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**, this is a good philosophy essay and a well-written one. You are grappling with a
difficult problem and making a good effort to work out an interesting, novel position.
The writing still does have some problems, and there are some important
ambiguities in the essay as it stands. But this essay shows promise. It could be very
good if you had chance to work further on it. Please see my comments in the text of
your Word-document essay, and also below.
These, below, are my main comments:
1. A philosophy essay like this one should carefully set up a problem very early on, and
then present its response to the problem. As with your first essay, you did not do this
well. You seem to be making an attempt to set up the problem in your first four
paragraphs. But what is the main question of your essay? Just in your introductory
paragraph, you put a number of different questions on the table:
(A) ‘How is it that we can derive a particular truth from two premises?’
(B) ‘How is it that we can know that [modus ponens] inferences produce true
conclusions [whenever their premises are true]?’
(C) ‘So I ask what is it exactly that takes place at the moment when the inference is
made? Is it necessary to include the conditional of an inference as a premise before
we are able to draw a conclusion?’
(D) ‘I intend to explore the relation between the premises in the following paper and
how it is that this relation gives us the knowledge of the conclusion and validates
the inference.’
2. Relatedly, one important point I’d like to make is that the main question of your paper
should be epistemological, not merely psychological. One good epistemological
question is: how do we know that the rule modus ponens is valid? Another one is: how
do we gain knowledge by modus ponens inferences? That first question is roughly your
question (B), above. The second question is roughly your question (D). But your
questions (A) and (C) look more like psychological questions. They are not questions
about our basic logical knowledge or about knowledge at all. They are questions about
the psychological event/process/act of inference. Question (C), for example, is basically
the question What is an inference. And sometimes this seems to be the main question
of your paper.
3. The psychological question of what an inference is, is indeed a central question of your
paper, I think. And your main question is: under what conditions do we gain knowledge
by modus ponens inferences? (Have I understood you correctly?) Unfortunately, none
of this is very clear. For example, on p. 3 you say that you will attempt to ‘better
explain’ a certain psychological event: ‘the action that takes place at the moment that
this [modus ponens] inference is made.’
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4. Your view (as I understand it) is that we gain knowledge by basic logical inference just
when we make a pure connection between the two premises of the relevant argument.
(And an interesting part of your view is that, in such a case, making the inference to the
conclusion just is making the pure connection between the two premises. Good.) But
what about basic logical cases involving just one premise? For example, consider the
form of inference: “It’s not the case that (A and B). Therefore, either not-A or not-B.”
This is a single-premise (form of) inference. How do people gain knowledge of the
conclusion when they carry out an inference of this form?
5. Lastly, I have two questions to ask. Is your theory at least partly a rational insight
theory? And, secondly, is your theory at least partly a “meaning-based” account?
Let me clear up what I mean by “insight” and “meaning-based” accounts. Take the
question: How do we know that modus ponens is valid. A rational insight theory might
say that we can in some sense “see” that it is valid. A meaning-based theory might give
an account of the meaning of the conditional, “if, then”. It might also give an account of
what it is to understand the conditional, and then use that account to explain how we
know that modus ponens is valid.
On p. 4 you write things that make me think that your theory is partly a “meaningbased” account. (See the quote below.) You also use some “rational insight” type
language in that same passage.
‘Considering how we can rightly see that two things that are equal to each other are
equal to the same thing, if you understand firstly what the word ‘same’ means and
secondly the concept of ‘being equal to the same’ and other geometrical
observations then the consequent that the two sides of a triangle equal to the same
length are equal to each other is found to be true and is justified by our
understanding and the connection that results from that.’
