Thomas Reid's theory of ideas

Friend and philosophy professor David Potts (City College of San Francisco) published Thomas Reid and the Theory of Ideas. Potts credits Reid's attributing intentionality to our ideas and criticisms of the Empiricist or representational views of John Locke, David Human, and George Berkeley.

I would need to read Thomas Reid's and John Locke's works again more closely to opine more, but I believe I would portray Locke's theory somewhat more favorably than David Potts and Thomas Reid did.

A posteriori and a priori #1

Frankenstein is the 1818 novel written by English author Mary Shelley that tells the story of Victor Frankenstein, a young scientist who creates a hideous sapient creature in an unorthodox scientific experiment. The monster has some, but not all, ordinary human characteristics.

The nature of the human mind according to the German philosopher Immanuel Kant has some parallels to the nature of Frankenstein’s monster. The cognitive aspect of mind Kant depicts as human is not an ordinary human mind. This is so regarding Kant’s a posteriori – a priori distinction. A priori and a posteriori ('from the earlier' and 'from the later', respectively) are Latin phrases used in philosophy to identify two types of knowledge, justification, or argument, characterized by the use of empirical evidence found in experience (a posteriori) or the lack thereof (a priori).

If Kant had kept closer to the Latin meaning of a priori, his theory of cognition would have differed. However, this is not how he made his distinction – nor is it -- twofold. According to Kant human a posteriori cognition is empirical, based on the content of experience. His distinction is threefold. Kant held that a priori knowledge is not entirely independent of the content of experience. However, he held that a priori cognition, in its pure form, that is without the admixture of any empirical content, is limited to the deduction of the conditions of possible experience. These pure a priori, or transcendental conditions, are seated in one's cognitive faculties, and are not provided by experience in general or any experience in particular (although an argument exists that a priori intuitions can be "triggered" by experience).

The reproductive and productive imagination that Kant discussed in his Critique of Pure Reason produce determinate (rule-governed) judgments. Kant's thoughts on the creative imagination, which produces indeterminate (non-rule-governed) judgments, as set down in his Critique of Judgment.

Judgment in general is the ability to think the particular as contained under the universal. If the universal (the rule, principle, law) is given, then judgment, which subsumes the particular under it, is determinative (even though [in its role] as transcendental judgment it states a priori the conditions that must be met for subsumption under the universal to be possible). But if only the particular is given and judgment has to find the general for it, then this power is merely reflective.(Critique of Judgment, 179).

Reflective judgments "do not constitute acts of knowledge, since they do not involve the determinate structuring of a field of representations according to a definite concept. Reflection is an imaginative activity in which the mind 'plays over' various representations (percepts, images, concepts) in search of possible ways that they might be organized, although this process is free from the control of the understanding (which is the faculty that supplies concepts)" (Johnson 1987,158).

In reflective judgment, there is no previous, given concept that is automatically applied to experience. This ability to generate new concepts and new organization in our experience is not guided by any concept that guarantees success, but it results in novel ideas that can make sense (Jetton 1991).

I don’t consider this very problematic. Kant’s pure a priori is the problem.

For the following I retain the Latin meanings. A posteriori means experienced, i.e. retrospective. A priori means prospective and experimental. The distinction will not be limited like Kant’s to knowledge, justification, or argument. It will be about cognition more widely, including what Kant called imagination or reflective judgment.

Consider trying to do some action X that you have done very successfully in your past experience. You wish to perform a future action that ist very similar to X under present, similar conditions. You consider how action X could be modified to X* to better fit the partly different present conditions. In other words, X is known a posteriori and X* is largely a posteriori but also partly a priori.

Another useful distinction is between identical – with exceptions for time and location – and similar. ‘Similar’ means identical in some respects but not all. Of course, there are degrees of similarity.

That is a very abstract thesis. One or more future posts will be more concrete.

References

https://en.wikipedia.org/wiki/A_priori_and_a_posteriori#Immanuel_Kant

Jetton, M. 1991. Imagination and Cognition. Objectivity 1.3. Online: http://objectivity-archive.com/volume1_number3.html#57

Kant, I. 1987 [1790]. Critique of Judgment. W.S. Pluhar, translator. Indianapolis: Hackett Publishing.

