Deductions about Deductive Arguments

Logic is a bit outside of the basic topic of this blog, but I haven’t been blogging much over the last couple of months and I am teaching logic this next semester.  Bear with me.  It does have some relevance to things I have been writing about here. 

I have always included a little basic logic in my Introduction to Philosophy course.  One thing that always troubled me was a difficulty in defining deductive arguments.  The standard definition goes like this:

A deductive argument is one in which it is claimed that the conclusion follows necessarily from the premises.

Unpacking that, “follows necessarily” means that it is logically impossible for the premises to be true and the conclusion false.  The meaning of “claimed” is more difficult.  It seems to be included in the definition to make it easier to define an invalid argument. 

An invalid argument is a deductive argument in which, even if the premises are true, it is still possible for the conclusion to be false. 

Now suppose you wanted to define a deductive argument without the “claim” part:

A deductive argument is one in which the conclusion follows necessarily from the premises.

That would result in a contradiction in the definition of an invalid argument.  Yet we clearly want “invalid arguments” to be deductive arguments that fail and not arguments that fail to be deductive.  The standard definition of deductive argument attempts to avoid this by including the reference to a claim. 

The problem I have with that is that it runs a serious risk of transforming any argument into a deductive argument if only someone claims that it is one.  Thus “the pavement is wet so it must have rained” becomes deductive if I claim (falsely) that the conclusion follows necessarily from the premise.  If we are to allow for the existence of failed deductive arguments, we must presumably include the intention of the argument in the definition; however, if we “deductive” to be an objective characteristic of an argument, then it cannot ride solely on intention.  Above all, we don’t want to christen any argument as deductive merely because it is called so. 

I suggest the following resolution by means of an analogy.  Consider the following scenario:

I believe that I will someday rob a bank.

Can you conclude from this alone that I am guilty of a crime?  I submit that you cannot.  What about this scenario?

I intend to someday rob a bank.

Knowing that I have formed such an intention, but knowing nothing else, can you conclude that I am guilty of any crime?  Again, I say not.  You may come to some unfavorable conclusions about my character, but nothing more. 

I plan to rob a bank; I have purchased a gun and a ski mask; I have discussed my plans with several partners. 

Now we have the makings of a good case for a conspiracy to commit robbery.  Even if I haven’t gone through with it yet, I am very probably guilty of a crime.  On the other hand:

I have purchased a gun and a ski mask and I have discussed the act of robbing a bank with several others; however, we have no plans to actually rob a bank. 

Without the actual intention, I might be nothing more than a would-be mystery writer who wants to stimulate his imagination.  I am guilty of nothing.  A genuine crime would seem to require that a genuine intention be expressed in some kind of action, even if the action involves only preliminary steps and planning. 

Using this analogy, I think we can understand what it means to commit a deductive argument, valid or invalid.  Arguments are mental actions.  Some arguments result in physical actions, as when I conclude that eating nuts is good for my health and then actually eat nuts.  Some do not, as when I conclude that there is no life on Mars.  I wasn’t going there anyway. 

A genuine deductive argument must be read as an expression of a certain intention: to logically guarantee some statement by inference from some statement or statements.  Only if my intention is expressed in the form of the argument can the argument be identified as genuinely deductive.  This may sometimes involve judgment calls, but there are at least some cases where objective verification is possible.  For example:

All mammals are animals.  My pet is a mammal.  Therefore it is an animal. 

While it is not impossible that such a series of statements is random, it is safe to assume that it expresses my intention to draw a necessary conclusion from two premises because this makes a genuinely valid argument.  If the premises are in fact true, the conclusion does necessarily follow.  Valid arguments are the easiest case.  What about this one:

All mammals are animals.  My pet is an animal.  Therefore it is a mammal. 

This argument is rather obviously invalid.  My pet might be an alligator: an animal but not a mammal.  Yet its structure suggests that I was aiming at certainty rather than probability.  This is a frequently committed fallacy: confirming the consequent.  That it has such a title means that we can recognize it as a failed attempt to construct a valid deductive argument. 

Returning to our first definition:

A deductive argument is one in which it is claimed that the conclusion follows necessarily from the premises.

We can now understand the meaning of claim to involve not only the motive or conception that the person making the argument may have, but the expression of intention in the form of the argument.  I take such forms to be platonic realities. 

Jesus v. Darwin

I have a copy of this cartoon on the wall outside my office at Northern:

For several reasons I have been thinking lately about the mutual hostility between conservatives (especially religious conservatives) and Darwinists.  The proximate cause of the quarrel is obviously political.  The two sides having drawn apart and against one another almost a century ago, they now dislike each other because they dislike each other.  That is how politics often (almost always) works. 

