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# What is the Objectivist explanation of how we know modus ponens?

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Modus ponens is, of course, the following pattern of inference:

1. If p, then q.
2. p.
3. Therefore, q.

What is the Objectivist position on how we come to know this inference rule?

"The Objectivist position" here can mean either the position taken by Rand or the position taken by an Objectivist intellectual. I am pretty sure Rand never addressed this in the official Objectivist literature.

Edited by William O

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Are you talking about conceptualization, rules of logic, or observing reality?

Not sure what you mean by your p's and q's....

If 1. is taken as true, and p and q are statements then  1. means "p implies q"

2. and 3. together are a kind of restatement of what "p implies q" means.

so...

Also, not sure what you mean by "come to know" this as a "rule"...

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1 minute ago, StrictlyLogical said:

Are you talking about conceptualization, rules of logic, or observing reality?

Not sure what you mean by your p's and q's....

If 1. is taken as true, and p and q are statements then  1. means "p implies q"

2. and 3. together are a kind of restatement of what "p implies q" means.

so...

Also, not sure what you mean by "come to know" this as a "rule"...

Thanks for responding, it shows me what I need to clarify.

p and q are variables that represent propositions. I could also have used any lowercase letter (a, b, c..., y, z). For example, p could stand for "the streets are wet" and q for "it rained last night." I'm under the impression that this is standard in formal logic.

I agree that modus ponens is a valid form of deductive inference - if 1 and 2 are true for some value of p and q, then 3 is always true. My question is how we know that according to Objectivism.

Objectivism holds that all knowledge originates from perception, meaning that our knowledge of modus ponens has to arise from perception. In other words, there has to be some series of observations and inferences leading to the conclusion that modus ponens is valid. So I'm asking for a detailed description of that series of observations and inferences.

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The same way we know all rules of logic: by applying the law of identity. If the identity of p includes q, and we have p, then we must also have q. Otherwise, we've made a mistake in identification.

Edited by MisterSwig
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I see Mr. Swig answered, but I was also going to say what you are describing sounds exactly like how I understand the law of identity.

Edited by EC
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12 minutes ago, MisterSwig said:

The same way we know all rules of logic: by applying the law of identity. If the identity of p includes q, and we have p, then we must also have q. Otherwise, we've made a mistake in identification.

Thanks for responding. I have a couple of follow-up questions.

First, what does this explanation add to modus ponens? Why isn't it just a repetition of the rule?

Second, how do we know through observation that the law of identity holds universally?

I know my second follow-up question is a bit of digression. However, it's something that I've been wondering about in its own right, and answering it is technically necessary in order to derive the universality of modus ponens from the law of identity.

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5 minutes ago, William O said:

First﻿, what does﻿ this explanation add to modus﻿ ﻿ponens? Why isn't it just a repetition of the rule?﻿

All rules of logic are some sort of reiteration or application of the law of identity. I hope you'll (re-)read the Lexicon entry for "logic," to which I linked.

You stated: ﻿"Objectivism﻿ ﻿holds that all knowledge originates from perceptio﻿﻿﻿n..." But that is not the complete Objectivist position. We do not perceive the laws of logic. They come from "a process of reason based on perceptual observation." Modus ponens comes from a process of reason based on the law of identity. So let us ask, which observations convinced us that the law of identity was valid?

My simple answer is: all of them. Never have I observed something be itself and not itself.

39 minutes ago, William O said:

Second﻿, how do we know through observation that the law of identity holds universally﻿?﻿﻿

If you expect to know from observation whether identity is valid throughout the universe, then you absolutely will never know, because you, I assume, are not an all-seeing god. However, if you take up a process of reasoning based on real observations, you might reach a valid induction. But keep in mind that your knowledge is still contextual. If you ever encounter a violation of identity, you'll have to modify your knowledge. Until then, though, it will serve you poorly to take the arbitrary too seriously.

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I will ask what you mean by " how we come to know this inference rul﻿e", but specifically, are you asking about real acquisition of knowledge, that is, is this a cognitive and scientific question, or are you asking about abstract logical relations between concepts? If the former, I claim what "we" do not know this rule, though some of us do, and qua rule we mostly learn it – to the extent that we firmly learned it – in Logic 150. There are other rules of logic (modus tollens, modus ponendo tollens) which "follow from" the law of identity: they are consequences of, but not the same as, the law of identity.