Teen: "Math isn't real" Revisited

Three months ago I commented on a teenager who made a video saying “Math isn’t real.” Link. The video went viral. She also said the math she learned in school is real. She was obviously confused and naive. She asked three related questions: 

1. How did people come up with algebraic formulas?
2. How did they know what they were looking for?
3. How did they know they were correct?

I gave answers to them then. However, yesterday something else occurred to me about the second question. Why did she assume one has to know what one is looking for in order to find it?

Maybe it is partly her age and experience. Being a teenager, searching on the Internet became a common activity before she was born. She likely does it a lot. For that activity, one does need to be aware of what one is looking for in order to find it. Sometimes when one is looking for something quite specific, one has to already be aware of exactly what one is looking for. Else the search engine returns can overwhelm what one is looking for. What you are looking for will be buried deep in the stack and thus hard to find. Whereas using optimal search terms will put what you are looking for at the top of the stack or close thereto.

I learned that when I did a search about myself and something specific. What I was looking for was very local news. Hence, it was reported in only one not widely read publication. Searching only for my name on Google, there were 1500 hits. That's with a very unique name (first and last together). What I was looking for was well below the middle of the stack. Searching for my name and two more terms, what I was looking for was on top of the stack. Imagine the more general search had millions of hits.  

This may seem like an insignificant point. However, it is more significant from a philosophical perspective. It is an aspect of Empiricism. Experience shapes and limits knowledge.

My first two JARS articles

My first two articles published in The Journal of Ayn Rand Studies can be read online free at JSTOR.org. Reading them requires being registered there, but registration is free. Reading newer articles requires payment somehow, but these articles are old enough to be read for free. (This is based on my personal experience. Somebody else's might differ.) 

Both articles are about epistemology, more specifically the nature of concepts.

Omissions and Measurement (2006)    https://www.jstor.org/stable/41560320
The Sim-Dif Model and Comparison (2011)   https://www.jstor.org/stable/41560412 

The Primary-Secondary Quality Distinction

This is another article (very lightly edited here) I wrote and posted on the Internet in 2009.

In the Appendix of the second edition of Introduction to Objectivist Epistemology Ayn Rand says the primary-secondary quality distinction (PSQD) is invalid. “The primary-secondary quality distinction is a long philosophical tradition which I deny totally. Because there isn't a single aspect, including length or spatial extension, which is perceived by us without means of perception. Everything we perceive is perceived by some means.” 

Of course, everything we perceive is perceived by some means, but the famous supporters of the PSQD, like Galileo Galilei and John Locke, did not deny this. Rand’s argument was against a straw man. 

Primary qualities are those of objects regarded as independent of any observer, such as solidity, extension, motion, number and figure (shape). They exist in the object self-contained and do not rely upon anything external. Secondary qualities are those that produce sensations in observers, such as color, taste, smell, and sound. A sensation or perception can differ due to different perceptual systems, e.g. color-blindness versus normal color vision, or what is external to the object, e.g. light conditions. The powers an object has to produce sensations in us depend on its primary qualities (John Locke, ECHU, II, VIII, 10). 

Rand says, “The primary-secondary distinction in fact starts from the idea that that which we perceive by some specific means is somehow not objective.” I disagree if “not objective” was intended to mean “subjective” in her vocabulary.  Using her intrinsic-objective-subjective trichotomy, the PSQD says that primary qualities are intrinsic rather than objective. Secondary qualities are objective in this regard. Indeed, next she says: “Now you can properly distinguish that which is in the object from the form in which you perceive that quality. But that isn't the same thing as saying color is a secondary quality but extension is a primary quality.” I agree it isn’t the “same thing”, but such distinguishing is what the PSQD does. 

In Objectivism: The Philosophy of Ayn Rand Leonard Peikoff says the dominant view by philosophers gives only two possibilities in regard to sensory qualities: they are "in the object" or "in the mind." The former is taken to mean qualities independent of man's means of perception; the latter is taken to mean "subjective and/or unreal." Why he says this view is dominant is beyond me, and it isn’t the case for the major supporters. More accurately, the PSQD does not say secondary qualities are solely "in the mind", but that they are not solely “in the object.” 