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The Connection between the Premises
How is it that we can derive a particular truth from two premises? Formal Logic has identified
many logical laws such like modes ponens and the law of non-contradiction. The
epistemology of logic asks how is it that we can know that these inferences produce true
conclusions when knowledge of their validity can only be proven by having basic knowledge
that the inference is true itself. So I ask what is it exactly that takes place at the moment when
the inference is made? Is it necessary to include the conditional of an inference as a premise
before we are able to draw a conclusion? I intend to explore the relation between the
premises in the following paper and how it is that this relation gives us the knowledge of the
conclusion and validates the inference. I propose that it is by the relation between the
premises that we have certainty of a conclusion. I would like to call this relation a connection.
We have an ability to arrive at basic knowledge empirically, like observing a car to be red.
Although some skeptics would argue that no such experience can give us knowledge I accept
for the sake of this paper that such an empirical experience that the car is red can be taken
as basic knowledge. Similar to this basic knowledge is knowledge that can be gained from
two corresponding ideas, for example a woman who has lost her husband to death and has
not yet remarried is called a widow. Because the above two concepts means one and the
same things we are rationally compelled to state that if Mary has lost her husband then Mary
is a widow. The antecedent implies the consequent. The above is what we call an inference.
The truth of Mary is discovered by the connection that takes place between these two basic
pieces of knowledge.
Philosophers have attempted to explain how (and if) it is possible to be sure that we can
validly know Z from premises A and B. Among these are the theories of Intuition, Rational
Insight (Boghossian 2003:230), Blind Reasoning (Boghossian 2003:236) and Entitlement
(Wright 2004:163). All these accounts are trying to represent how it is that we can be justified
in knowing Z from two prior premises A and B. I agree that we need the knowledge that an
inference is valid in order to render justification to any such inference. This justification of the
inference in turn justifies us in holding the conclusion to be valid.
Basically they want to validate an inference logically, like modus ponens for example, in order
to justify the conclusion. Ironically to have that done they need to prove the validity of the
inference using the inference itself and this will not do. I smile at the idea of blind reasoning
that endorses that our minds can clearly reason the inference but we have to call it blind
reasoning because we are unable to prove it. So it makes use of a rule-circular inference but
shows that it is nonetheless coherent (thanks to making use of the word blind). Similarly with
entitlement, in order to prevent a continuing regress, if we can insure certain conditions, for
example that our cognitive faculties are working and that our environment is broadly
cooperative then we can claim entitlement in our making inferences and reject such things as
skeptical doubt (Wright 2004:165).
After considering the above models I have come to see that the concept of the relation
between the premises and what that means or entails is not fully addressed. The inference,
such as modus ponens, has in some cases been taken as valid because accounts have been
made for the rather apparent jump (the jump from the premise(s) to the conclusion) that takes
place in the action of making an inference. Quickly taking a look at Lewis Caroll’s tale of
Achilles and the Tortoise we also see that the alternative, which is adding a proposition to the
antecedent, explaining the relation between the premise(s) and the conclusion (the jump),
only gives rise to regressive logic! (Caroll 1985:6).
To say that A and B affirms Z knowledge is needed of A and knowledge is needed of B and
knowledge of the relation between (A and B) and Z will be needed as well, this the Tortoise
suggest to Achilles (Carroll 1985:4). I think that this conditional is not necessarily an added
piece of knowledge that effects the truth-value of the consequent or assures the validity of the
inference (which never ends) but it is a definition of what actually happens at the moment of
the connection between the two premises! This connection is an action that produces the
consequent. The definition of what happens at that action can be written down in a statement
yes; A and B gives rise to Z, but it is not necessary to represent such a statement as part of
the propositions of the inference. Note the connection between A and B is different from the
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relation between (A and B) and Z. It is the connection between A and B that gives rise to Z. It
is this connection that I am interested in and would like to talk about.
There are a few metaphors I have come up with. Firstly, that of two dominos standing next
two one another. If ever one of them had to connect with the other the action of them both
toppling over is inevitable. The topple is not a necessary event in that it needs to be included
in the set up of the action for it will inevitably be included at the moment of the connection of
the two dominos (the dominos are metaphorical for the premises). This toppling illustrates the
work of logic and rationality. It happens when two true premises that are related to each other
are brought together. That two and three equals five can be understood as another metaphor.