Again, cognitively / developmentally, the law of identity is a very high level abstraction that generalizes over numerous specific laws. So I think it is important to distinguish how we learn, and what the resulting logical conclusio(s) are.

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2 minutes ago, MisterSwig said:

All rules of logic are some sort of reiteration or application of the law of identity. I hope you'll (re-)read the Lexicon entry for "logic," to which I linked.

You stated: ﻿"Objectivism﻿ ﻿holds that all knowledge originates from perceptio﻿﻿﻿n..." But that is not the complete Objectivist position. We do not perceive the laws of logic. They come from "a process of reason based on perceptual observation." Modus ponens comes from a process of reason based on the law of identity. So let us ask, which observations convinced us that the law of identity was valid?

My simple answer is: all of them. Never have I observed something be itself and not itself.

If you expect to know from observation whether identity is valid throughout the universe, then you absolutely will never know, because you, I assume, are not an all-seeing god. However, if you take up a process of reasoning based on real observations, you might reach a valid induction. But keep in mind that your knowledge is still contextual. If you ever encounter a violation of identity, you'll have to modify your knowledge. Until then, though, it will serve you poorly to take the arbitrary too seriously.

This is not the Objectivist position. More importantly, it does not work in its own right.

First, this isn't the Objectivist position:

"[An axiomatic concept] is the fundamentally given and directly perceived or experienced, which requires no proof or explanation, but on which all proofs and explanations rest."

Induction would be a form of "proof," which Rand denies is applicable to axioms above.

There is also a passage in OPAR where Peikoff explicitly denies that axioms are based on induction. I don't have OPAR with me, though.

Second, your explanation does not work in its own right because it is impossible to perform induction without presupposing the law of identity. The law of identity is presupposed in the process of concept formation that leads up to induction, since every concept is the concept of something with a determinate identity. The law of identity is also presupposed by the law of causality on which induction depends, since causality is a corollary of identity.

You also say that the law of identity is "contextually valid," which leads straight to skepticism since there is no rational way of delimiting the context of the law of identity. How would you ever know whether you were within the context? For example, if you're reasoning about cats, what would a cat that isn't a cat look like? Even if you did prove something - say, cats have kidneys - how would you know whether or not cats also lacked kidneys on that premise? And what if cats are cats today but not tomorrow?

You cannot prove anything without absolutely ruling out the possibility of a contradiction in reality ahead of time.

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8 minutes ago, DavidOdden said:

I will ask what you mean by " how we come to know this inference rul﻿e", but specifically, are you asking about real acquisition of knowledge, that is, is this a cognitive and scientific question, or are you asking about abstract logical relations between concepts? If the former, I claim what "we" do not know this rule, though some of us do, and qua rule we mostly learn it – to the extent that we firmly learned it – in Logic 150. There are other rules of logic (modus tollens, modus ponendo tollens) which "follow from" the law of identity: they are consequences of, but not the same as, the law of identity.

Again, cognitively / developmentally, the law of identity is a very high level abstraction that generalizes over numerous specific laws. So I think it is important to distinguish how we learn, and what the resulting logical conclusio(s) are.

Thanks for responding.

I attempted to explain what I meant by "how we come to know modus ponens" in an earlier post:

"Objectivism holds that all knowledge originates from perception, meaning that our knowledge of modus ponens has to arise from perception. In other words, there has to be some series of observations and inferences leading to the conclusion that modus ponens is valid. So I'm asking for a detailed description of that series of observations and inferences."

Another way of putting it is that I'm asking for a reduction of modus ponens to observation.

I think the derivation from the law of identity that MisterSwig gave earlier was pretty good, though.

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58 minutes ago, William O said:

Induction﻿ would be a form of "proof," which Rand denies is applicable to ﻿axioms above.﻿﻿

I'm talking about induction as a method of cognition, not proof. Even the axioms must be inferred from the facts of reality. You aren't born with such knowledge.

1 hour ago, William O said:

You﻿﻿ also ﻿say that the law of identity is "contextually valid," which ﻿leads straight ﻿to skepticism﻿ ﻿sinc﻿e ﻿﻿﻿﻿there is no rational way of delimiting﻿ the context of the law﻿ of identity﻿. Ho﻿w would ﻿you ever know wheth﻿er you were within the ﻿conte﻿x﻿﻿t﻿?﻿﻿ ﻿For ﻿example, if you're reasoning about cats, what would a﻿ ﻿cat that isn't a cat look ﻿like﻿?﻿﻿﻿

You are always within the context of your own knowledge. Like I said, don't be too concerned with the arbitrary. Cats that aren't cats don't exist.