Locke went on to say that our ideas of primary qualities resemble those qualities as they are in an object, but that is not true of our ideas of secondary qualities. He stated this as a conclusion without further explanation (ECHU II, VIII, 9). He did not use what I regard as a strong argument for the PSQD.  That is the nature of our various senses, something Aristotle noted long ago. According to Aristotle the “common sensibles” are motion, rest, shape, magnitude, number, and unity (De Anima III.1 425a16). (Different translations might use slightly different terms here.) They are apprehended by more than one sense – sight and touch. For example, extension and roundness can be perceived by both sight and touch. What Aristotle called the “special perceptibles” were those grasped by one sense only, e.g. warmth, color, taste, smell and sound. Aristotle did not make the PSQD. He treated all qualities of an object or body as belonging solely to the object or body. However, he gave one of the means to do it. 

Another argument in favor of the PSQD is that primary qualities are measurable or countable, but secondary qualities are not. Measuring decibels or sound wave frequency or amplitude is not measuring the sensation of sound. Measuring light wave frequency or amplitude is not measuring the sensation of color. 

In The Evidence of the Senses David Kelley makes a PSQD, but not in the same manner and for the same reasons as Locke did.  Kelley says primary qualities are macroscopic and extensive, while secondary qualities are microscopic and intensive (p. 114-15, hb). This macroscopic-microscopic difference is not about the qualities of an object intrinsically; it is about our knowledge. Primary qualities as physical attributes exist at the microscopic level, too. “[W]e find that certain dimensions can be explained by reference to the macroscopic attributes of objects. With other dimensions, however, we cannot find the intrinsic feature of the object itself, to which the senses are responding, unless we proceed to the microscopic level” (p. 116).  It may be a bit clearer to the reader to substitute “features” for “dimensions.”  

"The perception of size, shape, position, motion, and number seems to require enough perceptual integration to isolate as units the objects which possess these attributes.  …  Thus it seems that the awareness of secondary qualities first occurs at the level of sensations, but the awareness of primary qualities require the perceptual level and necessarily includes some awareness of secondary qualities" (p. 113) “Moreover, since the primary qualities are macroscopic, it is easy to measure them as they are apart from the forms in which we perceive them” (p. 117).  

Kelley also makes an intrinsic–relational distinction between primary and secondary qualities (p. 110, 111, 117, 231). At times Rand described the relationship of consciousness to existence as “objective.”  

Aristotle on the Common Sense

The following is an article (very lightly edited here) that I wrote and put on the Internet in 2009. I wrote it while reading the book Aristotle on the Common Sense. I later wrote a review of the book for Amazon here. 

The book's introduction outlines the basic issue. Plato gives his position in his dialogue Thaeatetus. Each kind of sense -- vision, touch, taste, hearing, smell -- is autonomous. Something contains the senses, but cannot use them. Having the senses and being able to use them is another part of being an animal, which includes other capacities and a suitable body. To perceive by means of the eyes suggests there is a subject that uses the sense of sight localized in the eyes. Plato calls this subject 'soul', where each of the senses converge. The soul can integrate the senses and use the result. The soul uses the senses primarily to receive impressions of the basic sensory qualities. Also, the soul applies 'sameness' and 'difference' to sensory qualities. Such coordination of the senses seems to involve thinking. In Plato's view the senses are not integrated at the level of perception, but at the level of thought. It is compatible with Plato's wider philosophy to dissociate knowledge from perception.

When later Aristotle considers perception, he tries to give an account of nonhuman animals as well. The often very complex behavior of animals might be explained on Plato's framework, provided one attributes some level of thought to nonhuman animals. It seems Aristotle would not, that his position was that nonhuman animals cannot think or form opinions. An animal's survival depends on the ability to differentiate and associate sensible qualities (e.g. cold and hard versus soft and warm, smell and taste). The animal seems to apply 'same' and 'different' to them. Aristotle agreed with Plato that integration occurs and the subject is able to use the result, but he disagreed about where or how. Per Aristotle the senses are not integrated at the same level as thinking, but by what he calls the 'common sense'. He wrote very little about it, but held such integration to be perceptual. It could thus be attributed to nonhuman animals.

An interesting aside is where each philosopher believed sensory integration to occur. Plato thought it was the brain, where he believed the rational soul was (in his dialogue Timaeus). Aristotle located the common sense to be in the heart. We can discount both views given the paucity of knowledge about anatomy when they lived, but it is fascinating to see Aristotle rationalize his position.

According to Aristotle the 'common sensibles', or 'common perceptibles', are motion, rest, shape, magnitude, number, and unity (De Anima III.1 425a16). (Different translations might use slightly different terms here.) Common perceptibles are those apprehended by more than one sense. For example, extension is perceived by both touch and sight. Would the reader consider time a common perceptible? What Aristotle called the 'special perceptibles' were those attributable to one sense only, e.g. warmth, color, taste, smell and sound.