If we had to look at either side of the equals sign we will see the amount five. There can be no
question whether the sum of the added premises (two and three) can mean anything other
than the unit five on the right hand side. The sum total when it comes to two and three will
always be five. This is inevitable.
So in the light of not being able to prove modus ponens how can we better explain the action
that takes place at the moment that this inference is made. ‘Drawing conclusions results from
seeing connections which comes firstly by believing particular premises and facts and
secondly by understanding them.’ (Wright 2000:189). A true connection in the purest sense of
the word cannot happen when there is no understanding of the premises. Under what
circumstance can we say that these connections produce true conclusions? How can we
define these connections? I understand this connection between two premises to be a
function. I see connections as producers of knowledge. I hope to show that the connection is
the actual action that acquires the knowledge.
For me asking how an inference achieves a true conclusion is the same as asking the
question of how basic knowledge is achieved. That is why I like the idea of connection. This
paper does not address the problem of skeptical paradox. The knowledge we as thinking
human beings have access to I understand as knowledge achieved by and as a result of a
connection. When our eyes notice a shape, we connect our primary learning, which our grade
one teacher taught us with the stimulus of a shape seen by the eyes, and conclude ‘Ah, I am
looking at a triangle!’ The connection between our eyes and the shape and the elementary
training of shapes give rise to this knowledge of a triangle. Knowledge gained through
inference is achieved in much the same way just on a more complex level with more
precarious connections.
The attempt to represent the achievement of a conclusion from various premises is counter
intuitive. Note this is the relation between the premises and the conclusion and not between
the premises themselves. The very thing we are trying to represent, the very maneuver from
premise to conclusion is the very art form that we call Logic. We accept that basic empirical
knowledge is gained through our senses. Some people might have bad eyesight and others
excellent, this does not discredit or open the debate whether sight in itself is a valid operation!
It is! Inasmuch as eyes are functionary in that they are able to observe an object and
determine the colour thereof on a more complex level the cognitive faculty functions by
putting the proverbial two and two together and determining the number four. The connection
between the premises, the moment of discovery is the function of out cognitive faculty.
I have come up with a concept I would like to call pure connection. In the same vein, yet quite
different from the four alternative cases previously mentioned addressing the problem of
justified knowledge, intuition, rational insight, blind reasoning and entitlement I would like to
draw some attention to the idea of a connection that takes places at the moment of inference.
As I have mentioned above these four cases define ways by which we can validate an
inference such as modus ponens in order to be justified in using it. I would like to entertain the
idea that at the moment of a pure connection between two true premises an inevitable act
happens that produces new knowledge. In the event of this pure connection the conclusion is
true and the inference is valid. An inference is merely a connection and the validity of the
inference is proportional to the purity of the connection. I am grappling with this thought that
the validity of an inference relates directly to the content of the premises and the connection
they have with each other?
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I did consider calling this connection an uniterfered connection but as it goes that word does
not exist. But I decided on pure, in the sense of being an uninterrupted and undefiled
connection, a connection that has not been interfered with on the one hand and true on the
other. When there is a pure connection between two premises the conclusion is true. When a
seed connects with water and sunlight this result in the growth of a plant yet only if there are
no interferences such as crows and pests. The function of the natural production of a plant
when sunlight and water connects with it is inevitable. Pure connection results in inevitable
truth. The only task we now have is defining exactly what pure in this case of the connection
between premises is!
Logical inference is formulated as an abstract system apart from the practical and variable
world. When inferences are applied to real situations, premises are subjected to a highly
complicated and variable world. For example, my friend goes to the gym on a Monday at four
for a two our session so I decided that on arriving home at four thirty I would call and invite
my mother over for tea. When I came in through the door I see her gym shoes lying on the
floor. In that moment because I know my friends lazy temperament I know she has decided to
not go today and is probably lying on the couch watching T.V. I find that she is. Truth is
proven and vindicated by the process of making connections. To acquire much knowledge
many pure connections need to be made. I inferred that my friend will only be home at six and
seeing that my mom lives just around the corner I can quickly organize a date with her yet
upon seeing a pair of gym shoes and knowing my friend, I knew that my previous inference
was mistaken.