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15 hours ago, William O said:

Modus ponens is, of course, the following pattern of inference:

1. If p, then q.
2. p.
3. Therefore, q.

What is the Objectivist position on how we come to know this inference rule?

"The Objectivist position" here can mean either the position taken by Rand or the position taken by an Objectivist intellectual. I am pretty sure Rand never addressed this in the official Objectivist literature.

As a side discussion, I don't think there is an answer exactly, Rand didn't do work on logic theory. Rand only wrote an introduction to her epistemology, we'd have to say her epistemology is incomplete, thus not everything can have "the Objectivist position on X." And we know from the schismatics, that they don't accept "a position taken by an Objectivist intellectual" to be the same thing as "Objectivism," right?

But I think this does have a possibility in textual interpretation of Rand's position in ITOE, specifically regards her theory of reference. Remember she wants a concept to mean all of its nature, whether known or unknown, and and that means all of its attributes and properties. If the major premise posits that "then Q" is an attribute of a P, then when the minor posits a P, it is the same as saying "here is a P, which includes all of its attributes and properties, one of which is 'then Q.'" Thus the conclusion "therefore Q" has a preserving or "containing within" all the attributes of P, such that if one believes the premises, it preserves all their attributes and properties, thus giving you a reason to believe the conclusion.

That is consistent with standard faire in classical logic, in which the conclusion "preserves" the truth of the premises, Rand would say it literally preserves the concepts contained in the premises. You are essentially applying what you already know to a new particular, or subsuming that new particular under a generalization that you already knew.

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For a thorough answer here we need to begin by explaining how we form the concepts "if" and "then".

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15 minutes ago, Doug Morris said:

For a thorough answer here we need to begin by explaining how we form the concepts "if" and "then".

Agreed and whether or not there is any valid conceptual difference between

p implies q

and

If p then q

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As Doug Morris says, we need to start by explaining how we form the concepts “if” and “then”. These are hard scientific questions about how children actually form concepts, but it is difficult to tell whether a child has actually formed a given concept at a particular time. Remember that adult concepts are not the same as child concepts (as Rand points out in ITOE). “Mama”, “dada” refer to individuals and are not concepts – they are the names of unique existents. But children can go through a phase of concept-formation where these are concepts (referring to adult family males, or females) and eventually de-conceptualize the words when they realize that “dada” in our culture doesn’t apply to the individuals “grandfather” or “uncle”. The child definition of “man” certainly does not involve knowing about a rational faculty.

Before we try to account for forming very high level logical concepts like “if” and “then” (meaning “therefore”, not meaning “at that time” or “subsequently”), we have to discover how children acquire their first logical concepts. The three most obvious to me are “concept”, “property” and “entity”. To be able to define “concept”, you have to have at the minimum the concept “entity” (the existents that can be perceived) and “property” (these entities have some defining property that sets them apart from those entities). If you have a concept “concept” as well as “property”, then you can form the concept “proposition” (the basis for forming the concept of “proposition” is actual propositions which are, in experience, statements about properties of an individual or concept). You can’t form a concept “if” if you don’t have a concept “proposition”. And so on.

I think the most that can be reasonably expected is making reasonable conjectures about how children might acquire higher-level knowledge, based on factual knowledge of what children actually do. Actually determining whether these conjectures are at least probably true is quite a tall order. As for the concept modus ponens, that is a concept that most adults do not have, and it is pretty clear that it is explicitly taught and not induced from examples (unless someone has finally figured out a lesson where people can actually induce modus ponens as distinct from modus tollens from examples). What we perceive is somebody saying or writing an explanation of the concept, and it’s similar to coming to know about “ion”, “valence”, “epistemology”.

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I am currently working on a theory which aims to show that the formal theory underlying the Objectivist process of concept formation is something very similar to Per Martin-Lof's Intuitionistic Type Theory.

If we understand Objectivist concepts as types, then a statement like A -> B says that there is a computable function which transforms any proof/construction of the concept/type A into a proof/construction of the concept/type B.

The rule of modus ponens is then simply function application. If f : A -> B, then the term

f a

, where a is a proof/construction of concept/type A, is a proof/construction of the concept/type B. Hence, from a proof of A and a proof of A -> B we derive a proof of B.