This concludes my presenting the views of Plato and Aristotle. What does Ayn Rand say about this? It did not surprise me that her view better aligns with Aristotle. However, she said so little about it. "A percept is a group of sensations automatically retained and integrated by the brain of a living organism. It is in the form of percepts that man grasps the evidence of his senses and apprehends reality" (ITOE2, p. 5). "Similarity is grasped perceptually" (p. 14). That is about all -- various sensory data is automatically integrated into percepts. Her published works barely reach beyond that. We could add that her view of thinking and consciousness being under volitional control buttresses her view that perceptual integration is automatic.

To some extent our sensory apparatus is under volitional control. For example, we can choose where to look or direct our attention to specific sounds. This, of course, raises the question of volition in nonhuman animals, a topic on which I venture no further here.

To conclude I present this short essay as food for thought. Often in philosophy more questions are raised than can be answered. This is a hazard of philosophy. On the other hand, such food is the nourishment of the soul.

The Knowledge Illusion #7

Continuing about The Knowledge Illusion:

To run a company or any organization, a team with complementary skills is most likely to satisfy all the demands made by the division of cognitive labor.

As individuals, we know little. There's not too much we can do about that; there's too much to know. Obviously we can learn some facts and theories, and we can develop skills. But we also have to learn how to make use of others' knowledge and skills.

The idea that education is for increasing intellectual independence is not entirely correct. That idea isn't wrong so much as incomplete. It ignores the fact that knowledge depends on others. For example, a car mechanic relies on others for parts, diagnostic tools made by others, maybe co-workers, and manuals. 

Science is about justification, which comes in various forms. But most conclusions in science aren't based on either observation or inference. They are based on authority, on what is written in a textbook or journal or what your expert friend tells you. That's one role of the community of knowledge, to supply facts when direct justifications would take too much time or be too costly or difficult. Everyone's understanding is dependent on what others know.

But we shouldn't take faith in whatever a community believes or whatever a credentialed expert says. We should have enough skepticism and a keen eye for charlatans and those who are confidently wrong.

This is my final post about The Knowledge Illusion.

The Knowledge Illusion #6

Continuing about The Knowledge Illusion:

Chapter 9 is Thinking About Politics.

A community of knowledge can become dangerous. When a group of people don't know much but share a position, the members reinforce one another's sense of understanding, even when there is no real expertise to give it solid support. Group-think diminishes independent thinking and political opposition through propaganda and even terror.

The authors did experiments exploring people's understanding of specific political positions. With few exceptions, the subjects had little to say when asked to explain how a policy worked, its mechanics. Usually when people talk about political policies, they are not engaged in causal thinking. Causal explanations may be hard; they require people to go outside their belief systems. You can't consider the implications of a policy by ruminating on how you feel about it.

When subjects in experiments were asked about their feelings, they didn't change their positions. When the subjects were asked for causal explanations, they better appreciated the shallowness of their understanding.

Proponents of political positions often cast policies in value-based terms in order to hide their ignorance, prevent moderation of opinion, and block compromise. An example is health care. The debate shouldn't be about basic values, because to most people they aren't the issue. The issue is the best way to achieve the best outcomes.

Ballot measures voted on directly by citizens can bypass politicians in power, but neglect the knowledge illusion. Individual citizens rarely know enough to make an informed decision about complex social policy issues even when they think they do.

The Knowledge Illusion #5

Continuing about The Knowledge Illusion:

Like it or not, the Internet has become a major player in our lives. It is our main source of information, a centerpiece in our community of knowledge. Technology is quickly transforming our lives. Humans are made for technological change. Our bodies and brains are designed to incorporate new tools into our activities as if they were extensions of our bodies.

There are some worrisome consequences. The Internet's store of knowledge is so accessible and vast that we may be fashioning a society where everyone with a smartphone and Wi-Fi connection becomes a self-appointed expert in multiple domains.

But notice what these machines don't do. They do not have intentions and hence do not share intentions with us the way people share intentions. Machines without the basic human ability to share attention and goals will never be able to read our minds and outsmart us because they won't even be able to understand us.

A chapter on science describes how the average person knows so little compared to the experts. Example topics given are (1) genetic engineering, and (2) bacteria, viruses, and antibiotics. What is actually in our heads -- our causal models -- are sparse and often wrong.

