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Consider:

> [A] 猫 **が** 好きだ

To me this means [A']"I like cats."

Contrast this to:

> [B] 猫 **は** 好きだ

To me this means [B']"I like cats (among other animals)"

I based my understanding of [B] from [Derek Schaab's answer to "What is the
difference between “に” and
“には”?"](https://japanese.stackexchange.com/a/1130/542):

> You'll see that while in the first sentence there is only one scope, the
> second actually has two:
>

>> (私【わたし】は）彼【かれ】と会【あ】わなかった。

>>

>>   * Scope (implied): I

>>   * Statement: Didn't meet with him.

>>

>>

>> (私【わたし】は）彼【かれ】とは会【あ】わなかった。

>>

>>   * Outer scope (implied): I

>>   * Inner scope (explicit): with him

>>   * Statement: Didn't meet.

>>

>
> Now as for what effect this has, **the は often adds a hint of comparison or
> contrast** , as repecmps mentioned. While both of the above sentences
> translate to, "I didn't meet with him," the second hints that although you
> didn't meet with him, you may have met with someone else.

So I deduced that は in [B] can perform that disambiguative role.

* * *

Now [A] can be interpreted to mean " **I** like cats" because of the implicit
first person as in `(私は)猫が好きだ`

Now let's make 私 explicit:

> [C]私は猫が好きだ - [C']"I like cats"

Now it is explicit that I am doing the liking.

Now reconsider [B]猫は好きだ:

Based on [C], I have another way to interpret [B]:

So now 猫は好きだ can mean [B'']"The cat likes (an unspecified object)"

* * *

**(Questions)** What is going on? Who is doing the liking and who is being
liked in each case? Are [B'] and [B''] both valid? What am I doing and
understanding wrong? If there is indeed ambiguity, how can I resolve it?

**EDIT:**

Can I resolve it by introducing another は element? E.g.

> 私は猫は好きです。 "I(thematic) like cats(disambiguated/anaphoric)"

Is it acceptable to have two はs in a sentence as above?
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grammar particles particle-は particle-が は-and-が
Problems with は and が
Dave M G's comment is right, you should see the sentence as 私は[先生が猫が好きだ]と思います.
So if you remove と思います, you remove 私は as well. 私は先生が猫が好きだ is not a correct
sentence.
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The phrase 〜は〜が好きだ is a little unusual, but it's not too hard to break down.

First, 好く is a verb meaning "to be fond of". For whatever reason (probably
because declaring your fondness for something is too direct in Japanese
culture), you never say 〜を好く.

Instead, we nominalize the verb by using the 〜い form: 好き (remember, nominalize
means to turn into a noun). We might translate this as "one that (I) like".

Because 好き is a noun, it cannot take 〜を. In fact, it can't even appear alone
at the end of a sentence. We need the copula, だ, meaning "is".

So, dropping the 〜は part, the phrase 〜が好きだ literally translates to "~ is the
one (I) like".

The full phrase is an example where the は particle introduces a topic that
isn't actually the subject. It's just like in the sentence 今は眠い, "As for now,
(I) am tired". 今 is not the subject. Similarly, when you have 私は猫がすきです, 私 is
not the subject. 猫 is, because it's doing the "being" in the sentence: As for
me, cats are things (I) like.

tl;dr,
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私は猫が好きだ means I like cats.

私は猫は好きだ has the same meaning and it's absolutely possible.

But in the second case you are putting emphasis on what you like for whatever
reason: maybe you are going to talk then about cats, or you want to remark
that you like a specific cat (私はこの猫は好きだ), or want to focus attention on cats,
etc.

The same emphasis can be put on other subjects marked with が.

> ドアが開いています。  
>  このドアは開いています。

Direct object can be marked with は instead of を for the same reason.
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