This explains a curious fact about the latter faction: the rare emphasis on a particular scientist.  While both Isaac Newton and Albert Einstein were certainly celebrated and influential and while both had their followers, as it were, it is rare to speak of Newtonians let alone Newtonism, or to hear someone described as a Relativist in the sense of Einstein.  Yet we speak of Darwinists and Darwinians all the time. 

This is so, I suggest, for the same reason as one speaks of Marxists or Lutherans for that matter.  To announce one’s acceptance of Darwin’s theory is a pledge of allegiance.  There is nothing especially wrong with this.  We are political animals.  This is what we do. 

There are deeper causes for the quarrel, however, and they require explanation.  Why did a hostility open up between Darwinian biology in particular and Christian (an increasingly other Abrahamic religions) and why has it been so persistent?  Why is there much less friction between religion and geology, for instance, or astronomy?  Such sciences once got the philosopher Anaxagoras expelled from Athens.  Today, only young earthers are offended by physics, and they are rather rare. 

One reason has to do with the historical moment at which Darwin’s theory appears.  The Nineteenth Century was the period in which the center of gravity in Western culture shifted decisively from religious authority to secular authority, both in science and in government.  Darwin’s achievement was neither the cause nor in any important sense a consequence of that shift; however, because it coincided with it, it came to be identified with it. 

A second reason for the quarrel is that religious thought in general and theology in particular had responded to the rise of modern science with what I call the Olympian Strategy.  The simple rule of this strategy is to imagine that the God or gods dwell somewhere that one cannot easily look.  An adolescent version of this strategy is to imagine that angels live on the tops of clouds, which works reasonably well until the invention of aircraft.  Before Darwin, it was tempting to suppose that while science could explain day and night, the stars and the seasons, and volcanos, only a creator God could explain the human eye or the wings of birds.  I note that the Intelligent Design movement seems still to be trying to sustain the Olympian Strategy. 

While both of these explanations are part of the story, I recently have come to think that something more deeply rooted in the history of Biblical Religion is at work.  Pagan gods lived in the world, even if largely out of sight and at high altitudes.  The Biblical God existed before the world that He created and therefore exists outside that world, however much or often he intervenes in it.  This separation of God from the world has very important existential consequences.  For pagans, the moon was a divine being, worthy of reverence and awe.  In Genesis, it is demoted to the status of a street light, hung in the heavens by the Creator.  Much the same thing is true of the sun. 

The Biblical God’s jealousy left no room for the vast population of gods, demigods, spirits, nymphs, etc., that had inhabited the ancient world.  This by no means precluded admiration of the natural world.  One could admire it as divine art in the same way that one admires the arts of human beings.  It did however, open up a persistent temptation to view that world with contempt.  Matter is mere matter, dead and inert, without spirit. 

The power of this temptation is evident from the wee small books towards the end of the New Testament.  Consider 1^st John 4:

Beloved, believe not every spirit, but try the spirits whether they are of God: because many false prophets are gone out into the world.

² Hereby know ye the Spirit of God: Every spirit that confesseth that Jesus Christ is come in the flesh is of God:

³ And every spirit that confesseth not that Jesus Christ is come in the flesh is not of God: and this is that spirit of antichrist, whereof ye have heard that it should come; and even now already is it in the world.

What is that bit about Jesus Christ “come in the flesh”?  As explained to me by a Biblical scholar (which I am not), the early church was infiltrated by Gnostics.  The latter believed that the material world (and hence, the flesh) was corrupt and bad.  If Jesus was indeed a savior, he could not have come in the flesh but only in the form of an immaterial spirit.  This teaching was resolutely rejected by the Church.  Christ was born of woman into flesh and blood.  When he rose he swung his legs off the slab and walked out of the tomb.  Why else was it necessary to roll away the stone? 

There is a lot to chew on here.  All the major churches teach the resurrection of the body, which acknowledges that human being is unthinkable apart from human bodies.  This view rather literally redeems the flesh.  I suggest, however, that Christian culture has not entirely escaped the Gnostic infection.  There remains a tendency to see the flesh and more the material components of flesh as low and ugly.  This explains the fact that today, most American Christians seem to be thorough going substance dualists.  They imagine, against church doctrine, that the spirit is altogether distinct from the flesh and floats away from it at death toward heaven or hell.  The resurrection of the body is largely forgotten in this gospel of Walt Disney. 

I suspect that it is a lingering Gnosticism in Christian culture that is offended by Darwinism.  From this point of view, if living organisms, including human beings, emerge by natural processes from inorganic matter, then life is corrupt beyond redemption. 

There is an alternative view.  If the world is God’s creation, then every part of it, down to the smallest particle, has God’s design in it.  The philosopher Hans Jonas argued that Darwinism was in fact the antithesis of materialism.  It means that life, mind, and spirit are potentially present even the most inert physical materials.  This is evident in every living human being, for living persons are made of living organs which are made of living cells which are made of dead molecules.  The resurrection of the dead is not something that happens (perhaps not only) on some coming day.  It happens at every breath. 