The Knowledge Illusion #4

Continuing about The Knowledge Illusion:

In nature we often see complex behavior arise through the coordination of multiple individuals. When multiple cognitive systems work together, group intelligence can emerge that goes beyond what each individual is capable of. The authors give a beehive as an example. Wolves in packs and lions in a pride after prey are others. Historically hunting was a communal enterprise requiring a level of cooperation unique to humans. Consider the variety of trades that participate in building a home.

Living in a group also demands certain cognitive abilities. It requires the ability to communicate in sophisticated ways, to understand and incorporate the perspectives of others, and to share common goals. Humans have an ability that no machine or other animal does. They can share their attention with someone else. Russian psychologist Lev Vygotsky made pioneering insights into the idea of a community of knowledge.

There is teamwork in many human efforts, such as the medical health professions. People tend to remember what they have to within a particular community to best make their contribution to the division of cognitive labor. They rely on experts to remember everything else. In a community of knowledge, what matters more than having ready knowledge is having access to knowledge.

The Knowledge Illusion #3

Continuing about The Knowledge Illusion:

Causal reasoning serves as an infrastructure of thought, but that doesn't mean people are ideal causal reasoners. We shouldn't berate ourselves for not being ideal. Think about what it would take to make correct causal inferences in every situation, even unfamiliar ones. People do excel at causal reasoning, but tend to do it superficially outside their expertise.

The decisions we come to quickly and intuitively aren't the same as those we come to through careful deliberation. Intuition gives us a simplified, coarse, and usually good enough analysis, and gives us the illusion that we know a fair amount. But when we deliberate, we come to appreciate how complex things really are, and this reveals how little we really know.

Reasoning isn't limited to the brain. Our bodies support it. The authors use the example of a baseball player catching a fly ball. The trajectory of a ball can be calculated with mathematical equations, but the player doesn't do that (and hasn't enough time to). External aids support reasoning, too. Example are doing arithmetic on a chalkboard and writing things down to help develop and fine-tune one's thoughts.

The Knowledge Illusion #2

Chapter 1 of The Knowledge Illusion is titled What We Know. To illustrate how we can believe we know more than we actually do, the authors describe experiments in which people tried to draw a bicycle. Some couldn't draw the pedals and chains correctly.

Deliberation is only a tiny part of what goes on when we think. Most of cognition consists of intuitive thought that occurs below the surface of consciousness.

Chapters 2 and 3 are about why and how we think. We mainly think in order to act. Just as people don't think only by association, people do not always reason via logical deduction. We think about how causes produce effects, what kinds of things disable or prevent effects, and what factors must be in place for causes to have their influence. Rather than thinking in terms of propositional logic, which tells us whether a statement is true or false, people think in terms of causal logic, which incorporates knowledge about how events actually come about in order to reach conclusions. Sometimes people ignore alternative causes when thinking about cause and effect because their mental simulations have no room for them.

Stories may be communal entities, but telling them requires that individuals possess a cognitive system that's up to the task. The cognitive system's ability to represent and reason about causal systems is limited, and we can't as individuals deal with all the complexity of the world. This is surely why stories tend to simplify and sometimes oversimplify events.

The Knowledge Illusion #1

I read this book. “Don’t judge a book by its cover” is relevant. It doesn’t claim that all knowledge is illusory. The subtitle doesn’t mean we cannot think alone. It may sound wrong to some people, since in some sense we always think alone. That is, nobody can think for me is analogous to nobody else can digest the food I swallow. Adding to the analogy, we assimilate knowledge and ideas produced by other people similar to eating food produced by other people.

The rest of this post will be from the Introduction and provides an overview of the book.

“The human mind is not like a desktop computer, designed to hold reams of information. The mind is a flexible problem solver that evolved to extract only the most useful information to guide decisions in new situations. As a consequence, individuals store very little detailed information about the world in their heads. ... To function, individuals rely not only on knowledge stored within their skulls but also knowledge stored elsewhere: in our bodies, in the environment, and especially in other people. When you put it all together, human thought is incredibly impressive. But it is a product of a community, not of any individual alone.”

“Our point is not that people are ignorant. It’s that people are more ignorant than they think they are. We all suffer, to a greater or lesser extent, from an illusion that we understand how things work when in fact our understanding is meager.”