True premises are needed for true conclusions. The purity of the connection is determined by
the degree that the premises are understood which enables the discerning of their truth-value.
When premises are clearly understood the purity of the connection is protected. Pure
connections are directly related to the truth-value and comprehension of the premises. I
understood what gym shoes on the floor meant at that time on that day and this ensured the
truth-value of my new conclusion. This might be a random example but it should illustrate my
point. When connection happens and the premises are true and understood the function of
the pure and uninterrupted connection validates the inference.
A connection is not a cognitive achievement but it is the very mechanics by which knowledge
is produced. Crispin Wright says that connections are made when there is understanding of
the statements being connected, (Wright 2000:189). The connection is the revelation of
additional knowledge. The relation or connection between premise 1 and premise 2 in the
case of it being a pure connection vindicate the process towards the conclusion 3 and in turn
justify the knowledge. The conclusion is itself new knowledge in the moment that the
connection is made. The relationship between the two premises does not yield a bigger
network of premises but yields activity and production, the activity of a movement of thought
and the production of knowledge. This new knowledge can then be used as a premise for
another inference.
The connection itself is not a piece of knowledge that can be understood or is needed in order
for the conclusion to be validly true. The connection between premise 1 and premise 2 is
merely an action that takes place on a more complex plane but in the same sense as the
reception of colour through the eyes. The logical connection concludes X where in the latter
case the brain concludes red. The knowledge of the mechanics is not needed for the function
to take place. By logic and reason we draw conclusions. The function of our thinking is the
connecting action. Good and bad logic can be described and distinguished from each other
as we develop the understanding of our premises. Considering how we can rightly see that
two things that are equal to each other are equal to the same thing, if you understand firstly
what the word ‘same’ means and secondly the concept of ‘being equal to the same’ and other
geometrical observations then the consequent that the two sides of a triangle equal to the
same length are equal to each other is found to be true and is justified by our understanding
and the connection that results from that.
A connection can perhaps be obvious but the obviousness is not what enables the
conclusion it is the connection that establishes, enables, vindicates and produces the
conclusion. The ability of the connection to do that comes from the understanding of the
premises. Understanding produces the connecting action that produces the conclusion. The
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producing action need not be part of the antecedent stated as a proposition. Both antecedent
and consequent affirms each other.
In conclusion I contend ensuring as pure a connection as possible is a means to validate the
inference and the discovery of new knowledge. Similarly a pure connection is merely an
explanation of what exactly it is that happens at the moment of inference. Yes we can have
models that validate our inferences this I believe is necessary. Yet the above paper has in
somewhat of a rogue way looked at such an inference and come to a sort of a conclusion that
the connection is what the actual inference is and that an inference is not based on a pure
connection but is the very act of that connection. And so I substitute valid inference with pure
connection.
Secondly, on coming to this conclusion I proceeded to describe how we are able ensure the
purity of the connection. I concluded that the purity comes from understanding the premises.
And so understanding begets pure connection and pure connection begets a valid conclusion.
Therefore my model of the connection between the premises justifies my assertion that a
pure connection results in a true conclusion. Where a valid inference is itself a pure
connection. Finally, I can say that true knowledge comes by pure connection, which being
directly related to understanding grants the statement, ‘Let us be sure to understand before
we conclude!’
REFERENCE
Boghossian, P. (2003) Blind Reasoning
Caroll, L. (1985) What the Tortoise said to Achilles
Stroud, B. (1979) Inference Belief and Understanding
Wright, C. (2004) Intuition, entitlement, and the epistemology of basic logical laws
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