is just a bare assertion without a shred of basis, or truth.

DeleteDid not Lewis itself argued that his modal realism is the only way to make sense of modal truths or something?

DeleteI mean, it is a silly view and we realists about universals can laugh at the argument, but it is not really a assertion.

Since the comment I had early on left praising this entry for its interest and value -probably shortly after it was put up - never took, let me second those who have commented on this intellectually satisfying yet very approachable and casual review.

ReplyDeleteSomeone had mentioned Sommers earlier, and it reminds me that I still have "The New Old Logic" edited by Oderberg, which you {Ed] may have recommended as worth study, still unread. The same, insofar as an uncompleted read goes for Heidegger's "The Metaphysical Foundations of Logic" which treats "judgments"; a term which always puts me off a bit when used in connection with logic, but which is common in European treatments of it.

If anyone has made a careful study of that latter work, perhaps they can save me, and anyone else potentially interested, the full slog through it with a few insights.

Leibniz ... "judgements" ... Gaia save me ...

Can I just remark how much better this combox is from just a few months ago. It's a shame it has taken Feser personally vetting comments to weed out the low value contributions from Gnus and trolls, but it does greatly improve the experience.

ReplyDeleteWe developed a tape measure to measure this magic place we live in, only we forgot about the magic place and became enamored by the tape measure.

ReplyDeleteThe thing for which I am most indebted to Feser is the understanding that we cannot get more metaphysics out than we first put in. If people really understood that, it would, no doubt, end a lot of gibberish debates posing as intellectual.

What kind of cool name is Veatch? Sup Veatches!

I recently managed to get a new copy of 'Two Logics' from Amazon for less than half price, and I'm hoping that Editiones Scholasticae will reprint Veatch & Parker's 'Logic as a Human Instrument'. Second-hand copies are very expensive, and although you can read it online at the internet archive library, it's not downloadable and you can only borrow it for an hour at a time.

ReplyDeleteAnother downside of modern predicate logic (Logic as Humean Instrument?), aside from those which Ed has pointed out, is that it's so damned hard to learn and apply,in comparison with term logic. The most difficult step is translating from natural language into 'Logicese'. True, it does have the characteristic of being 'ontologically explicit', in that it forces you to make clear just what does and doesn't exist, which is arguably an advantage for certain subjects such as abstract mathematics and computer science. The trade-off is that this generally makes proofs much longer than they would be in a term logic. For philosophy and everyday reasoning we need something more user-friendly. Logic should be for everybody, and in my opinion should be taught from grade 7 or 8 (it is, after all, simpler than arithmetic in many ways).

Nor is the oft-touted superiority of predicate logic in terms of inferential power justified, as Sommers has shown. Indeed, there are sentences which can be formulated in term logic but not predicate logic, and the latter would find arguments involving numerical quantifiers, such as the following, incredibly long and tedious:

At least 13 artists are dentists

At most 3 beekeepers are not carpenters

At most 1 carpenter is not a dentist

Therefore, at least 9 artists are dentists

But using the extended syllogistic it's no more difficult than solving an ordinary categorical syllogism.

See here for an outline of Sommer's term logic, including an extension for numerical arguments.

Logic in sense (a) is for everybody. But in sense (b)?

DeleteAlso, I'm curious on what grounds you advocate the teaching of logic ((a) or (b)). I wonder how useful it is. I've spent enough time with students who have studied an intro to logic but who are completely useless at real reasoning to wonder if there is any real benefit in it. (Joe Schmid, for example, very bright young guy, probably got A+ in all his logic courses, but it seems to me his formal knowledge of logic helps him very little in real logical (sense (a)) tasks, that is, in attempting to actually engage in a constructive way with real arguments; and he's picked up some bad 'analytic' habits which positively hinder him from doing so.)

David, it's not quite clear to me that there is a significant difference between logic in sense (a) and sense (b). Just what are the rules that determine the difference between good and bad reasoning? There are many, and which to use depends on the kind of argument. But then, can you have such a set of rules which are NOT codified in a specific way?

ReplyDeleteI guess you could take Aristotle's three laws of thought as the common ground of good reasoning, although there are logical systems which deny one or more of them (but of course, you can only deny them and not give reasons for denying them, otherwise you would be using them). Then there are the basic rules of validity for deductive logic, rules to ensure that inductive arguments are strong, etc, but are there not metaphysical presuppostions involved here, too? Don't the basic rules also constitute a formal system?

I don't think you can separate metaphysics, epistemology and logic; they are in a sense different aspects of the same thing.

Also, on reflection, it seems to me that Veatch exaggerates the difference between the two logics, at least in regard to his central argument. If, as he says, we "distinguish what a thing is from the relations it bears to other things" (and I agree), why is he so critical of modern logic's limitation (according to him) that it can only express relations? Any system of logic is about making connections. That is to say, establishing relations between terms (concepts) and/or propositions.

As for teaching logic, I'm not sure whether it's ever been tried, but I believe if you start early enough -- grade 7, or maybe even earlier, when kids start learning arithmetic, it would pay huge dividends later in both their academic careers and life. What's so important is being able to grasp the principle that statements should be justified and explained through the process of argument, and that this is a virtue and the mark of a civilized society (so there is a moral element there, too).

In my opinion, this what education should be about, not merely learning "stuff", which it too often is, even now in a time when we have never had such easy access to facts and information. In teaching mathematics, for example, there is the tendency to emphasize that the goal of getting the right answer is of supreme importance, rather than justifying the steps taken to reach it. There is a lot of logic involved in mathematics, but it's largely implicit. Making it explicit would enable students to understand what they are doing and give them more confidence. And actually, studies have shown that this is the case, with regard to mathematics, at least. I see no reason why it should not apply across the board. Logic should not be seen as a 'subject', primarily, but as a tool to be used and applied in every domain.

"What's so important is being able to grasp the principle that statements should be justified and explained through the process of argument, and that this is a virtue and the mark of a civilized society (so there is a moral element there, too)."

ReplyDeleteWell I certainly agree with that. But then this general point should pertain to all of education, not just logic class; and if it does, then maybe the logic class per se is unnecessary; and if it doesn't, then maybe the logic class will be inevitably insufficient, and maybe not even helpful. The logic will end up being just more "stuff" that is learned. And I suspect that's indeed what happens in the real world when students take logic courses.

I was wondering what professor Feser thinks about Socratic Logic by Peter Kreeft and David Kelley's The Art of Reasoning. Also, just curious what you think of Aristotelian Logic( traditional square, existential import..etc.)

ReplyDeleteThe question is what must already be assumed about logic in order to adjudicate different views of it.

ReplyDelete