We all have domains in which we are experts, but in most subjects we only abstract bits of information, and what we know is little more that a feeling of understanding we can’t really unpack. While the function of thought might have evolved to represent the world, it could also be to communicate, for problem-solving or decision-making. The authors’ thesis is that thought is for action.

“Because we think communally, we tend to operate in teams. This means that the contributions we make as individuals depend more on our ability to work with others than on our individual mental horsepower.” Examples are a space vehicle launch and a large, complex business.

Blanshard on Implication and Necessity #5

This post is less about what Blanshard says in his book than the earlier ones and my last in this series.

Blanshard's critique is excellent. Still, I wonder why he did not say something like: Why are two of the rows in the truth table, when p is F in post #1, even relevant? To wit, what logical truth is implied by '7 < 4' or 'the moon is made of cheese'?

Subsequent to the problems with "material implication" logic being noticed and acknowledged, relevance logic arose. It was proposed before Blanshard’s book was first published in 1939. However, it didn’t become prominent until the 1970s.

Blanshard on Implication and Necessity #4

Blanshard next summarizes his critique. But what does “necessity” mean?

“It means, replies the empiricist, only that certain parts have been presented together with such unfailing regularity that we have become unable to dissociate them. … Formalism we have found more plausible. It admits the element of necessity that empiricism denies; its peculiarity is that it confines the necessity within certain highly general forms. … As for symbolic logic, we found it [ ] less helpful than the older logic, primarily because with its decision to ignore intension, it had abandoned interest in necessity. Of its three principal ways of conceiving implication, material, formal, and strict, we recognized an advance over the others, but could find in none of them a definition that would cover, even approximately, the necessity actually used in inference and understanding. We are left with this conclusions; necessity is not a habit, induced in us by an inexplicable regularity of presentation. Necessity is not a form or skeleton which, while sustaining the fleshy matter of the world, is sharply distinct from it” (397-8).

Blanshard’s use of “empiricist” clearly includes Hume, Mill, and other later philosophers. He references Hume and Mill. He doesn’t reference Locke, and I believe it would be unfair to include John Locke, the leading empiricist, among those whom Blanshard critiques. Locke wrote about habit and ideas by association (in ECHU), but he is not mentioned in The Nature of Thought, Volume 2, nor did he reduce all inference to habit like Hume did.

Blanshard on Implication and Necessity #3

This post is about Mr. Blanshard’s critique of strict implication as posited by C. I. Lewis.

Professor Lewis “would agree that when p implies q materially or formally this gives no assurance that q is deducible from p, nor does it give us what we usually mean by implication. He believes that his own system of ‘strict implication’ gives us both. This relation he defines as follows (the symbol stands for ‘strictly implies’ and  for ‘possible’ or ‘self-consistent’): p  q. = .   (p  q); that is, ‘ “p strictly implies q” is to mean “It is false that it is possible that p should be true and q false” or “The statement ‘p is true and q false’ is not self-consistent.” When q is deducible from p, to say “p is true and q is false” is to assert, implicitly, a contradiction” (385).

Note: is not the symbol in Blanshard’s book, but I couldn’t find how to use his and is often used to mean imply.

“There is no doubt that this sense of ‘implies’ is far nearer to the ordinary meaning than the previous senses. It no longer asks us to say anything so alien to common usage as that every true proposition implies every other, or that every false proposition implies all conceivable propositions; it is far more critical and selective” (385)

“Take an instance. ‘If anything is red, then it is extended.’ This, I think, is a fair example of implication in an ordinary sense. Now when we say that anything’s being red implies that it is extended, it is our meaning this, that if we denied that it was extended we whould also have to deny that it was red? I do not think so. I agree, of course, that when p implies q, to deny q does commit us to denying p also; I agree that in such a case to affirm p and deny q would be inconsistent. … When I say that p implies q, I am saying that a certain relation holds between them. The inability to insert not-q consistently instead of q is not the same as that relation, but something that holds in virtue of it” (386-7).

Blanshard on Implication and Necessity #2

This post is about Mr. Blanshard’s critique of formal implication.