One could then argue that the rule of modus ponens is somehow inherent in any process of computation. This is just what it means for a concept to be "axiomatic" in Objectivist terminology.

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^^ I hate when people try to turn something that's relatively simple like concepts and concept formation, that can be stated and explained in simple english, into rationalistic nonsense. The rationalistic nonsense of most philosophies is the reason most people properly think that most of philosophy is complete nonsense only studied by idiots in universities that aren't intelligent enough to study a real subject. Please don't do this to Objectivism. It's the only philosophy that doesn't do this idiotic nonsense that pretends to be intelligent.

Edited by EC
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20 hours ago, SpookyKitty said:

I am﻿ ﻿currently﻿﻿ working on a theory which aims to show that the formal theory underlying the Objectivist process of concept formation is something﻿ very similar to Per﻿ Martin-﻿﻿Lo﻿﻿f﻿﻿'﻿s﻿ Intuitionistic Type Theory﻿.

Is that because Rand was also a huge fan of Kant?

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5 hours ago, EC said:

I hate when people try to turn something that's relatively simple like concepts and concept formation, that can be stated and explained in simple english, into rationalistic nonsense. The rationalistic nonsense of most philosophies is the reason most people properly think that most of philosophy is complete nonsense only studied by idiots in universities that aren't intelligent enough to study a real subject. ﻿Please don't do this to Objec﻿tivism﻿.

People who say this are usually people who didn't get past undergrad (or have animosity towards people who do get up to the PhD or graduate level). It's a kind of anti-intellectualism. Have you taken graduate courses in philosophy? Have you taken time to understand really complex philosophy, even if you didn't agree? I'm not trying to demean you here - I'm asking that you check your premises that you can and should badmouth people who dare to say something formally in philosophy as would be expected of people in universities who do philosophy of math or logic.

What SK is saying isn't really so scary in all. Oist epistemology is not simple or easy. Sometimes people think it might be, but this is because Rand only wrote an introduction. Adding some formalism doesn't destroy anything. If Oist epistemology can't survive some formal treatment, then it would be a trash epistemology. But the cool thing is that it can. Type theory is probably the absolute best avenue to follow to improve or fairly criticize Oist epistemology from a formal perspective. If you don't like philosophy from a very formal perspective (which this thread is about), that's fine. If you want to participate with it though, you should take the time to understand before criticizing. Rand was generally informal about her philosophy. That doesn't mean it can't get a fair formal treatment.

Edited by Eiuol
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9 hours ago, EC said:

^^ I hate when people try to turn something that's relatively simple like concepts and concept formation, that can be stated and explained in simple english, into rationalistic nonsense. The rationalistic nonsense of most philosophies is the reason most people properly think that most of philosophy is complete nonsense only studied by idiots in universities that aren't intelligent enough to study a real subject. Please don't do this to Objectivism. It's the only philosophy that doesn't do this idiotic nonsense that pretends to be intelligent.

5 hours ago, MisterSwig said:

Is that because Rand was also a huge fan of Kant?

Thank you for your intelligent and thoughtful contributions. You two are truly the bearers of a deep and enlightening philosophy. I will immediately file away these incredible insights alongside the deep wisdom I acquired from flat-earthers, creationists, and post-modernists.

As a more direct answer to William O from a more traditional Objectivist perspective, some concepts are formed solely through introspection. These are what Rand called "concepts of consciousness", and modus ponens is one of them. I am currently writing up a short paper which explains how the various concepts of logic ("and" "or" "not" "implies") are derived from introspection, and I will hopefully have something posted sometime tonight. I can't guarantee that I will get to modus ponens, but I can guarantee that I will get to conjunctive and disjunctive introduction and elimination rules, the rule of assumption, and ex falso quodlibet.

Edited by SpookyKitty
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“If p, then q” is taken in logic texts to be identically equivalent to “Not (p and not-q).” “Not (there is a naturally evolved bird with talons, and it is not a bird of prey)” is identically equivalent to “If there is a naturally evolved bird with talons, then it is a bird of prey.” It seems that we know up front that this “identically equivalent” relation holds however much our knowledge of birds increases; it cannot be found false. Whether there are presently unknown conditions under which this particular “If p, then q” can be found false is open, though until specific prima facie plausible conditions of that sort are proposed (at least in a sketchy way), that open possibility is a vacuous possibility, a degenerate, impotent sort of possibility, whether the if-then concerns nature or mathematics. The nature of birds is a matter of identity, but it seems a wider sort of identity than that in the “identically equivalent” relation. And the latter would seem to be something one learns about later than the former, although maybe the latter is already present in a precursor way in prelinguistic action schemata (eg. there’s more than one way to get attention, more than one form under the schema get attention).