I do not take sides in the quarrel between religion and Darwinism because I think that the quarrel arises from a mistake.  The quarrel will subside when we learn to take a more generous view of the natural world.  Nothing in it is irredeemable. 

Four Thoughts on Free Will

I am lecturing on free will this week.  This is one topic that is logically well organized in the history of modern philosophy.  There are two fundamental questions: are human choices determined by the past, and can human beings be morally responsible for their choices?  These give rise to four possible positions. 

Hard Determinism.  This position may be described by the following argument:

1.       If human choices are determined by the state of the Kosmos (D) prior to those choices, then free will is impossible (~F). 

2.      D. 

3.      Therefore: ~F. 

That is a straight forward modus ponens argument, and so it is valid.  If you do not want to accept the conclusion, then you have to reject one of the two premises.  Here F can be understood as metaphysical freedom (uncaused action) or moral freedom (an action for which the actor is morally responsible).  The hard determinist rejects both kinds of freedom. 

The strength of this view is that it preserves the principle of the uniformity of nature, if that principle implies determinism as many thinkers suppose. 

Libertarianism.  This position may be defined by a modus tollens which begins with the same premise:

1.       If human choices are determined by the state of the Kosmos (D) prior to those choices, then free will is impossible (~F). 

2.      F. 

3.      Therefore: ~D.

Again, this is a valid argument.  As hard determinists boldly state D, libertarians boldly state F.  Libertarians conclude that determinism is false, at least as applied to human beings, who they believe to be agents capable of uncaused action. 

The strength of libertarianism is that it preserves our common sense experience of choosing.  My sense of having choices is as vivid as my sense that the world is solid underneath my feet. 

Because they share premise 1, the two positions are both called incompatibilist.  Hard Determinism and Libertarianism both regard determinism and free will to be incompatible. 

Compatibilism.  The third view, perhaps the dominate one in philosophy, rejects premise 1 above and may be expressed in a simpler argument. 

1.       F and D. 

2.      Therefore F.

3.      Therefore D. 

Again that is valid, if tautological.  Compatibilists believe that free will is not only logically compatible with determinism, but that it actually requires it.  Why do we praise a person as good because of her good actions if not because her good character determined those actions?  It is likewise with blameworthy actions. 

Compatibilists think that hard determinists and libertarians are focusing on the wrong things.  Am I free to leave the room I am sitting in?  To answer that question we don’t need to ask whether my decision to leave is determined by the state of the cells in my brain prior to my decision.  We need to ask whether the door is locked or not, or whether I know that someone is waiting outside to do me harm. 

Human actions are free, in this view, if at least two conditions are met:

1.       The agent is not compelled to act or not act (either by physical constraints or compelling threats) and

2.      If the agent had acted otherwise, she would have done otherwise. 

I suspect that condition one is contained in condition two.  The question is not whether my choices are caused by prior states of the Kosmos (they are, according to the compatibilist) but whether my choices are causes of my actions.  To the extent that the latter is true, I am free.

The strength of Compatibilism is that it saves moral responsibility by immunizing the same against determinism.  Why do we seem largely agree to hold sane people responsible for the crimes that they commit while holding that insane people are not responsible?  This is because sane people respond in more or less predictable ways to moral sanctions.  They understand that they will be punished for infractions and so are less likely to commit them.  Insane people are incapable of a rational response to such sanctions.  Precisely because sane people are more or less responsive to legal sanctions (along with moral opprobrium) such moral sanctions make sense.  There is no point in applying them to a full tilt loon. 

It occurs to me, however, that there is a fourth position.  This is in fact my position.  This position is compatibilist in so far as it denies that determinism and free will are incompatible.  I think that what matters is that my choice determine my action, regardless of whether my choice is determined by the past.  In that respect, I agree with the compatibilists. 

However, I don’t see any reason to accept determinism.  No reasonable person would deny that the past influences the future.  If yesterday you offered me a lot of money to write an essay, I am more likely to write it today.  However, influenced and determined are never the same.  If X influences Y in a very robust way, then Y is predictable from X.  That is the kind of relationship that science mines.  It is enough to calculate the influence.  Does X result in Y 99% of the time?  That is a robust finding.  Science rarely if ever gets to %100.  All or almost all science is probabilistic rather than determinist. 

It is common to assume that this is because of limits on the data or apparatus.  We can only measure anything to within some margin of error.  But why assume that?  The assumption is unnecessary.  This state of X makes the subsequent state of X more or less probable.  That is the best we can ever do. 

Determinism is one of the great myths of modern science.  It is an attractive idea, useful to some degree in thought, and altogether unfounded in reality.