“We turn, then, to formal implication. Our hopes rise as we do, for Mr. [Bertrand] Russell describes it as ‘a much more familiar notion’ which as a rule is really in mind even when material implication is mentioned. But these hopes sink again as we learn what formal implication means. ‘Formal implication is a class of material implications; it asserts that in every case of a certain set of cases material implication holds. … In the statement ‘Socrates is a man implies Socrates is mortal’ we have the expression of a material implication. In the statement ‘If anything is a man then it is mortal’ we have the expression of a formal implication …”

“Now as an account of necessity do we find here any advance? Certainly not so far as concerns the items summarized. Each statement of  a implying  a,  b implying  b, etc., is merely a factual statement that  a and  a (the truth of  a and the falsity of  a), etc. do not occur together. And we have seen there is no necessity there. Does it appear then in review by which we take in all the items as a glance? No again. If the connection of p with q in some one case falls short of being necessary, that same connection does not become so merely holding in all cases.”

“We begin to see, then, in what such logic involves us. It cuts us off altogether from the knowledge of universal truth” (381-2).

“The ignoring of necessity on the part of what is offered as logic, where if anywhere one would expect to find necessary connection, is a legitimate ground of dissatisfaction with the newer logistic disciplines … Stripped of its symbolism and regarded in bare logical essentials, this is the well worn atomism of Hume and Mill. There are no necessary propositions, only statements of class inclusion. There are no necessary inferences; what look like these are statement of exceptionless conjunction” (383).

“When he [the formalist] says ‘triangles have internal angles equal to 180 degrees’, does he mean ‘no triangles do in fact lack this characteristic'? If this is all he means, he has no reason to be surprised if he finds a triangle tomorrow with half or twice that number; there never was any must in the case; the new fact is merely one to be noted, and added to his collection. … Indeed extensional logic has here reversed the true order of priority; it is only because we have a prior insight into the nature of the triangle and what this nature involves that we can be so sure about particular cases. When we say a implies b, we surely mean that a in virtue of being a rather than c or d, implies b; the implication is bound up with intension. And we are clear that in the intension or content upon which thought is directed, we find connections far more intimate than the de facto togetherness to which material and formal implication are both restricted.” (384-5).

Blanshard on Implication and Necessity #1

In The Nature of Thought, Volume 2, chapter XXIX, Brand Blanshard critiques modern logic. He addresses three versions of ‘p implies q’ – material, formal, and strict. This post will be about the first of these. If the reader gets the notion that Blanshard made a straw man, see Wikipedia’s article strict conditional.

Take two propositions at random, p and q. There are 4 possible combinations of their being true or false. What that means for ‘p implies q’ (p → q) in a modern logic truth table is as follows.

          p    q    p → q

          T    T       T

          F    T       T

          F    F       T

          T    F       F

“Now in the usage of the formal logicians one proposition is said to imply the other materially when any one of the first three possibilities holds” (375). That is, when p → q is T. If the two propositions are both true, then they imply each other, even if one of them is ‘snow is cold’ and the other ‘grass is green’. That’s because we could assign either to p and the other to q.

“If two propositions are both false, again they imply each other, regardless of what they assert; ‘Darwin discovered gravitation’ implies ‘Benedict Arnold wrote Jerusalem Delivered. Finally, if the first proposition is false and the second true, once more the first implies the second; ‘Darwin discovered gravitation’ implies that Roosevelt was re-elected in 1936. It will be noted that our false proposition about Darwin has been used twice and that it implies not only every false proposition that can be made, but all true propositions as well; ‘a false proposition implies all propositions’. In sum: p always implies q except when p is true and q is false.”

“What are we to say of implication so defined? Does it describe or define the element of necessity we are seeking? On the contrary, necessity does not enter into it at all.”

“We shall see this more clearly if we ask whether it provides a basis for inference. For it will be admitted that in inference, if anywhere, we are generally using necessity, and that any satisfactory account of necessity must accord with the use we make of it there. Now it is plain that in the actual work of inference we constantly succeed in passing from one proposition to another without knowing the second independently. What sort of relation must hold between them to make this possible? It must be one in which the second is a consequence of the first. Mr. [Bertrand] Russell writes, as we have seen, ‘in order that one proposition may be inferred from another, it is necessary that the two should have that relation which makes the one a consequence of the other’ (375-6).

The logician “would admit that in the proposition ‘snow is cold’ there is not the slightest hint that grass is green, but would add that that is quite irrelevant to whether one implies the other” (376).

“A logic whose propositions are bound together only by this sort of implication is a logic in which, strictly speaking, nothing follows from anything else” (377). “Material implication itself is not, we have seen, a necessary relation” (379).