In his book How We Know, Harry Binswanger takes syllogistic inference to be a case in which what is already implicit in the premises is drawn out and made explicit in the conclusion. That is a common perspective on deductive inference. The syllogism is a form of “If p, then q” in which p is a conjunction of two propositions: “If r and s, then q.” For r and s to be true and to bear implicit truths, of course, r and s both have to express awareness of facts (254–55). This viewpoint is smooth with the views of Rand that logic is a form of identification and that existence is identity.

In his book Objectivism: The Philosophy of Ayn Rand, Leonard Peikoff remarked: “The method of logic . . . does reflect the nature and needs of consciousness. It also reflects the other factor essential to a proper method: the facts of external reality. The principle which logic provides to guide man’s mental steps is the fundamental law of reality” (120–21). There are no contradictory facts in reality, I should add, to be thought in conjunction if thought is aimed at fact. To put forth without evidence or design for evidence the thesis that there are naturally evolved birds with talons that are not birds of prey contradicts evident facts without resolving the purported contradiction with other (not-adduced) evident facts. I suggest that denials of modus ponens should be understood as that sort of denial under the basic conception of logic in Objectivism. Logical validities are never independent of all facts of reality.

Some excerpts from Nathaniel Branden’s lectures The Basic Principles of Objectivism: “Logic is the tool of reason. Logic is based on facts, on the fact that that which is, is; but it is not a science of facts. It is a science of method (75).” “One proves a proposition by demonstrating that it is logically necessitated, that its denial would contradict facts already known to exist. . . . . “Until one has grasped that A is A, and that contradictions cannot exist, there can be neither proof nor the concept of ‘proof’. . . . “The Law of Identity is a genetic root of the concept of ‘proof’. . . . (73, transcription in The Vision of Ayn Rand)

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8 hours ago, SpookyKitty said:

Thank﻿ you for﻿ your intelligent and thoughtful contribution﻿s.﻿﻿﻿﻿

You're welcome. Here's a bonus contribution. You say:

8 hours ago, SpookyKitty said:

...some﻿ ﻿concepts are formed solely through introspection. These are what Rand called "concepts of consciousness", and modus ponens is one of them. I am currently writing ﻿up a short paper which explains how the various concepts of logic ("and" "or" "not" "implies") are derived from introspecti﻿o﻿﻿﻿n﻿﻿﻿...

Rand foresaw your attack and responded in ITOE. But you already know that, right? I hope your paper addresses her actual theory on how we derive conjunctions like "and."

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17 hours ago, Eiuol said:

Rand was generally informal about her philosophy. That doesn't mean it can't get a fair formal treatment.

No. It's adding pure rationalism to subject matter that is naturally anti-rationalistic. Responding in a way that appears "intellectual" just gives the subject intellectual credence that the subject matter doesn't deserve. Are we to take Karl Hopper's philosophy seriously also? Because that's what this thread looks like it's converging to in my eyes.

I'm not anti-intellectual, but I hate seeing people over-complicate things that are actually simple. It usually comes from people who are faking their intellectual abilities, which is annoying. If something can't be stated in plain English it's unlikely to be true.

Edited by EC
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14 hours ago, SpookyKitty said:

I can't guarantee that I will get to modus ponens, but I can guarantee that I will get to conjunctive and disjunctive introduction and elimination rules, the rule of assumption, and ex falso quodlibet.

So you're going to go through a bunch of rationalistic mental gymnastics that leads nowhere then? Have fun.

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I would express the modus ponens inference in Objectivese as an identification of reality. We induce propositions such as "the street is wet, therefore it rained very recently."

It's possible that the street is wet because the fire department flushed nearby hydrants. However, if all roofs and back yard lawns less than a mile away are also wet, then flushing fire hydrants being the cause is eliminated.

While modus ponus can be used deductively, I don't regard it as a deduction from the the law of identity. I believe that is too "ivory tower." The facts we observe that justify modus ponens are also facts that justify the law of identity.

Boydstun wrote: “If p, then q” is taken in logic texts to be identically equivalent to “Not (p and not﻿-q).”

So "the street is wet, therefore it rained very recently" cast in that form is: "Not (the street is wet and it didn't rain.)

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